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1

CHAPTER 7

Design for Quality and Product Excellence

Teaching Notes

The precise manner in which a person or team approaches product design, solving problems to
achieve product excellence, or developing product reliability is not as critical as doing it in a
systematic fashion. Students have been exposed to process management and improvement in
Chapter 7, but they may still have some difficulty in understanding how measurement
(metrology) and Six Sigma projects can be used at the design stage to make frequent, but gradual
changes as an approach to process improvement.

Key objectives for this chapter should include:

• To explore the typical structured product development process consisting of idea
generation, preliminary concept development, product/process development, full-scale
production, product introduction, and market evaluation.

• To learn that concurrent, or simultaneous, engineering is an effective approach for
managing the product development process by using multi-functional teams to help
remove organizational barriers between departments and therefore reduce product
development time. Design reviews help to facility product development by stimulating
discussion, raising questions, and generating new ideas

• To introduce the concept of Design for Six Sigma (DFSS) consisting of a set of tools and
methodologies used in the product development process to ensure that goods and services
meet customer needs and achieve performance objectives, and that the processes used to
make and deliver them achieve Six Sigma capability. DFSS consists of four principal
activities of: Concept development, Design development, Design optimization, and
Design verification. These activities are often incorporated into a variation of the
DMAIC process, known as DMADV, which stands for Define, Measure, Analyze,
Design, and Verify.

• To define concept development as the process of applying scientific, engineering, and
business knowledge to produce a basic functional design that meets both customer needs
and manufacturing or service delivery requirements. This involves developing creative
ideas, evaluating them, and selecting the best concept.

Design for Quality and Product Excellence 2

• To appreciate the concepts of innovation and creativity. Innovation involves the
adoption of an idea, process, technology, product, or business model that is either new or
new to its proposed application. Creativity is seeing things in new or novel ways. Many
creativity tools are designed to help change the context in which one views a problem or
opportunity, thereby leading to fresh perspectives.

• To explore Quality Function Deployment (QFD) -- a planning process to guide the
design, manufacturing, and marketing of goods by integrating the voice of the customer
throughout the organization. A set of matrices, often called the House of Quality, is used
to relate the voice of the customer to a product’s technical requirements, component
requirements, process control plans, and manufacturing operations.

• To investigate manufacturing specifications, consisting of nominal dimensions and
tolerances. Nominal refers to the ideal dimension or the target value that manufacturing
seeks to meet; tolerance is the permissible variation, recognizing the difficulty of
meeting a target consistently.

• Tolerance design involves determining the permissible variation in a dimension. A
scientific approach to tolerance design uses the Taguchi loss function. Taguchi assumes
that losses can be approximated by a quadratic function so that larger deviations from
target correspond to increasingly larger losses. For the case in which a specific target
value, T, is determined to produce the optimum performance, and in which quality
deteriorates as the actual value moves away from the target on either side (called
“nominal is best”), the loss function is represented by L(x) = k(x - T)
2
.

• To study the dimensions of reliability—the ability of a product to perform as expected
over time. Formally, reliability is defined as the probability that a product, piece of
equipment, or system performs its intended function for a stated period of time under
specified operating conditions. In practice, the number of failures per unit time
determines reliability during the duration under consideration (called the failure rate),
look at functional failure at the start of product life (The early failure period is
sometimes called the infant mortality period), reliability failure after some period of
use.

• To understand why reliability is often modeled using an exponential probability
distribution and use the reliability function, specifying the probability of survival, which
is: R(T) = 1 – e
-T
.

• To explore systems composed of individual components with known reliabilities,
configured in series, in parallel, or in some mixed combination, and how it ties into
various aspects of design, including optimization, tolerance design, and design
verification.

• To learn that design optimization includes setting proper tolerances to ensure maximum
product performance and making designs robust; a scientific approach to tolerance
design uses the Taguchi loss function. Techniques for design verification include

Design for Quality and Product Excellence 3

formal reliability evaluation, using techniques such as accelerated life testing and burn-
in.

• To examine the characteristics of Design Failure Mode And Effects Analysis
(DFMEA) -- a methodology to identify all the ways in which a failure can occur, to
estimate the effect and seriousness of the failure, and to recommend corrective design
actions.

• Fault Tree Analysis (FTA), sometimes called cause and effect tree analysis, is a
method to describe combinations of conditions or events that can lead to a failure. In
effect, it is a way to drill down and identify causes associated with failures and is a good
complement to DFMEA.

• To investigate good product design, which anticipates issues related to cost,
manufacturability, and quality. Improvements in cost and quality often result from
simplifying designs, and employing techniques such as design for manufacturability
(DFM) – the process of designing a product for efficient production at the highest level
of quality.

• To study social responsibilities in the design process including product safety and
environmental concerns, which have made Design for Environment (DfE) and design
for disassembly important features of products, because they permit easy removal of
components for recycling or repair, eliminate other environmental hazards, and makes
repair more affordable.

• To explore Design for Excellence (DFX), an emerging concept that includes many
design-related initiatives such as concurrent engineering, design for manufacturability
design for assembly, design for environment and other “design for” approaches. DFX
objectives include higher functional performance, physical performance, user
friendliness, reliability and durability, maintainability and serviceability, safety,
compatibility and upgradeability, environmental friendliness, and psychological
characteristics.

• To introduce concept engineering (CE) -- a focused process for discovering customer
requirements and using them to select superior product or service concepts that meet
those requirements.

• To appreciate that the purpose of a design review is to stimulate discussion, raise
questions, and generate new ideas and solutions to help designers anticipate problems
before they occur.

• To understand techniques for design verification including formal reliability evaluation.
These include accelerated life testing, which involves overstressing components to
reduce the time to failure and find weaknesses; and burn-in, or component stress testing,
which involves exposing integrated circuits to elevated temperatures in order to force
latent defects to occur.

Design for Quality and Product Excellence 4

• To appreciate that Six Sigma performance depends on reliable measurement systems.
Common types of measuring instruments used in manufacturing today fall into two
categories: “low-technology” and “high-technology.” Low-technology instruments are
primarily manual devices that have been available for many years; high-technology
describes those that depend on modern electronics, microprocessors, lasers, or advanced
optics.

ANSWERS TO QUALITY IN PRACTICE KEY ISSUES

Testing Audio Components at Shure, Inc.

1. The general definition of reliability as: the probability that a product, piece of equipment,
or system performs its intended function for a stated period of time under specified
operating conditions, is thoroughly tested by Shure. Tests are tailored to various market
segments, according to the type of use (or abuse) the equipment is likely to incur. For the
consumer market, Shure uses the cartridge drop and scrape test, which is particularly
important to test for, in the light of how “scratch” DJ’s use the equipment. For
presentation and installation audio systems, they use the microphone drop test and
perspiration test. For mobile communications, the two above tests, temperature, and cable
and cable assembly flex tests are applicable. For the performance audio, the microphone
drop test, perspiration test, sequential shipping, cable and cable assembly flex, and
temperature storage would all be appropriate. The purpose of the tests is to simulate
actual operating conditions so that the products can sustain accidents and rough handling
and perform effectively over a useful life. Quality characteristics that are studied are
achieved reliability and performance.

2. For the microphone drop test, the measures are probably variable measures of sound and
response levels, within an acceptable range. Thus, standard variables control charts may
be used. For the perspiration test, it may be that a p-chart or u-chart is used for attribute
measures. The cable and cable assembly flex test might use a p-chart to measure the
percentage of cables tested that failed due to rocking motions or twisting motions. The
sequential shipping tests would probably show varying proportions of failures due to
dropping, vibration, and rough handling. These might be sorted out using a Pareto chart.
Then efforts could be made to improve the most frequently occurring causes. The
cartridge drop and scrape test could also use p- or np-charts (see Chapter 13) to show
results per sample of 100 repetitions of the test. The temperature tests would most likely
use standard variables charts to measure whether test performance was within control
limits, or not.

Applying QFD in a Managed Care Organization

1. Although this example of QFD involved the design of a tangible items, it is more difficult
to implement in a service context, as opposed to a pure manufacturing context, because

Design for Quality and Product Excellence 5

both customer requirements and technical requirements are harder to quantify and assess
that with tangible products.

2. The detailed calculations in the Importance of the hows row and Percentage of
importance of the hows row used to arrive at these figures can be shown and verified on
the spreadsheet labelled QIP-QFD Healthcare.xlsx. Note that some discrepancies
involving incorrect multiplication, were found in part of the QFD “House of Quality.”

Design for Quality and Product Excellence 6

Direction of Rate of Co. Rate of Absol. % Font Use of Gloss. Q&A Tbl. of Lang.
Improvement Import. Now Plan Improv. Wgt. Improve size Update Photos colors Terms Sect. Contnt. Frindly.
Ease-use 4.5 3.2 4.5 1.4 6.3 25.2% 3 1 3 3 9 3 9 3
Accuracy 5.0 3.1 4.6 1.5 7.4 29.5% 9 1 3 1
Timeliness 3.2 3.8 3.8 1.0 3.2 12.7% 9 1
Clarity 3.8 2.6 3.9 1.5 5.7 22.7% 1 1 3 1 9 3 1 3
Conciseness 2.5 4.1 4.1 1.0 2.5 9.9% 1 1
Import. of hows 108.1 427.9 153.4 98.2 460.0 244.7 249.1 173.0
% of Import. of hows 5.65% 22.35% 8.01% 5.13% 24.03% 12.78% 13.01% 9.04%

The numbers in the original table were verified by the calculations shown above (some columns of the original table were rearranged for convenience
of calculation). The rates of improvement, absolute weights, and percent improvements, based on the given values for “rate of importance” and
“company now” and “plan” were validated. As in the original table, the “importance of hows” and “percent of importance of hows” turned out to be
accurately calculated. Specific factors shown as the most important were “glossary terms” and “updates.”

Design for Quality and Product Excellence 7

3. The lessons that can be learned and applied to other service organizations that seek to
design or redesign their products and services include the facts that QFD provides for a
systematic approach to linking the “voice of the customer” to operational requirements.
By doing so, operating efficiencies can be realized and customer satisfaction can be
enhanced. In addition, employee satisfaction often can be improved, as well, as found in
the case. It must be recognized that time and effort is involved in gathering, sorting, and
analyzing the characteristics and factors. Also, there is subjectivity in applying ratings
and weights to variables. Hence, the results are not easy to predict and guarantees are
limited.

ANSWERS TO REVIEW QUESTIONS

1. Product design and development consists of six steps:
• Idea Generation. New or redesigned product ideas should incorporate customer
needs and expectations.
• Preliminary Concept Development. In this phase, new ideas are studied for
feasibility.
• Product/Process Development. If an idea survives the concept stage, the actual
design process begins by evaluating design alternatives and determining
engineering specifications for all materials, components, and parts. This phase
usually includes prototype testing, design reviews, and development, testing, and
standardization of the manufacturing processes
• Full-Scale Production. If no serious problems are found, the company releases the
product to manufacturing or service delivery teams.
• Market Introduction. The product is distributed to customers.
• Market Evaluation. An ongoing product development process that relies on
market evaluation and customer feedback to initiate continuous improvements.

2. Competitive pressures are forcing companies to reduce time to market, which means that
the time for product development is also squeezed. The problems incurred in speeding up
the process are well known. If done too hastily, the result will be the need to revise or
scrap the design, cost increases or project over-runs, difficulty in manufacturing the
product, early product failure in the field, customer dissatisfaction, and/or lawsuits due to
product liability. One of them most significant impediments to rapid design is poor intra-
organizational coordination. Reducing time to market can only be accomplished by
process simplification, eliminating design changes, and improving product
manufacturability. This requires involvement and cooperation of many functional groups
to identify and solve design problems in order to reduce product development and
introduction time.

3. Concurrent engineering is a process in which all major functions involved with bringing a
product to market are continuously involved with product development from conception
through sales. Such an approach not only helps achieve trouble-free introduction of
products and services, but also results in improved quality, lower costs, and shorter
product development cycles. Concurrent engineering involves multifunctional teams,
usually consisting of 4 to 20 members and including every specialty in the company. The

Design for Quality and Product Excellence 8

functions of such teams are to perform and coordinate the activities in the product
development process simultaneously, rather than sequentially. Companies exploit
concurrent engineering to achieve a competitive advantage. Typical benefits include 30 to
70 percent less development time, 65 to 90 percent fewer engineering changes, 20 to 90
percent less time to market, 200 to 600 percent improvement in quality, 20 to 110 percent
improvement in white collar productivity, and 20 to 120 percent higher return on assets.

4. Design for Six Sigma (DFSS) uses a set of tools and methodologies in the product
development process to ensure that goods and services will meet customer needs and
achieve performance objectives, and that the processes used to make and deliver them
achieve Six Sigma capability. DFSS consists of four principal activities:
• Concept development, in which product functionality is determined based upon
customer requirements, technological capabilities, and economic realities;
• Design development, which focuses on product and process performance issues
necessary to fulfill the product and service requirements in manufacturing or delivery;
• Design optimization, which seeks to minimize the impact of variation in production
and use, creating a “robust” design; and
• Design verification, which ensures that the capability of the production system meets
the appropriate sigma level

5. Concept development is the process of applying scientific, engineering, and business
knowledge to produce a basic functional design that meets both customer needs and
manufacturing or service delivery requirements. Developing new concepts requires
innovation and creativity.

Innovation involves the adoption of an idea, process, technology, product, or business
model that is either new or new to its proposed application. The outcome of innovation is
a discontinuous or breakthrough change and results in new and unique goods and services
that delight customers and create competitive advantage.

Innovations can be classified as:
1. An entirely new category of product; for example the iPod
2. First of its type on the market in a product category already in existence; for
example, the DVD player.
3. A significant improvement in existing technology, such as the blu-ray player
4. A modest improvement to an existing product, such as the latest iPad.
Creativity is seeing things in new or novel ways. In Japanese, the word creativity
has a literal translation as “dangerous opportunity.” Many creativity tools, such as
brainstorming and Brainwriting—a written form of brainstorming, are designed to
help change the context in which one views a problem or opportunity, thereby
leading to fresh perspectives. A creativity tool that finds extensive use in product
design is TRIZ, which is a Russian acronym for the Theory of Inventive Problem
Solving. TRIZ was developed by a Russian patent clerk who recognized that
concepts of inventive problem solving could be taught, in order to foster creative
problem solving.

Design for Quality and Product Excellence 9

Concept development is an important tool for assuring quality because it provides a
systematic process that leaves a strong audit trail back to the voice of the customer. This
makes it difficult to challenge the results of skeptics and convert them. The process also
helps to build consensus and gives design teams confidence in selling their concept to
management. However, it takes a lot of discipline and patience.

6. Conceptual designs must be translated into measurable technical requirements and,
subsequently, into detailed design specifications. Detailed design focuses on establishing
technical requirements and specifications, which represent the transition from a
designer’s concept to a producible design, while also ensuring that it can be produced
economically, efficiently, and with high quality.

7. QFD benefits companies through improved communication and teamwork between all
constituencies in the production process, such as between marketing and design, between
design and manufacturing, and between purchasing and suppliers. Product objectives are
better understood and interpreted during the production process. Use of QFD determines
the causes of customer dissatisfaction, making it a useful tool for competitive analysis of
product quality by top management. Productivity as well as quality improvements
generally follow QFD. QFD reduces the time for new product development. QFD allows
companies to simulate the effects of new design ideas and concepts. Companies can
reduce product development time and bring new products into the market sooner, thus
gaining competitive advantage.

8. In the QFD development process, a set of matrices is used to relate the voice of the
customer to a product’s technical requirements, component requirements, process control
plans, and manufacturing operations. The first matrix, called the House of Quality,
provides the basis for the QFD concept.

Building the House of Quality consists of six basic steps:

* Identify customer requirements.
* Identify technical requirements.
* Relate the customer requirements to the technical requirements.
* Conduct an evaluation of competing products or services
* Evaluate technical requirements and develop targets.
* Determine which technical requirements to deploy in the remainder of the
production/delivery process.
The first House of Quality in the QFD process provides marketing with an important tool
to understand customer needs and gives top management strategic direction. Three other
“houses of quality” are used to deploy the voice of the customer to (in a manufacturing
setting) component parts characteristics, process plans, and quality control. The second
house applies to subsystems and components. At this stage, target values representing the
best values for fit, function, and appearance are determined. In manufacturing, most of

Design for Quality and Product Excellence 10

the QFD activities represented by the first two houses of quality are performed by
product development and engineering functions.

In the last two stages, the planning activities involve supervisors and production line
operators. In the third house, the process plan relates the component characteristics to key
process operations, the transition from planning to execution. Key process operations are
the basis for a control point. A control point forms the basis for a quality control plan
delivering those critical characteristics that are crucial to achieving customer satisfaction.
This is specified in the last house of quality. These are the things that must be measured
and evaluated on a continuous basis to ensure that processes continue to meet the
important customer requirements defined in the first House of Quality.

9. Manufacturing specifications consist of nominal dimensions and tolerances. Nominal
refers to the ideal dimension or the target value that manufacturing seeks to meet;
tolerance is the permissible variation, recognizing the difficulty of meeting a target
consistently. Traditionally, tolerances are set by convention rather than scientifically. A
designer might use the tolerances specified on previous designs or base a design decision
on judgment from past experience. Setting inappropriate tolerances can be costly, since
tolerance settings often fail to account for the impact of variation on product
functionality, manufacturability, or economic consequences. The Taguchi loss function is
a scientific approach to tolerance design. Taguchi assumed that losses can be
approximated by a quadratic function so that larger deviations from target cause
increasingly larger losses.

10. The Taguchi loss function is a useful concept for process design. Taguchi suggests that
there is not strict cut-off point that divides good quality from poor quality. Rather, he
assumed that losses can be approximated by a quadratic function so that larger deviations
from target correspond to increasingly larger losses. For the case in which a specific
target value, T, is determined to produce the optimum performance, and in which quality
deteriorates as the actual value moves away from the target on either side (called
“nominal is best”), the loss function is represented by L(x) = k(x - T)
2
where x is any
actual value of the quality characteristic and k is some constant. Thus, (x – T) represents
the deviation from the target, and the loss increases by the square of the deviation.

11. Reliability is the probability that a product, piece of equipment, or system performs its
intended function for a stated period of time under specified operating conditions. There are
four key components of this definition, including probability, time, performance, and
operating conditions. All of these have to be considered in a comprehensive definition of
reliability. Probability allows comparison of different products and systems, time allows us
to measure the length of life of the product, performance relates to the ability of the product
to do what it was designed to do, and operating conditions specify to amount of usage and
the environment in which the product is used.

12. A functional failure is one incurred at the start of the product's life due to defective
materials, components, or work on the product. A reliability failure is one that is incurred
after some period of use. For example, if a new TV set suffers a blown picture tube during

Design for Quality and Product Excellence 11

the first week, it's a functional failure. There was obviously a defect in the manufacture of
the tube. If the vertical hold feature of the set goes out (perhaps 3 days after the 1 year
warranty is up), that is a reliability failure. It should reasonably be expected to last much
longer than one year, but it didn't.

13. Reliability engineers distinguish between inherent reliability, which is the predicted
reliability determined by the design of the product or process, and the achieved
reliability, which is the actual reliability observed during use. Achieved reliability can be
less than the inherent reliability due to the effects of the manufacturing process and the
conditions of use.

14. Failure rate is defined as the number of failures per unit of time during a specified time
period being considered. For example, if 15 MP-3 players were tested for 500 hours and
there were two failures of the units, the failure rate would be: 2 / (15 x 500) = 1 / 3750 or
0.000267.

15. The product life characteristics curve, is the so-called "bath-tub curve" because of its shape.
It is actually the failure rate curve, described above. Such curves can be used to understand
the distinctive failure rate patterns of various designs and products, over time.

16. The reliability function represents the probability that an item will not fail within a certain
period of time, T. It is directly related to the cumulative distribution function: F(T) =
1 - e
-T
, that yields the probability of failures. Since F(T) is the probability of failure, the
reliability function, R(T) can be defined as the complement, e.g. probability of not failing:

R(T) = 1 - (1 - e
-T
) = e
-T

It can also be expressed using the mean time to failure (MTTF) value  as: R(T) = e
-T/

17. The reliability of series, parallel, and series parallel is relatively easy to compute, given the
reliability of components in each system. For the series system, RS = R1R2R3. Thus
reliabilities are multiplicative.

For a parallel system, the relationships are a little more complex, since the units are designed
to use redundant components, so that if one unit fails the system can continue to operate.
The system reliability is computed as:

RS = 1 - [(1 - R1)(1 - R2)(1 - Rn)]

For series-parallel systems, the equivalent reliabilities of each parallel sub-system are
calculated, successively, until there are no more parallel sub-systems. The system is then
reduced to a serially equivalent system in which all component reliabilities can be
multiplied to get the final reliability value.

18. Robust design refers to designing goods and services that are insensitive to variation in
manufacturing processes and when consumers use them. Robust design is facilitated by

Design for Quality and Product Excellence 12

design of experiments to identify optimal levels for nominal dimensions and other tools
to minimize failures, reduce defects during the manufacturing process, facilitate assembly
and disassembly (for both the manufacturer and the customer), and improve reliability.

19. The purpose of Design Failure Mode and Effects Analysis (DFMEA) is to identify all the
ways in which a failure can occur, to estimate the effect and seriousness of the failure,
and to recommend corrective design actions. A DFMEA usually consists of specifying
the following information for each design element or function: Failure modes; effect of
the failure on the customer; severity, likelihood of occurrence, and detection rating;
potential causes of failure, and corrective actions or controls. A simple example of a
DFMEA for an ordinary household light socket is provided in the chapter.

20. Fault Tree Analysis (FTA), sometimes called cause and effect tree analysis, is a method
to describe combinations of conditions or events that can lead to a failure. In effect, it is
a way to drill down and identify causes associated with failures and is a good
complement to DFMEA. It is particularly useful for identifying failures that occur only
as a result of multiple events occurring simultaneously. In other words FTA is a tool for
carrying out the entire DFMEA process.

21. Product design can have a major impact on manufacturability. If careful thought and
planning is not done by the designer (or design team), the end product can end up being
difficult or impossible to build due to placement of components, methods for
attachments, “impossible” tolerances, difficulties in attaching or fastening components
and/or difficulties in getting the whole assembled “system” to work smoothly, even with
the highest quality components. In addition time, materials, and other resources may be
wasted unnecessarily due to a poor manufacturing design.

The concept of Design for Manufacturability (DFM) is the process of designing a product so
that it can be produced efficiently at the highest level of quality. Its goal is to improve
quality, increase productivity, reduce lead time (time to market, as well as manufacturing
time) and maintain flexibility to adapt to future market conditions.

22. Key design practices for high quality in manufacturing and assembly include: 1) analyze all
design requirements to assess proper dimensions and tolerances, 2) determine process , 3)
identify and evaluate possible manufacturing quality problems, 4) select manufacturing
processes that minimize technical risks, and 5) evaluate processes under actual
manufacturing conditions.

23. Social responsibilities in the design process include safety and environmental concerns,
which have made Design for Environment (DFE) and Design for Disassembly important
features of products. Legal and environmental issues are becoming critical in designing
products and services, today. Product safety and its consequences, product liability, should
be of primary concern because of the damage that hazardous designs can do to consumers of
the product. Also, liability lawsuits can do major damage to the financial health of an
organization, as well as its image and reputation in the marketplace. Records and

Design for Quality and Product Excellence 13

documentation relating to the design process are the best defense against liability lawsuits.
These would include records on prototype development, testing, and inspection results.

Environmental issues involve questions of whether “environmentally friendly” designs
(those that minimize damage to the environment in manufacture and product use) are being
developed, what impacts will the design of the product have on the environment when it is
scrapped, and how can consumers be given the most value for their money, while balancing
the other two issues? The above questions can often be addressed by considering it as a
“design for environment” concept (often combined with and “design for disassembly”).
What is the best design for repairability/recylability?

24. Design for Excellence (DFX) is an emerging concept that includes many design-related
initiatives such as concurrent engineering, design for manufacturability design for
assembly, design for environment and other “design for” approaches. DFX objectives
include higher functional performance, physical performance, user friendliness, reliability
and durability, maintainability and serviceability, safety, compatibility and
upgradeability, environmental friendliness, and psychological characteristics. DFX
represents a total approach to product development and design involves the following
activities:
• Constantly thinking in terms of how one can design or manufacture products better,
not just solving or preventing problems
• Focusing on “things done right” rather than “things gone wrong”
• Defining customer expectations and going beyond them, not just barely meeting them
or just matching the competition
• Optimizing desirable features or results, not just incorporating them
• Minimizing the overall cost without compromising quality of function

25. The purpose of a design review is to stimulate discussion, raise questions, and generate
new ideas and solutions to help designers anticipate problems before they occur. To
facilitate product development, a design review is generally conducted in three major
stages of the product development process: preliminary, intermediate, and final. The
preliminary design review establishes early communication between marketing,
engineering, manufacturing, and purchasing personnel and provides better coordination
of their activities. It usually involves higher levels of management and concentrates on
strategic issues in design that relate to customer requirements and thus the ultimate
quality of the product. The preliminary design review evaluates such issues as the
function of the product, conformance to customer’s needs, completeness of
specifications, manufacturing costs, and liability issues.

After the design is well established, an intermediate review takes place to study the
design in greater detail to identify potential problems and suggest corrective action.
Personnel at lower levels of the organization are more heavily involved at this stage.
Finally, just before release to production, a final review is held. Materials lists, drawings,
and other detailed design information are studied with the purpose of preventing costly
changes after production setup.

Design for Quality and Product Excellence 14

26. Methods of product testing for reliability include: life testing, accelerated life testing,
environmental testing and vibration and shock testing. In life and accelerated life testing the
product is tested until it fails. The latter speeds up the process by overstressing the item to
hasten its eventual failure. Environmental and shock tests are performed to determine the
product's ability to survive and operate under adverse conditions of heat, cold, or shock.

SOLUTIONS TO PROBLEMS

Note: Data sets for several problems in this chapter are available in the Excel workbook
C07Data on the Student Companion Site for this chapter accompanying this text. Click on the
appropriate worksheet tab as noted in the problem (e.g., Prob. 7-5) to access the data.

1. A hospital developed a design process consisting of the following steps: Plan, Design,
Measure, Assess, and Improve. Below is a list of specific activities that comprise these five
steps in random order. Place the activities in the most appropriate order within the correct
step of the design process.
Pilot or test design
Submit proposal
Define measures to assess design performance
Implement design
Identify potential solutions to reduce out of control conditions
Develop business plan
Disseminate improvements throughout the organization
Monitor process performance
Select the best solution to improve control
Identify out of control conditions
Propose new concept
Create design to meet requirements
Identify new improvement opportunities
Monitor the new process design
Implement the best solution to improve control
Verify proposal alignment with strategic objectives
Establish design team
Identify causes of out of control conditions
Analyze causes
Identify and validate customer requirements
Identify and evaluate best practices

Answer

1. Although the terms might vary slightly, the following model captures the stages of the
design process for the hospital:

Design for Quality and Product Excellence 15

2. Newfonia, Inc., is working on a design for a new smartphone. Marketing staff conducted
extensive surveys and focus groups with potential customers to determine the
characteristics that the customers want and expect in a smartphone. Newfonia’s studies
have identified the most important customer expectations as
• Initial cost
• Reliability
• Ease of use
• Features
• Operating cost
• Compactness

Develop a set of technical requirements to incorporate into the design of a House of
Quality relationship matrix to assess how well your requirements address these
expectations. Refine your design as necessary, based upon the initial assessment.
Answer

2. Analysis of customer responses for Newfonia’s proposed smartphone indicates the
likelihood of several strong relationships between customer requirements and associated
technical requirements of the design, such as value vs. price; features vs. compactness; and
ease of use vs. features. Operating costs may possibly be distantly related to initial cost and
features. Technical characteristics required to translate the “voice of the customer” into
operational or engineering terms might be measures of purchase cost, operating programs
(e.g., BranchOS, or other similar systems), number and type of features, weight, dimensions,
battery life, cost of replacement batteries, and peripherals.

Design for Quality and Product Excellence 16

3. Newfonia, Inc. (Problem 2), faces three major competitors in this market: Oldphonia,
Simphonia, and Colliefonia. It found that potential consumers placed the highest
importance on reliability (measured by such things as freedom from operating system
crashes and battery life), followed by compactness (weight/bulkiness), followed by
flexibility (features, ease of use, and types of program modules available). The operating
cost was only occasionally noted as an important attribute in the surveys. Studies of their
products yielded the information shown in the table in C07Data file for Prob.7-3on the
Student Companion Site for this chapter. Results of the consumer panel ratings for these
competitors are also shown in that spreadsheet. Using this information, modify and
extend your House of Quality from Problem 1 and develop a deployment plan for the
new smartphone. On what attributes should the company focus its marketing efforts?

Answer

3. With the new data given for Newfonia’s potential customers, a partial House of Quality
for the design of the smartphone can be built, as shown below. Note the strong
relationships between customer requirements and associated technical requirements of
the smartphone design.

The inter-relationships of the roof are not shown (limitations of MSWord software), but
these may be sketched in. For example, they would show a strong inter-relationship between
size and weight.

PARTIAL HOUSE OF QUALITY MATRIX
FOR NEWPHONIA’S SMARTPHONE CASE

Cost Size
(in.)
Wt.
(oz.)
Featr.
(num.)
Opr.P
rog.
Bat.
Life
Opr.
Cost
Importan
ce

12 3 45
Compet
Eval.
12 3 45
Selling
Pts.
1 2 3 4
5
Reliable Keeps
operating
   • x G S H *
Compact Fits
pocket
• x GSH
Not heavy   •  x S G Q
Features Calendar,
contact
mgt., etc.
 •  x G S H *
Ease of
use
Intuitive
operations
 • • x QS G *
Value Good
value
•  • x Q SG *
Competitive
Evaluation:
Oldphonia

3

4

5

4

5

5

5

Simfonia 5 4 3 2 2 2 3 • = Very strong relationship
Colliefonia 4 4 3 3 4 3 4 = Strong relationship

Design for Quality and Product Excellence 17

Targets $250 5 x
3.2
6 oz. 10 Win.
CE
35 Mod
.
 = Weak relationship

Deployment * * *

This analysis suggests that Newfonia should try to position itself between Simfonia and
Colliefonia in price and features. It should build on the strength of the customer’s reliability
concern, keeping battery life near 35 hours and use a proven operating program, such as
BranchOS. Enough features (10) should be offered to be competitive. If Newfonia can
design a high-value smartphone and sell it at an attractive price (say, $250 or less), it
should be a very profitable undertaking.

4. Georgio’s Giant Gyros conducted consumer surveys and focus groups concerning a new
giant gyro sandwich design, and the facility to sell it, and identified the most important
customer expectations (not in any order of priority) as
• Tasty, attractive, moderately healthy food
• Speedy service
• An easy-to-read menu board
• Accurate order filling
• Perceived value
Develop only a set of technical requirements to incorporate into the design of the product
and its delivery. Use a House of Quality relationship matrix to assess how well your
requirements address these expectations. Include some technical dimensions that may be
used to measure tasty, attractive, and “healthy” food; speedy service, acceptable menu
boards, order accuracy, or perceived value. Refine your design as necessary based upon
the initial assessment.

Answer

4. Analysis of customer responses for Georgio’s Giant Gyros indicates that there are likely to
be several strong relationships between customer requirements and associated technical
requirements of the product and delivery system that Georgio designs (for example, a giant
gyro product). Some strong relationships may be seen between moistness/flavor and trans-
fat; calories/sodium/t-fat and nutrition; staffing levels and work procedures; kitchen capacity
and facility layout; value and price; etc..

Note the three customer response categories that are unrelated to the design of the gyros --
order accuracy, speedy service, and menu board. These factors will probably require a
separate analysis as part of a facility and process design, thus focusing on the product in one
case, and the service delivery system in the other.

Design for Quality and Product Excellence 18

PARTIAL HOUSE OF QUALITY MATRIX
FOR GEORGIO’S GIANT GYROS

Price Size Calories Sodium % t-Fat
Facility
layout
Work
procedures
Imprtnce

12 3 45
Compet.
Eval.
12 3 4 5
Selling
Pts.
1 2 3 4 5
Taste Moistness     •  
Flavor     •  
Health Nutritious   • • •  

Visual Visually
Appealing
      
Speedy
service
Number of
staff
      •
Kitchen
capacity
     • •
Menu Size & font      • 
Order
accurac
y
Order check
process
      •

Value Good Value •      

Competitive Evaluation:

• = Very strong relationship
= Strong relationship
 = Weak relationship

Design for Quality and Product Excellence 19

5. Georgio’s Giant Gyros (Problem 4) acquired some additional information about product
characteristics. It found that consumers placed the highest importance on taste appeal
(especially flavor) and order accuracy, followed by healthy food (measured by sodium
content and calories), value, and service. The menu board was only casually noted as one
of the least important attributes in the surveys. Georgio faces three major competitors in
this market: Mario’s, Gyroking, and Antonio’s. Studies of their products yielded the
information shown in the worksheet tab Prob.7-4 in the Excel file C07Data on the
Student Companion Site for this chapter. Results of the consumer panel ratings for each
of these competitors can also be found there (a 1–5 scale, with 5 being the best). Using
this information, modify and extend your House of Quality from Problem 2 and develop
a deployment plan for a new gyro. Assume that a separate study will be made on the
physical facilities. On what attributes should the company focus its marketing efforts?
Answer
5. With the new data given in C07Data.xlsx for Prob. 7-05 for Georgio's customers, a partial
House of Quality for the design of the gyros can be built, as shown below. Note that the
relationships between customer requirements (flavor, health, value) and associated
technical requirements (% fat, calories, sodium, price) of the gyro design are strong. Note
also that the focus here is on design of the product, not the service aspects of order
accuracy and service.
The inter-relationships of the roof are not shown, due to the limitations of MS
Word® software. These may be sketched in. For example, they would show strong
inter-relationship between % t-Fat and calories.

Design for Quality and Product Excellence 20

PARTIAL HOUSE OF QUALITY MATRIX
FOR GEORGIO’S GIANT GYROS

Price Size Calories Sodium % t-Fat
Facility
layout
Work
procedures
Imprtnce

12 3 45
Compet.
Eval.
12 3 4 5
Selling
Pts.
1 2 3 4 5
Taste Moistness     •   A GK G A K
Flavor     •   AKG G K A
Health Nutritious   • • •  
AKG K AG *
Visual Visually
Appealing
      
AKG AG K
Speedy
service
Number of
Staff
      •
AKG K A G
Kitchen
capacity
     • •
AKG A G K *
Menu Size & font      •  A K G A KG
Order
accuracy
Order check
process
      •
KAG K A G *
Value Good Value •       K A G K A G *
Competitive Evaluation:
Georgio’s 5 3 5 3 5 4 5

Gyroking 3 5 4 5 2 3 4

Antonio's 4 4 3 3 4 5 3

Georgio’s Targets
$0.51/
oz.
5.5
oz.
70/oz 110/ oz.

13% Improve Hold gains
• = Very strong relationship
= Strong relationship
 = Weak relationship

Design for Quality and Product Excellence 21

ANSWER – CONTINUED

5. The Importance and Competitive Evaluation of customer requirements can be read
from the survey results in the data tables in spreadsheet Prob07-05.xlsx that are provided,
and placed under their respective columns

Georgio’s Giant Gyros technical requirements must be placed on a more equal basis, which
would best be shown as units/ounce, except for the percent fat value. These are shown
below.

Company Price/Oz. Calories/Oz.* Sodium/Oz.* Fat (%) *
Georgio's $0.545 80.0 159.1 13
Kingyro $0.567 85.3 124.0 23
Antonio's $0.542 90.0 158.3 16

* Lower is better

Thus, we can see from the competitive evaluation of technical characteristics and Georgio’s
targets, that if Georgio’s is already low in price per ounce, as well as calories, and percent
fat, its new product is leaner and healthier, as well as being cost effective. This analysis
suggests that Georgio’s might consider increasing its size and flavor, which may indirectly
affect its visual appeal, as well. However, Georgio has not targeted the size for an increase.
At the same time, it should build on the strength of the nutrition trend by keeping the percent
fat and sodium low. Georgio's has targeted sodium for a major reduction, from 159/oz. to
110/oz., and slightly reducing the number of calories per ounce, from 80 to 70, to be even
more competitive. The facilities need some minor improvements, but their work procedures
appear to be customer-pleasing. They merely need to hold the gains. If Georgio’s can
design a flavorful, healthy, 5.5 oz. gyro and continue to sell it at the current attractive
price or $3.00, it should be a very profitable undertaking.

6. A blueprint specification for the thickness of a refrigerator part at Refrigaria, Inc. is 0.300
± 0.025 centimeters (cm). It costs $25 to scrap a part that is outside the specifications.
Determine the Taguchi loss function for this situation.

Answer

6. The Taguchi Loss Function for refrigerator part at Refrigaria, Inc. is: L(x) = k (x - T)
2

$25 = k (0.025)
2

k = 40000

 L(x) = k (x - T)
2
= 40000 (x - T)
2

7. A team was formed to study the refrigerator part at Refrigaria, Inc. described in Problem
6. While continuing to work to find the root cause of scrap, they found a way to reduce
the scrap cost to $15 per part.
a. Determine the Taguchi loss function for this situation.

Design for Quality and Product Excellence 22

b. If the process deviation from target can be reduced to 0.015 cm, what is the Taguchi
loss?

Answer

7. The Taguchi Loss Function is: L(x) = k (x - T)
2

a) $15 = k (0.025)
2

k = 24000

 L(x) = k (x - T)
2
= 24000 (x - T)
2

b) L(x) = 24000 (x - T)
2

 L(0.015) = 24000 (0.015)
2
= $5.40

8. A specification for the length of an auto part at PartsDimensions, Inc. is 5.0 ± 0.10
centimeters (cm). It costs $40 to scrap a part that is outside the specifications. Determine
the Taguchi loss function for this situation.

Answer

8. The Taguchi Loss Function is: L(x) = k (x - T)
2

$40 = k (0.10)
2

k = 4000

 L(x) = k (x - T)
2
= 4000 (x - T)
2

9. A team was formed to study the auto part at PartsDimensions described in Problem 8.
While continuing to work to find the root cause of scrap, the team found a way to reduce
the scrap cost to $20 per part.
a. Determine the Taguchi loss function for this situation.
b. If the process deviation from target can be reduced to 0.040 cm, what is the Taguchi
loss?

Answer

9. The Taguchi Loss Function is: L(x) = k (x - T)
2

a) $20 = k (0.10)
2

k = 2000

 L(x) = k (x - T)
2
= 2000 (x - T)
2

b) L(x) = 2000 (x - T)
2

Design for Quality and Product Excellence 23

 L(0.040) = 2000 (0.040)
2
= $ 3.20

10. Ruido Unlimited makes electronic soundboards for car stereos. Output voltage to a
certain component on the board must be 12 ± 0.5 volts. Exceeding the limits results in an
estimated loss of $60. Determine the Taguchi loss function.

Answer

10. The Taguchi Loss Function is: L(x) = k (x - T)
2

$60 = k (0.5)
2

k = 240

 L(x) = k (x - T)
2
= 240 (x - T)
2

11. An electronic component at Eltcomp has a specification of 100 ± 0.4 ohms. Scrapping
the component results in a $81 loss.
a. What is the value of k in the Taguchi loss function?
b. If the process is centered on the target specification with a standard deviation of 0.2
ohm, what is the expected loss per unit?

Answer

11. For Eltcomp’s specification of 100 ± 0.4 ohms:

a) L(x) = k (x - T)
2

$81 = k (0.4)
2

k = 506.25

b) EL(x) = k (
2
+ D
2
) = 506.25 ( 0.2
2
+ 0
2
) = $20.25

12. An automatic cookie machine at AutoCM, Inc., must deposit a specified amount of 25 ±
0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a
defective cookie. A sample of 50 cookies was drawn from the production process, which
has been determined to be approximately normally distributed, and the results, in grams,
can be found in worksheet tab Prob.7-12 in the Excel file C07Data file on the Student
Companion Site for this chapter.
a. What is the value of k in the Taguchi loss function?
b. Determine how much the process varies from the target specification, based on the
mean difference and standard deviation of the sample results. What is the expected loss
per unit?

Answer

12. For a specification of 25 ± 0.3 grams and a $0.03 scrap cost:

Design for Quality and Product Excellence 24

Analysis of the dataset for Prob. 7-12 provides the following statistics:
x
= 25.0056; D = 25.0056 - 25.00000 = 0.0056
 = 0.0566

a) L(x) = k (x - T)
2

$0.03 = k (0.3)
2

k = 0.333

b) For  = 0.0566

EL(x) = k (
2
+ D
2
) = 0.333 (0.0566
2
+ 0.0056
2
) = $0.0011

See spreadsheet Prob07-12.xlsx for details.

13. A computer chip designed by the MicroKeeb Co. has a specification for the distance
between two adjacent pins of 2.000 ± 0.002 mm. The loss due to a defective chip is $4. A
sample of 25 chips was drawn from the production process and the results, in millimeters,
can be found in the worksheet tab Prob. 7-13 in the Excel file C07Data file.
a. Compute the value of k in the Taguchi loss function.
b. What is the expected loss from this process based on the sample data?

Answer

13. For a specification of 2.000 ± .002 mm and a $4 scrap cost:

Analysis of the dataset for problem 7-13 provides the following statistics:
x
= 2.00008; D = 2.00008 - 2.00 = 0.00008
 = 0.00104

a) L(x) = k (x - T)
2

$4 = k (0.002)
2
 k = 1,000,000

b) EL(x) = k (
2
+ D
2
) = 1,000,000 ( 0.00104
2
+ 0.00008
2
) = $1.088

See spreadsheet Prob07-13.xlsx for details.

14. In the production of Raphael Transformers, any output voltage that exceeds 120 ± 10
volts is unacceptable to the customer. Exceeding these limits results in an estimated loss
of $200. However, the manufacturer can adjust the voltage in the plant by changing a
resistor that costs $2.25.
a. Determine the Taguchi loss function.
b. Suppose the nominal specification is 120 volts. At what tolerance should the
transformer be manufactured, assuming that the amount of loss is represented by the cost
of the resistor?

Design for Quality and Product Excellence 25

Answer

14. a) The Taguchi Loss function is: L(x) = k (x - T)
2

200 = k (100)
2

k = 0.5

So, L(x) = 0.5 (x-T)
2

b) $2.25 = 0.5 (x-120)
2

4.50 = (x - 120)
2

(x - T)Tolerance = 50.4 = 2.12 volts

2.12 = x - 120

 x = 122.12

15. At Elektroparts Manufacturers’ integrated circuit business, managers gathered data from
a customer focus group and found that any output voltage that exceeds 55 ± 0.5 volts was
unacceptable to the customer. Exceeding these limits results in an estimated loss of $75.
However, the manufacturer can still adjust the voltage in the plant by changing a resistor
that costs $2.00.
a. Determine the Taguchi loss function.
b. Suppose the nominal specification remains at 55 volts. At what tolerance should the
integrated circuit be manufactured, assuming that the amount of loss is represented by the
cost of the resistor?
Answer

15. a) The Taguchi Loss function is: L(x) = k (x - T)
2

75 = k (0.5)
2

k = 300

So, L(x) = 300 (x-T)
2

b) The Taguchi Loss function is: L(x) = k (x - T)
2

$2.00 = 300 (x-55)
2

0.00667 = (x - 55)
2

(x - T)Tolerance = 00667.0 = 0.0817 volts

0.0817 = x - 55

Design for Quality and Product Excellence 26

 x = 55.0817

16. Two processes, P and Q, are used by a supplier to produce the same component, Z, which
is a critical part in the engine of the BearingPort 778 airplane. The specification for Z
calls for a dimension of 0.24 mm ± 0.03. The probabilities of achieving the dimensions
for each process based on their inherent variability are shown in the table found in the
C07Data file for Prob.7-16 on the Student Companion Site for this chapter. If k =
60,000, what is the expected loss for each process? Which would be the best process to
use, based on minimizing the expected loss?

Answer

16. For the BearingPort 778 plane parts (see spreadsheet Prob07-16.xlsx for detailed
calculations):

Specifications are 24 ± 3 mm

L(x) = 60000 (x - T)
2

For a typical calculation:

 L(0.21) = 60000 (0.21 - 0.24)
2
= $ 54.00

Weighted loss = 0.12 X $54.00 = $ 6.48

BearingPort Airplane Co.

Calculation of Taguchi Loss Values

Value

Loss ($)
Process P
Probability
Weighted
Loss ($)
Process Q
Probability
Weighted
Loss ($)
0.20 96.00 0 0.00 0.02 1.92
0.21 54.00 0.12 6.48 0.03 1.62
0.22 24.00 0.12 2.88 0.15 3.60
0.23 6.00 0.12 0.72 0.15 0.90
0.24 0.00 0.28 0.00 0.30 0.00
0.25 6.00 0.12 0.72 0.15 0.90
0.26 24.00 0.12 2.88 0.15 3.60
0.27 54.00 0.12 6.48 0.03 1.62
0.28 96.00 0 0.00 0.02 1.92
Expected Loss 20.16 16.08

Therefore, Process Q incurs a smaller loss than Process P, even though some output of Q
falls outside specifications.

Design for Quality and Product Excellence 27

17. The average time to handle a call in a the Call-Nowait call processing center has a
specification of 6 ±1.25 minutes. The loss due to a mishandled call is $12. A sample of
25 calls was drawn from the process and the results, in minutes, can be found in the
C07Data file for Prob.7-17 on the Student Companion Site for this chapter.
a. Compute the value of k in the Taguchi loss function.
b. What is the expected loss from this process based on the sample data?

Answer

17. For a specification of 6  1.25 minutes and a $12 call mishandling cost:

x = 6.016; D = 6.016 - 6.00 = 0.016
 = 0.8957

a) L(x) = k (x - T)
2

$12 = k (1.25 )
2
;  k = 7.68

b) E [L(x) = k (
2
+ D
2
)] = 7.68 ( 0.8957
2
+ 0.016
2
) = $6.164

(See spreadsheet Prob07-17.xlsx for details).Note this spreadsheet is a slightly adjusted
version of the Ch6BasicStats spreadsheet from Chapter 6.

18. Massive Corporation’s tested five motors in a 900-hour test. Compute the failure rate if,
three failed after 200, 475, and 750 hours and the other two ran for the full 900 hours
each.

Answer

18. Massive Corporation’s motors have a failure rate of:

= 3 = 3 = 0.00093 failures / hour
[(2 x 900) + 200 +475 + 750] 3225

19. The life of a Supercellular phone battery is normally distributed with a mean of 950 days
and standard deviation of 40 days. Using the Excel functions (see Chapter 6), determine
the following:
a. What fraction of batteries is expected to survive beyond 1010 days?
b. What fraction will survive fewer than 900 days?
c. Draw a chart of the reliability function using Excel.
d. What length of warranty is needed so that no more than 10 percent of the batteries will
be expected to fail during the warranty period?

Answer

Design for Quality and Product Excellence 28

19. a) P(x > 1010) = 1 – P(x < 1010)

Using the Excel NORMDIST (1010,950,40,TRUE) = 0.9332

P(x > 1010) = 1− ??????(??????<
??????− ??????̅
??????
)=1− ??????(??????<
1010−950
40
)=1−0.9332=0.0668
or 6.68% should survive beyond 1010 days.

b) P (x < 900) = ??????(??????<
??????− ??????̅
??????
)= ??????(??????<
900−950
40
)=0.1057 or 10.57% should survive
less than 900 days

NORMDIST (900,950,40,TRUE) = 0.1057 can be read directly.

c) The reliability function looks approximately as follows (see spreadsheet Prob07-18.xlsx
for details):

c) Let xw be the limit of the warranty period.

P (x < xw) = 0.10; z = -1.28, for ??????(??????=
??????−950
40
)= −1.28 , xw = 898.8 hours for the
warranty limit.

Using the Excel NORM.S.INV (0.10) we find z = -1.28. The approximate value can be
read from the tabulated and curve values as being between 898 and 902 on the Z Value
Given Probability tab of spreadsheet Prob07-18.xlsx.

0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
775800825850875900925950975100010251050
Probability
Battery Life - Hours
Reliability Curve
Reliability

Design for Quality and Product Excellence 29

20. Widetred, Inc. makes automobile tires that have a mean life of 60,000 miles with a
standard deviation of 2,000 miles. Using Excel functions (see Chapter 6), determine the
following:
a. What fraction of tires is expected to survive beyond 63,250 miles?
b. What fraction will survive fewer than 56,600 miles?
c. Draw a chart of the reliability function using Excel.
d. What length of warranty is needed so that no more than 5 percent of the tires will be
expected to fail during the warranty period?

Answer

20. a) P(x > 63250) = 1 – P(x < 63250)

Using the Excel NORMDIST (63250,60000,2000,TRUE) = 0.9479

P(x > 63250) = 1− ??????(??????<
??????− ??????̅
??????
)=1− ??????(??????<
63250−60000
2000
)=1−0.9479=0.0521
or 5.21% should survive beyond 63,250 miles.

b) P (x < 56600) = ??????(??????<
??????− ??????̅
??????
)= ??????(??????<
56600−60000
2000
)=0.0446 or 4.46% should
survive less than 56,600 days

NORMDIST (56600,60000,2000,TRUE) = 0.0466 can be read directly.

c) The reliability function looks approximately as follows (see spreadsheet Prob07-20.xlsx
for details):

Design for Quality and Product Excellence 30

d) Let xw be the limit of the warranty period.

P (x < xw) = 0.05; z = -1.64, for ??????(??????=
??????−60000
2000
)= −1.64 , xw = 56,720 miles for the
warranty limit.

Using the Excel NORM.S.INV (0.05) we find z = -1.64. The approximate value can be
read from the tabulated and curve values as being between 56,600 and 56,800 on the Z
Value Given Probability tab of spreadsheet Prob07-20.xlsx

21. Livelong, Inc.’s computer monitors have a failure rate of 0.00095 units per hour. What is
the reliability function? Assuming an exponential distribution, what is the probability of
failure within 5,000 hours? Calculate your answer using the appropriate mathematical
formula and verify your result using Excel.

Answer

21. The reliability function for Livelong, Inc.’s monitors is R(T) = 1 - F(T) = e
-T

 = 0.00095; Use F(T) = P(x < 5000)

F(T) = P(x < 5000) = 1 - e
-0.00095 (5000)
= 1- 0.008652 = 0.99135 or 99.14% probability that a
monitor will survive less than 5,000 hours

Note that the cumulative exponential distribution in spreadsheet Prob07-21.xlsx shows the
same value for EXP.DIST (5000,0.00095, TRUE) = 0.99135.

22. An electronic component in a satellite radio has failure rate of = .000015. Find the mean
time to failure (MTTF). What is the probability (assuming an exponential probability
distribution) that the component will not have failed after 12,000 hours of operation?
Calculate your answer using the appropriate mathematical formula and verify your result
using Excel.
Answer

22. The MTTF for the component is ??????=
1
??????
=
1
0.000015
; so,  = 66666.67

R (T) = e
- T/
= e
- 12000 / 66666.67
= e
-0.18
= 0.8352 or 83.52% probability of surviving for at
least 12,000 hours

Note that the cumulative exponential distribution in spreadsheet Prob07-22.xlsx shows the
value for EXP.DIST (12000,0.000015, TRUE) = 0.16473, which is the cumulative
probability of failure. Then, the probability of NOT failing is 1- 0.16473 = 0.8352.

23. The MTBF of an integrated circuit made by Outer Limits, Inc.is 18,000 hours. Calculate
the failure rate.

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osoitti hänen epäluuloaan — entä jos hän todellakin olisi nähnyt Karl
Augustin!
Hän istuutui puun juurelle etäisimpään holviin eikä ollut
huomaavinaan keveiden askelten asteettaista lähenemistä. Mutta
äkkiä askeleet tulivat nopeammiksi, ja isä seisoi hänen edessään
ilmeisestihämmästyneen näköisenä.
— Mitä sinä täällä teet, tyttö? — kysyi hän karskisti, luoden
samalla raunioihin pitkän, viipyvän katseen, joka näytti tunkevan
jokaiseensopukkaan.
— Istun mietiskelemässä, isä-kulta, — sai Alma sanotuksi.
— Hiiteen moiset mietiskelyt! Minä mietiskelin myöskin hieman
tullessani sattumalta eteiseen ja nähdessäni sinun livistävän
rakkaille raunioillesi. Mutta katso, ettet mieti sellaista, joka saattaa
sinulle käydä liian kalliiksi — ja kavahda, ettet vastedes tee niin
pitkiäkävelyretkiä paitsi isäsi ja sulhasesi seurassa!
— Et ole kieltänyt minulta sellaista ennen!
— Teen sen siis nyt — mene!
Onnellisena päästessään näin vähällä Alma kiiruhti edeltäpäin; ja
huulet yhteenpuristettuina, rypistäen kulmakarvojaan, keppi
kainalossa ja piippu hyvää vauhtia heiluen edestakaisin
ylijahtimestari tulireippain askelin perässä, katsoen silloin tällöin
taakseen ja parikertaa mutisten: — Hitto tuota poikaa — juuri hän se
oli, jonka minä iltapäivällä näin vilahtavan puistossa. Mutta
odotahan, odotahan, kylläolet turhaan heittänyt koukkusi!

Siitä hetkestä alkaen vakoilevat silmät vartioivat Almaa niin
ankarasti, että hän pelosta tavata Karl Augustia ei uskaltanut mennä
ovesta ulos. Mutta Karl August oli aikoja sitten kiinnittänyt itsensä
Hjo'hon, missä hän joka ilta istui Vetterin rannalla, katsellen milloin
valtavaa Ombergia, jonka helmaan hänen vastainen onnensa oli
kätketty,ja milloin loistavaa juovaa, jonka pyhän Birgitan jalanjälki oli
jättänyt sekä venäläisten kasakkain varjoja, jotka mustilla hevosillaan
kiitivät yli Vetterin sinisen kalvon.
Siten vähitellen lähestyi ratkaiseva päivä…

XX.
Pilvinen taivas sateineen ja myrskyineen oli ensimäinen tervehdys,
jonka Alma vastaanotti yhdeksäntenätoista syntymäpäivänään.
Ketään vierasta ei ollut nyt kutsuttu, mitään hyörinän kalistelua ei
kuulunut keittiöstä, ei edes Neta-tädin äänikään kajahdellut
eteisessä tahi portaissa: kaikki oli hiljaista, ikäänkuin päivällä ei olisi
ollutmitään merkitystä.
Alma oli kauhuissaan, itki ja rukoili mitä palavimmin, samalla
huokaillen: — Jospa jo olisi ilta!
— Hyvää huomenta, lapsi-riepu! — kuului vihdoin ovesta, ja Neta-
neiti, kädessään pieni, mitätön kukkaseppele, astui makuusijan
ääreen. —Katsoppa, — sanoi hän laskien seppeleen peitolle, — ota
nyt se, koska et tahdo parempaa. Sinulle olisi muutoin soveltunut
paremmin tänään kantaa seppelettä ja kruunua — silloin täälläkin
olisi ollut toinenääni kellossa.
— Onko täti nähnyt isää tänään?
— Olen niinkin, luulen kyllä nähneeni — vastikään kutsui minut
soittokellolla niin kiivaasti, että luulin nauhan katkeavan! Nyt etsaa

puhua majurin etkä kenenkään toisenkaan kanssa, ennenkuin sinut
kutsutaan sisälle, eikä se tapahdu aamiaiseksi, jonka ylijahtimestari
tänään syö yksinään. Senjälkeen hän odottaa majuria — ja sitten
lopuksisinuakin, arvelen.
— Ja sillä aikaa, — valitti Alma, — minä menehdyn
levottomuuteen! Eiketään, jonka kanssa puhella, — jonka kanssa
neuvotella — voi, miten kaipaankaan äitiä: hyvää, hellää äitiäni, —
hän ei olisi kovuudellalykännyt luotaan tytärtään, hän.
— Ja teenkö minä niin? — kysyi Neta-neiti hiukan lempeämmällä
äänellä. — Enkö tee enemmänkin kuin mistä kohtuudella saattaisin
vastata, kunen puhu erästä asiaa, jonka sinä kai itse tiedät, joskaan
et luulekenenkään muun tietävän.
— En ymmärrä, — sanoi Alma hiljaa.
— Vai niin, sinä et ymmärrä, että tuolla vanhalla luostarinröttelöllä
on useampia korvia kuin luuletkaan… no, no, no, älähän keikahda
kumoon! Koska olen voinut pysyä vaiti kokonaisen kuukauden, voin
kaitänäänkin.
— Täti… täti! — Alma vapisi niin rajusti, ettei saanut suustaan
sanaakaan.
— No, no, rauhoitu nyt — siellä ei ollut muita kuin sisäkkö-Sohvi,
joka toisella puolella oli tapaamassa omaa hempukkaansa. Mutta
minä annoin hänelle jokseenkin hyvät kengät, jotta hän pitäisi
suunsa kiinni.
Silloin Alman kasvot hehkuivat häpeän voimakasta punaa. —
Vakuutan teille, täti, — sanoi hän, ja leimahtavaa ylpeyden tunne

antoi voimaa ja elämää hänen sanoilleen, — minä vakuutan, että
minä itse tänä päivänä sanon sen isälle! Ja silloin sekä hän että täti
ja kaikki, jotka saavat sen tietää, huomaavat, ettei kellään ole
oikeuttaloukkaantua siitä tapaamisesta!
— Siunaa ja varjele, — huudahti Neta-neiti, ja löi
hämmästyksissään kätensä yhteen, — miten topakaksi olet tänään
tullutkin, lapseni — älävaan tule hämillesi, kun joudut silmätysten
isäsi kanssa!
* * * * *
Omassa huoneessaan ylijahtimestari istui aamiaispöytänsä
ääressä. Kolme kertaa hän oli kiinnittänyt lautasliinan napinreikään
ja jälleen irroittanut sen siitä; ja Neta-neiti, jonka itsensä piti häntä
palvella, oli niinikään kolme kertaa nostanut kyljysvadin kannen ja
laskenut sen jälleen paikoilleen, koska huomasi, ettei aika ollut vielä
tullut.
Tämä hiljaisuus oli aivan kuulumatonta liukaskielisen
ylijahtimestarin tapaiselle miehelle; tekipä se Neta-neidinkin
voimakkaihin hermoihin sellaisen vaikutuksen, että hän — ensi
kerran ylijahtimestarin taloontultuaan — olisi toivonut saavansa
muutamiksi tunneiksi jättäätehtävänsä.
— Tuokaa tänne pullollinen reininviiniä ynnä lasit ja toimittakaa
sitten sana majurille, että pyydän hänen tekemään minulle sen
kunnian,että joisi täällä kerallani lasillisen aamiaiseksi!
Neta-neiti leijaili ovelle.
— Odottakaa hetkinen — oletteko ollut tänään Alman luona?

— Olen tietysti!
— No?
Kykenemättä käsittämään, mikä vastaus ylijahtimestaria
tämäntuulisena miellyttäisi, Neta-neiti rajoittui lyhyeen "mitä"-
kysymykseen.
— Samantekevä — tehkää mitä olen pyytänyt!
Jäätyään yksin omien ajatustensa seuraan ylijahtimestari asteli
piippu kädessä kiivaana edestakaisin. Näki hänen olevan
voimakkaiden mielenliikutusten vallassa, jotka vuorotellen pyrkivät
voitolle hänen sielussaan. Silloin tällöin hän huiskautti piippuaan
ilmaan ikäänkuin karkoittaakseen jotakin; hän ei tahtonut suoda sijaa
lempeämmilletunteille.
Hetkisen kuluttua Neta-neiti palasi kantaen uutta tarjotinta, ja
vähän jälkeenpäin saapui majuri, levollisena, mutta hieman tavallista
kalpeampana.
— Jättäkää meidät, — sanoi ylijahtimestari luoden katseen
taloudenhoitajattareensa.
Herrat istuutuivat pöytään…
Järjestelmällisellä pitkäveteisyydellä ylijahtimestari oli avannut
pullon, pyyhkäissyt pois lakan, täyttänyt lasit ja asettanut pullon
paikoilleen.
— No, veliseni, meillä on tänään juhlapäivä, joka ei varmaankaan
ole veljelle samantekevä. — Näin puhuessaan ylijahtimestari
sinkahuttimajuriin silmiensä salamat.

— Ei, ei suinkaan — nythän on Alman syntymäpäivä.
— Oikein, ja samalla sinun ja hänen kihlauksensa vuosipäivä…
Saammekai juoda morsiamesi maljan!
— Alman maljan! — änkytti majuri.
— Miksi eroittaa hänen nimeään siitä arvonimestä, joka on hänelle
tuleva — mitä, häh, majuri, mitä sellainen merkitsee? Juon sinun
morsiamesi maljan, ja toivon, ettet kieltäydy vastaamasta siihen!
— Veli… kuule minua!
— Kuulen, — sanoi ylijahtimestari, samalla kun antoi käden, jonka
oliojentanut tarttuakseen lasiin, verkalleen laskeutua, — minä
kuulen,mutta veli ajatelkoon, mitä aikoo puhua.
— Olen jo ajatellut! Asianlaita ei voi, ei saa olla toinen: minun
kunniani, minun sanani ovat panttina… minun täytyy lunastaa ne —
tästä päivästä alkaen ovat Alman siteet katkaistut!
— Ahaa, suurkiitos, varsin mielenkiintoisia keksintöjä! — vastasi
ylijahtimestari kylmänivallisesti samalla kun polttava verivirta
syöksähti hänen kasvoilleen. — Veli on niinmuodoin ollut sitä
mielipidettä, että minä olen mies, jonka kanssa saattaa leikkiä mielin
määrin? Mutta sitä ei tehdä! Minun tyttäreni kättä ei pyydetä sitä
varten, että se jälleen muitta mutkitta hyljätään — ei, hyvä herra, ja
sen minä sanon, että silloin ei ole tunnettu, mikä on se mies, jota on
niin karkeasti loukattu!
— Veli, veli, — sanoi majuri äänensävyllä, jonka syvä
sydämellisyys jonkun verran hillitsi ylijahtimestarin rinnassa riehuvaa
myrskyä, — tämä on liikaa! Älä tee minulle uhria vaikeammaksi kuin

se on, vaan kuule minua kärsivällisyydellä — tee se meidän
monivuotisenystävyytemme tähden!
— Juuri sen vuoksi ei tämän hetken olisi pitänyt koskaan tulla.
— Sitä ei saattanut estää. Se on kuitenkin minun oma syyni,
ainoastaan minun… veli muistaa varmaankin vuosi sitten vallinneet
suhteemme? En saata antaa itselleni anteeksi, etten silloin heti
päättävästi vetäytynyt takaisin. Mutta heikkous, heikkous — enkö
silloin koettanutuskotella itselleni, että Alma uusissa olosuhteissa
pian unohtaisi mieltymyksen, jota pidin ohimenevänä kuumeena. No,
niin, veli: sillähetkellä, jolloin pyysin saada olla kahdenkesken Alman
keralla, houkuttelin hänet vuodeksi… koevuodeksi… tekemään
sitoumuksen kerallani, ja jätin hänelle kunniasanallani oikeuden
saada jälleen vapautensa siinä tapauksessa, että hänellä vielä
tämän ajan jälkeen olisi silloin tuntemansa taipumus. Ehdotukseni
näytti minusta silloin viisaimmalta — koska… koska, — lisäsi hän
verkalleen, — olin hullu saattaessani uskoa, että vanhemman
miehen rehelliset ja hellät huolehtimiset saattaisivat hävittää sen
vaikutuksen, minkä nuoruus, kauneus ja rakkaus kerran ovat
tehneet.
— Leikkiä niinmuodoin, ainoastaan leikkiä, — sanoi ylijahtimestari
verkalleen, katkerasti, — leikkiä minun kerallani! Ja onko minun
tyttäreni, jonka pidin lunta valkoisempana, onko hän vuoden,
kokonaisen vuoden saattanut valehdella isälleen, joka kuitenkin niin
lämpimästi, yli kaiken mitä kieli voi kertoa, on häntä rakastanut! —
Hänen näin lausuessaan herahti kyynel hänen silmäänsä ja tuiman
tuskan piirrekuvastui hänen ryppyiselle otsalleen.
— Herran nimessä, veli, — pyysi majuri hellyttävällä äänellä. —
Älköön veljen viha, veljen suru kohdistuko häneen! Minä olen

ohjannut hänet harhaan; minä olen nähnyt hänen suuren tuskansa,
hänen vastahakoisuutensa, hänen ahdistuksensa ja — sanonko sen,
veli… anna anteeksi, veli, että tuotan vielä enemmän kipua…
sanonko sen suoraan, pelko, tuo kauhistava tunne, joka on niin
arvoton olemaan lapsen jaisän sydämen välillä, se antoi Almalle
rohkeutta mihin hintaan hyvänsä ostamaan itsensä vapaaksi isänsä
vihasta.
— Heikkoutta se oli, viheliäistä, halveksittavaa heikkoutta! —
huudahti ylijahtimestari; mutta hänen äänessään ei ollut tuota
kiivasta kuohuntaa, joka tavallisesti ennusti myrskyä: siinä oli
kumeasti suhisevan tuulen ääni, joka katkee kesken kaikkein
raivokkaintarynnistystään.
— Veli, minä houkuttelin, syy oli minun!
— Niin oli, — lisäsi ylijahtimestari, verkalleen saavuttaen tavallisen
määrätyn mielenmalttinsa, — ja veljen velvollisuus on korjata paha.
— Juuri sitä minä sydämestäni ja sielustani toivon!
— Toivo siten, kuin miehelle sopii! Teemme leikistä toden; hänen
täytyyvielä, niin, hänen täytyy tulla veljen puolisoksi!
— Heitä tämä mieliharha! — pyysi majuri lämpimästi ja hartaasti.
—
Se on mahdotonta: hänen sydämensä on peruuttamattomasti
luovutettu.
Veli ei saata tahtoa hänen onnettomuuttaan. Ja ajatteleppa
vastuunalaisuutta… ajatteleppa sitä niin kauan kun on aika!

— Minä teen sen! Minä tiedän mikä on hänen onnensa ja
onnettomuutensa, paremmin kuin hän itsekään… Jätä minut, majuri,
jätä minut! Tahdon selvittää ajatukseni; tahdon puhua tytön keralla;
tahdon nähdäsaattaako hän katsoa minua silmiin!
— Veli, veli!
— Veli, veli — hiton pitäisi olla veljen veli eikä minun, kun veli
panee toimeen tuollaisia hulluinhuoneseikkailuja! Mutta jollen minä
tule veljen apeksi kaikella asianmukaisella kunnialla, niin — on
mennyttä sekä vanha ystävyys, että myöskin se kunnioitus, jonka
olen lahjoittanut veljelle… mene nyt, mene ja salli minun koota
ajatuksiani!
Ylijahtimestari kulautti pari viinilasillista, hieroi otsaansa, heittäytyi
sohvalle, mutta nousi jälleen ylös ja asettui keskelle lattiaa odottaen
tytärtään.

XXI.
Ovi aukeni hiljaa. Alma astui kynnyksen yli. Silmät, jotka olivat luodut
lattiaan, todistivat hämminkiä, mutta samalla mitä nöyrintä rukousta
lempeyteen.
— Tule esille, lapseni! — sanoi ylijahtimestari, ei lämpimästi, ei
kylmästi, mutta mitä suurin alakuloisuus äänessään.
Alma kohotti katseensa. Hänen silmissään oli kirkkaat kyyneleet;
netipahtivat yksitellen isän kädelle, kun tytär syvään kumartuen
painoisen huuliaan vasten.
— Minulla on sinulle puhumista, tyttäreni; mutta pyydän ettet
vastaa lapsen tavoin, joka joka hetki pelkää vitsaa; vaan avoimesti,
kuten tyttären tulee hänen puhuessaan ensimäisen ja parhaan
ystävänsä kanssa!
— Oi, isä, mikä hyvyys! — änkytti Alma, hämmästyneenä vaipuen
polvilleen; — en ole sitä ansainnut — tunnen, etten ole sitä
ansainnut!
— Siitä olen minäkin vakuutettu, — vastasi ylijahtimestari
kohottaen hänet ylös; — mutta se mikä ei ole tapahtunut, saattaa

vielä tapahtua: katuvaiselle, hellälle tyttärelle on isä aina valmis
antamaan anteeksi, tottelemattomalle… mutta sinä et kai enää tahdo
lukeutua sellaisiin —suo minun uskoa se, Almani!
— Ah, isä, minä…
— Kas niin, kas niin, mitäs äsken sanoin: suo minun päästä näistä
huokauksista äläkä enää huutele "ah" ja "mutta", kyynäränpituisin
keskeytyksin — puhu selvästi!
— Juuri sitä haluan, isä!
— No, hyvä, no alkakaamme: — Piditkö itseäsi tehdessäsi
sitoumuksen majurin kanssa ja tunnustaessasi minulle, isällesi, itsesi
hänenmorsiameksensa, — piditkö itse itseäsi jonakin muuna?
— Pidin itseäni pakosta häneen vuodeksi sidottuna, sidottuna
hänen morsiamekseen nimellisesti. Huomasin myöskin pian, että
hän uskoi pakon vuoden kuluessa muuttuvan vapaaksi tahdoksi,
mutta niin ei käynyt.
— Nyt vastasit enempään kuin mitä sinulta kysyttiin. Oliko sinulla
myöskin mielestäsi majuria kohtaan ne velvollisuudet, jotka
hyvinkasvatetulle tytölle sopivat sitä kohtaan, jonka kanssa hän on
tehnyt niin tärkeän sitoumuksen?
— Niin, luonnollisesti, majuri oli myöskin ottanut minulta sellaisen
lupauksen.
— Ja sinä kuitenkin rikoit sen… — Ylijahtimestari astui
kirjoituspöytänsä ääreen, ja otti siitä pienen kiven pitäen sitä Alman
silmien edessä.

Näkyi selvästi, että hän oli odottanut tästä menettelystään jotakin
onnellista, jotakin suurta tulosta, että hän oli odottanut näkevänsä
Alman ahdistuksessa ja tuskassa pyytävän häneltä anteeksi; mutta
mitään sellaista ei kuulunut. Alma otti kiven käteensä, katseli
lemmittynsä nimen alkukirjaimia ja sanoi sitten hiljaa ja
sydämellisesti: — Se tuliminun tietämättäni, isä, se on totta, samoin
kuin sekin, että minä pari kertaa hämärässä näin Karl Augustin
varjon vilahtavan puitten välitse hänen tehdessään tänne
salaperäisen retkensä, luulin sitä hänen haamukseen; mutta
koskaan hän ei tullut esille, koskaan hän eipuhutellut minua!
— No, oletko senjälkeen nähnyt Adonistasi, ollut kirjevaihdossa
tahitavannut häntä?
— Olen, mutta ainoastaan yhden kerran, — vastasi Alma, joka nyt
olitehnyt sen lujan päätöksen, ettei salaisi vähintäkään.
Ylijahtimestari virnisti kauheasti. — Niin, kauniisti sinä olet
täyttänyt lupauksesi — olethan unohtanut soveliaisuuden
vaatimuksetkin!
— En milloinkaan, isä! En saattanut menetellä toisin pelkäämättä
jotakin vielä pahempaa! — Ja yksinkertaisesti ja totuudenmukaisesti
Alma kertoi Kultakäpälän salaisen lähetyksen ja syyn, joka pakotti
hänet, saatuaan kirjelipun, tapaamaan nuorta miestä raunioilla.
— Joskin minä teidät viipymättä keskeytin?
— Niin kävi, isä, vieläpä ennen kuin juuri sanaakaan oli vaihdettu!
Mutta olen varma, ettei Karl August tahtonut tavata muusta syystä
kuin varottaakseen ja vannottaakseen minua, etten toista kertaa
uudistaisi sitä heikkoutta, jota olen ehtinyt niin kauan katua. Ja nyt,

hyvä isä, usko minua, kun vakuuttamalla vakuutan, että tämän
ainoan kerran olen tavannut, tämän ainoan kirjeen olen saanut, siitä
lähtien kun annoinmajurille lupaukseni.
— Hyvä, olkoon niin. Mutta toivon, ettet kuitenkaan kuvittele
mielessäsi sen muuttavan rahtuakaan asiaa ja sitä suunnitelmaa,
jonkaolen viitoittanut sinun tulevaisuudellesi?
— Toivon, isä, sitä toivon sydämeni pohjasta, ja vieläkin
suuremmallasyyllä, kun majuri tänäpäivänä antaa minulle vapauteni!
— Tahtoi, aikoi antaa sinulle vapautesi! — oikaisi ylijahtimestari.—
Hän teki tosiaankin varsin vakavia yrityksiä siihen, mutta etkai
suurestikaan ihmettele, kun sanon sinulle, etten minä ole semies,
jolle saa tehdä pilaa kunnia-asioista! Hän on pyytänyt sinua
vaimokseen, sinä olet ilmaissut olevasi halukas siksi tulemaan, ja
niinmuodoin minä en salli minkään romanttisen kujeen häiritä
parastasuunnitelmaa, mille konsanaan olen iloinnut!
— Isä — huudahti Alma syvästi kiusaantuneena — asia ei saata
olla niin;itse majurikin peruuttaa kosintansa!
— Sitä en ihmettele, kun hän näkee sen tällä tavalla palkituksi.
Mutta jos sinä, Alma, kuten minä äsken, olisit nähnyt tuon
kunnollisen, rehellisen ja voimakkaan miehen, surun ja katkeran
kaipuun masentamana, tyytymättömänä itseensä ja koko
maailmaan, hylkäävän toivonsa ja ilonsa ja kerjäläisen tavoin
lähtevän sen taivaan ovelta, jonka hänen liian arka kunniantuntonsa
itse sulki; jos olisit nähnyt sen, Alma, jos olisit kuullut miten
lämpimästi hän puolusti sinua, miten hellästi hän rukoili puolestasi,
niin en saata uskoa, että olisit sellainen kivisydän, ettet olisi tullut
liikutetuksi! Jotakin aivan toista onkuitenkin miehen syvä, vakava ja

hiljainen suru kuin nuorukaisen myrskyävä ja helposti ohimenevä
tuska.
Almaan teki vaikutuksensa isän äänen huomattavan hento sävy.
Ylijahtimestarilla oli suuri vaikutusvalta, kun hän äänellään kykeni
ilmaisemaan syvimpiä tunteitaan. Hän teki Almaan tällä hetkellä
voimakkaamman vaikutuksen kuin koskaan ennen; hän huomasi sen
jalisäsi: — Alma, sinä tuotat minulle suurimman surun mitä minulla
on eläissäni ollut — sinä lasket isäsi hautaan, jollet täytä hänen
toivomustaan!
— Oi, isä, isä, laske minut ensiksi sinne! — pyysi tyttö ja puhkesi
itkuun, niin kiivaaseen, niin rajuun, että ylijahtimestaria kauhistutti se
epätoivo, joka oli koko hänen olemuksessaan… — levätkäämme
kernaammin siellä molemmat — mutta anna minulle anteeksi, oi,
annaminulle anteeksi, muutoin en saata elää enkä kuolla!
— Älä itke, Alma lapseni, rakas, pikku Almani, älä itke — eihän
isäsi ole mikään tyranni! — ja sydämellisesti ja kauan syleillen isä
sulki vapisevan tyttären rinnoilleen… — Mutta kuule nyt minun
menettelytapani vaikuttimia; sillä tällä hetkellä tulee Alman jahänen
isänsä sydämen välillä olla täysi luottamus — kuule rauhassa ja
ymmärryksellä!
— Minä kuulen! — kuiskasi Alma; ja istuen isän vieressä hän
kuunteli yhä kasvavassa jännityksessä hänen huuliltaan lähteviä
sanoja:
— Hento, ruumiiltaan ja sielultaan hento nainen, Alma, tarvitsee
elämänsä tärkeimmässä askeleessa vanhemman, vakavan
seuralaisen —seuralaisen, joka juuri sen vuoksi, ettei itse enää ole
nuori, tuntee itsensä tyytyväiseksi, niin, onnelliseksi, ihastuneeksi,

kun vain hyvä, lempeä lapsi, nuori, ystävällinen puoliso hymyilee ja
leikkii hänen ympärillään. Sinä, Almani, joskin sinä jonkin kerran,
erikoisissa tilaisuuksissa, voit olla hieman ryhdikäs, olet kuitenkin
tuollainen hento olento. Sinä, lapseni — olen sanonut, että
puhuisimme suoraan tällä hetkellä — joskin olet kaunis, miellyttävä
ja rakastettava, etole suinkaan saanut runsaasti järjenlahjoja.
Minulle tekee kipeää sanoa tätä, ja näen poskillasi tapahtuvasta
värivaihtelusta, että sinun laitasi on sama sitä kuullessasi; mutta
totuus on totuus. Minun vakaumukseni on nyt se, että sinä eläessäsi
yhdessä kunniallisen jakelpo majurimme kanssa et koskaan kaipaisi
näitä älyn korkeampia etuja, kun sinä taasen miehen kanssa, jolla on
erilainen luonne, terävämpi katse, lyhyesti sanoen syvät, voimakkaat
tunteet, mielikuvitusta jarunoutta j.n.e., kaipaisit niitä varsin paljon.
Ylijahtimestari pysähtyi hetkiseksi, jolloin hän kädellään hiveli
Almankumarassa olevaa otsaa. Senjälkeen hän jatkoi:
— Kun kuherruskuukaudet ovat menneet ja niiden keralla
ensimäinen rakkaudenhuuma, hakee jälkimäinen mies toisenlaisia
aarteita kuin lapsellisen kauneuden ja lapsellisen sopertelemisen
pikku viehätyksiä; hän tahtoo puolison, joka saattaa käsittää,
ymmärtää ja seurata häntä, itse jutella ja keskustella hänen
kanssaan, kun hän väsyneenä päivänsä työstä palaa jälleen kotiin.
Mutta kun hän hyvinkin pian surukseen huomaa, ettei toinen
sellaiseen kykene, kun vaimo silloin salaisella hämmästyksellä
näkee, miten mies vetäytyy syrjään, ja huomaa hänen tehneen
havaintoja, jotka vahingoittavat hänen rakkauttansa — miten käy
silloin: salainen kärsimys, vaikea masentuminen kalvaa vaimon
sielua; hän huomaa, ettei hän enää olemiehelleen kaikki kaikessa,
ja mitättömyytensä tunne tekee hänet yhä alakuloisemmaksi ja
araksi, saattaa hänet kykenemättömäksi käyttämään niitäkin

viehätyskeinoja, joita luonto on hänelle antanut. Vakava suru on
mato, joka kalvaa elämän kukkaa. Nainen menettää kauneutensa,
sen mukana erään mahtavimpia aseitansa, joita hänellä on ollut; sen
tuottama epätoivo vähentää hänen olemuksensa viehätysvoimaa,
hyvyyttä ja rakastettavaisuutta, ja kauniista, ujosta, nuoresta,
leikillisestä tytöstä on tullut ruma, tyytymätön, luulosairas vaimo, joka
ei kykenetekemään omaansa eikä miehen elämää iloiseksi!
— Isä, isä, — huudahti Alma ja kohotti hehkuvat kasvonsa, —
sopiiko tämä kuva minuun — olenko minä tyhmä, yksinkertainen,
avuton olento?
— Et mikään niistä, lapseni, sinä olet lahjoiltasi vain
keskinkertainen; ja jos olisit antanut minun rauhassa lopettaa
kuvaukseni, niin olisin sitten näyttänyt sinulle, että juuri ne
ominaisuudet, joita sinulla on, olisivat kehittyneet sinussa — josolisit
mennyt naimisiin majurin kanssa, — miehen, joka on tasainen,
levollinen ja perin rehellinen ja joka koko elämänsä olisi sinua
käsillään kantanut, — puhtaimmaksi ja korkeimmaksi onneksi,
onneksi, jonka kestävyys ei olisi häiriintynyt. Itse intohimottomana,
tyynenä, lempeämielisenä ei hän olisi koskaan pyytänyt sinulta mitä
itse ei olisi tarvinnut, ja sinä olisit lisännyt niiden harvain, mutta
onnellisten naisten lukua, jotka täyttäessään hellän puolison ja äidin
velvollisuuksia, ympärillään paras mitä elämällä on, kunnioitus ja
hyvinvointi, eivät joudu tuntemaan senlaatuista nöyryyttävää
köyhyyttä, jonka tietoisuus avaa sen haudan, mihin moni nuori
nainen on nähnyt elämänsä onnen vaipuvan… Ja nyt, Almani, olen
sanonut kaiken. Ajatteleppa, että isäsi, jonka katse on seurannut
sinua varhaisimmasta lapsuudestasi, täytyy tuntea sinut paremmin
kuin itse tunnet itsesi — ja huomaa nyt, mitä hän on tahtonut, mitä

toivonut: huomaa, ettei hänellä koko maan päällä ole pyhempää ja
lämpimämpää toivomusta kuinettä näkisi sinut onnellisena!
Muutamia hetkiä isän vaiettua Alma istui hiljaa. Jo aikoja sitten oli
hänen poskillaan palanut tumma purppura, hänen silmissään oli
loistanut voimakas ja vilkas tuli. Nyt hän kohosi ylös, laski kätensä
isän käteen ja sanoi levollisesti, mutta varmasti: — Suo minulle
anteeksi, isäni, mutta minä… minä tohdin uskoa, että lausuntosi tahi
ainakin osa siitäon johonkin määrin erehdyttävä!
— Mitä sanot, Alma? — kysyi ylijahtimestari ja katsoi
hämmästyneenätyttöä silmiin: — erehdyttävä?
— Niin, isä, en ole koskaan ennen tuntenut sitä mitä tässä
hetkessä tunnen, mutta jokin minussa nousee sanojasi vastaan, isä,
ja vakuuttaa minulle, etteivät ne sovellu minuun; ja nyt, jos sallit, isä,
tahdon minäkin sanoa, miksi liitto majurin kanssa, kaikissa oloissa —
vaikka en olisi tuntenutkaan Karl Augustia — olisi tullut minulle ylen
vastenmieliseksi… ajatteleppa, isä, vaan nuorta tyttöä, joka eiole
lahjoiltaan niinkään keskinkertainen, mutta joka ensimäisistä
lapsuusvuosistaan alkaen on tottunut konemaiseen tottelemiseen,
tottelemiseen, joka ei ole koskaan antanut tilaa tahi aavistustakaan
oikeaa tahi väärää koskeville ajatuksille eikä edes minkäänlaista
ajatuksenvapautta: jos tämä tyttö nyt vähitellen alkaa tuntea, että
hänelläkin on jotakin arvoa, että hänenkin pitäisi osata tuntea,
ajatella ja menetellä omin neuvoin, niin hänen ensimäinen ja hartain
halunsa on se, että hän, jos hänen on erottava isästä, jota hän on
niin sydämellisesti rakastanut, silloin saisi seurata miestä, joka
antaisi hänelle, ei ainoastaan vaatteita ja ruokaa ja pitäisi ystävällistä
huolta hänen pikku huviensa ja oikkujensa tyydyttämisestä, vaan
myöskin ennen muuta tulisi hänen rakkaimmaksi seurakseen, mutta

yhtäkaikki ei olisi häntä niin paljoa korkeammalla, etteivät he voisi
kohdata toisiaan kaikilla niillä aloilla, joilla miehen ja naisen
ymmärryksenja tunteen tulee olla tasapainossa.
— Mistä, Herran nimessä, — huudahti ylijahtimestari keinuen
tuolillaedestakaisin, — olet saanut kaiken tämän, tyttö?
— Olen saanut sen yksinomaan omasta tunteestani, isä. Mutta
milloin, isäni, olisit huomannut, että Almasi olisi ymmärtänyt muuta
kuin totella, leikkiä ja hyväillä: minähän en ole koskaan muulloin
paitsi tänään, kun sinä itse avasit tien, uskaltanut avoimesti lausua
ajatustani. Mutta, isä-kulta, anna minulle vapaus ja oikeus siihen —
jasilloin saat nähdä, etten minä ole se nuori nainen, jota sinä
kuvailet, vaan että minä tahdolla, tunteella, käytöksellä ja
ymmärryksellä kyllä koetan pitää kiinni siitä miehestä, jonka olen
valinnut. Jos minä sensijaan pakosta tahi houkutuksesta tekisin sen
synnin, että antaisin kunnialliselle miehelle käden ilman sydäntä, niin
olisin ollutta jamennyttä, silloin kuihtuisin ja kuolisin kuin köyhä,
tallattu kukka, ja niinmuodoin tuottaisin itseeni luottavalle miehelle
elinkautisen katumuksen kotoisen ilon asemesta. Olisiko se hyvä,
isä?… Ei, hyvä se ei olisi, sillä minun täytyy lopettaa tunnustamalla,
etten luuleitsessäni olevan luonnetta kestämään pilalle mennyttä
elämää.
Ylijahtimestarin kasvoilla oli pitkän aikaa taistellut valtava
mielenliikutus; mutta sinä hetkenä, jona Alma lakkasi puhumasta,
sanoi hän melkein hennolla äänellä: — Tule syliini, lapsi! Sellaisena
sinun olisi pitänyt esiintyä aikoja sitten — olen tyytyväinen sinuun,
Alma, hyvin tyytyväinen. Jumala katsoo tahtoon: sinun hyväsi oli
kuitenkinjoka tapauksessa aina minun päämääränäni.

— Ja nyt… — änkytti Alma, nojaten polttavan poskensa isän
poskeen.
— … saamme ajatella asiaa, ennenkuin toimimme, lapseni! En
anna tämän jälkeen suorastaan kieltävää vastausta, mutta
minunkaan ikäisenäni ei kernaasti luovuta, kaikkein vähimmin
väkivaltaisesti, lempiajatuksestaan… Koetan keksiä jonkun keinon,
joka saattaisi sovittaa meidän kaikkien tunteet. Mutta nyt, lapseni,
jätä minut rauhaan — — olet todellakin saanut minut vakuutetuksi
siitä, ettet olese, miksi olen sinut kuvannut: ja niin iloinen olen siitä,
että olen tehnyt yhdeksäntoista vuoden pituisen erehdyksen, että
tästä hetkestä alkaen annan sinulle täyden vapauden avoimesti
lausua ajatuksesikaikista asioista.
— En käyttäisi sitä väärin, isä! — sanoi Alma, nöyrästi suudellen
isänsä kättä, jolle vierähti muutamia kyyneliä. — Sillä koskaan en ole
samassa määrässä kuin nyt tuntenut halua tottelemisella ja
sanomattomalla hellyydellä ansaita rakkauttasi, isä.
— Hyvä, hyvä, lapseni — luulin, sieluni kautta, että juuri tänään
tapahtuisi jotakin erittäin merkillistä. — Ylijahtimestari ajatteli repeter-
kelloa, jonka vetämisen hän ensimäisen kerran niin moniinvuosiin oli
unohtanut.
Niin, ja mitkä vallankumoukset hänen valtakunnassaan olivat
tapahtuneet parin tunnin kuluessa: majuri hylkää kihlauksen, Alma
heittää pois vanhan ihmisen ja tulee uudeksi — ja hän itse saa
selville, että hän yhdeksäntoista vuoden ajan on ollut erehdyksessä
oman tyttärensäluonteesta!
Saman päivän iltapuolella oli ylijahtimestarilla, kun hän koko ajan
oli ollut sulkeutuneena omaan huoneeseensa, majurin kanssa pitkä

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