Lesson: Process Capability Index (Cp and Cpk)

Are you struggling to consistently meet customer expectations and deliver high-quality results? You’re not alone. Many organizations find it challenging to understand and improve their process capability, which is critical for maintaining consistency and excellence.

At www.LearnLeanSigma.com, we’ve designed this lesson to be your guide on this journey. You’ll dive deep into the concepts of Cp and Cpk—key indices that reveal how well your processes perform within specified limits. We break down complex calculations into easy-to-follow steps, using real examples so you can confidently apply these techniques in your own work.

Here’s what you’ll gain:

1. Clarity on Cp and Cpk: Start with a clear understanding of what Cp and Cpk are, why they matter, and how they impact your process performance.

2. Step-by-Step Calculation: We’ll guide you through the exact process to calculate these indices, ensuring you have the skills to assess your process capability accurately.

3. Insightful Interpretation: Learn what your Cp and Cpk values mean for your processes, and uncover whether your process is just capable, highly capable, or needs improvement.

4. Actionable Improvement Strategies: Discover how to enhance your Cp and Cpk through practical methods, including reducing variability and centering your process mean. These strategies will help you optimize your processes and reduce defects.

5. Visual Tools for Better Communication: Use histograms and capability plots to easily visualize and communicate your process performance to stakeholders.

By the end of this lesson, you’ll be equipped not just with knowledge, but with the practical skills to improve your organization’s process capability. This is your step towards delivering consistent quality and exceeding customer expectations every time. Let’s transform your processes together.

1. UNDERSTANDING
Process Capability
Your Path To Operational Excellence

2. Contents
01 Introduction
What is process capability?
Process Capability key terms
Specification Limits
Natural Variation
Control Limits
02 Understanding
Process Capability
Standard Deivation σ
Cp and Cpk Indexs
03 Calculating
Process Capability
Collecting data
Calculating standard deviation σ
Applying Cp and Cpk Formulas
Example of Cp and Cpk Calculation
04 Graphical
Representaton
Histograms
05 Interpreting Results
What do the results mean?
Common interpretation mitakes
06 Improving
Process Capability
Reduce Variability
Centering the Process
07 Resources
Process Capability
Analyzer
Process Capability
Calculator
LearnLeanSigma.com - Your Path To Operational Excellence

3. 01 Introduction
What is Process Capability?
LearnLeanSigma.com - Your Path To Operational Excellence

4. What is Process Capability?
What is Process Capability: Process capability measures how well a process can produce outputs that
meet the specifications or tolerance limits. It quantifies the inherent variability in the process relative
to the allowed specification limits.
LearnLeanSigma.com - Your Path To Operational Excellence
Machines
Variation can be in:
Method
Material
Labour
Envionment

5. What is Process Capability?
LearnLeanSigma.com - Your Path To Operational Excellence
E.g. in the manufacturing process below the material thickness output will have variation.
This variation could be:
Common cause variation
Variation within control limits
Special cause variation
Variation outside control limits
This variation is measured and monitored using control
charts to identify if the variation is common or special
cause.

6. Below is an example of a control chart measuring the variation of a process output.
20 data points have been taken
From the data, the following were calculated:
Mean (average) of data points
Upper Control Limit (UCL)
Lower Control Limit (LCL)
Data Points Mean Upper Control Limit Lower Control Limit
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Process Capability Key Terms
LearnLeanSigma.com - Your Path To Operational Excellence
This helps to understand the variation:
Inside the control limits is common
cause variation
Outside the control limits is special
cause variation
Special Cause Variation
The Control Chart tells us how good and stable a process is
*Calculation of control limits is cover later in the lesson

7. Data Points Mean Upper Control Limit Lower Control Limit
Upper specification limit Lower Specification Limit
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Process Capability Key Terms
LearnLeanSigma.com - Your Path To Operational Excellence
Now if we consider our customers will have specification limits for our products, any variation outside
of this would be classed as a defect as it does not meet the customer requirements.
Defect
Defect
Outputs outside of the Upper
Spec Limit (USL) and the Lower
Spec Limit (LSL) are classed as
defects
Spec limits can be tighter or
more relaxed than the control
limits

8. Data Points Mean Upper Control Limit Lower Control Limit
Upper specification limit Lower Specification Limit
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Process Capability Key Terms
LearnLeanSigma.com - Your Path To Operational Excellence
Industries with a high risk of a severe impact from defects such as Aviation and Pharmaceuticals will
have very strict levels of specification limits.
These industries tend to run at 6 Sigma
levels of performance, meaning they
produce less than 3.4 Defects Per 1 Million
Opportunities *(DPMO).
*DPMO is covered in more detail in the DPMO lesson

9. Review of Process Capability key terms so far:
Variation - Movement in a process output.
Common cause variation - Variation inside of the control limits.
Special cause variation - Variation outside of the control limits.
Upper Control Limit (UCL) - The calculated upper control limit of the
process based on input data.
Lower Control Limit (LCL) - The calculated lower control limit of the
process based on input data.
Mean - Average of data points
Upper Specification Limit (USL) - Upper specification limit set by customer
Lower Specification Limit (LSL) - Lower specification limit set by customer
Process Capability Key Terms
LearnLeanSigma.com - Your Path To Operational Excellence

10. Key elements of a Control Chart
Process Capability Key Terms
LearnLeanSigma.com - Your Path To Operational Excellence
Mean
Lower Spec Limit (LSL)
Upper Spec Limit (USL)
Upper Control Limit (UCL)
Lower Control Limit (LCL)
Data Points
Special Cause Variation

11. 02 Understanding
Standard Deviation and Process
Capability Indexes
LearnLeanSigma.com - Your Path To Operational Excellence

12. Understanding Standard Deviation
LearnLeanSigma.com - Your Path To Operational Excellence
Before calculating process capability it is important to understand standard
deviation (σ) and the bell curve showing distribution.
This bell curve displays the variation of a data output in
green. Statistically, 99.72% of all common cause
variation will fall within +/—3 standard deviations from
the mean.
68.26% of data points will be +/- 1σ from the mean.
95.44% of data points will be +/-2σ from the mean.
99.72% of data points will be +/-3σ from the mean.
0.28% of data points will be outside of the bell
curve representing special cause variation. This is
statistically a 3.4 out of a million chance of
occurring.

13. The Output result of the index will be a number that will
allow you to understand how the process is performing:
This number can also be used to bench mark process
results with other processes to identify which
process is performing the best.
The Cp value can also be used to measure if
improvements have reduces process variation.
Understanding Standard Deviation
LearnLeanSigma.com - Your Path To Operational Excellence
Tighter curve (lower variation)
Wider curve (greater variation)
Variation in measured output
These outputs can be visually demonstrated
with bell curves or histograms. The higher the
Cp value the tighter the curve, demonstrating
a lower variation.

14. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Understanding Standard Deviation
LearnLeanSigma.com - Your Path To Operational Excellence
If you think about the process variation of the control charts with data
points up and down and rotate that 90degrees, you will see the variation of
the control chart on a bell curve.

15. There are two process capability indexes you need to be aware of:
Cp - Process Capability Index
Cpk - Process Capability Index adjusted for mean shift
Understanding Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
Cp is a measure of a process's potential capability. It compares the width of the specification
limits (USL - LSL) to the natural variability of the process, represented by 6σ (where σ is the
standard deviation). The 6σ range covers almost all the data in a normal distribution (99.73% of
data), making it a standard way to measure how well the process fits within the specification
limits.
Cp =
USL - LSL
6σ
The Formula is

16. Understanding Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
Cpk measures the process capability while taking into account the process mean (μ) and how
centered it is between the specification limits. Unlike Cp, which only measures the spread of the
process, Cpk also considers whether the process mean is shifted towards either the USL or LSL.
By using the minimum value between the two calculations, Cpk reflects the worst-case scenario
of the process’s ability to produce within the specification limits.
Cpk = min
USL - μ
3σ
The Formula is
μ - LSL
3σ
( )
,
This means the Cpk is the lowest of the two calculations.
USL - Mean, divided by 3 X Standard Deviation, or
Mean - LSL, divided by 3 X Standard Deviation.
We will explain these calculations with examples in more detail in the calculation part of the lesson.

17. 03 Calculating
Standard Deviation and
Process Capability Indexes
LearnLeanSigma.com - Your Path To Operational Excellence

18. Go To Calculator
Collecting Data
LearnLeanSigma.com - Your Path To Operational Excellence
To Calculate the Cp and Cpk process capability indexes
for your processes you will need data.
Accurate process capability calculations require a
representative sample of data.
As a rule of thumb, 30 data points is the suggested
minimum.
A strong recommendation is to use a sample size
calculator to calculate how many data points you need.
In general the larger the sample size the more reliable
the reasults.

19. Collecting Data
LearnLeanSigma.com - Your Path To Operational Excellence
Going back to our machine example:
Our operators will use a calibrated gage to measure the
material thickness every 10 meters.
These will be our data points for calculating process
capability and measuring variation.
During the data collection it is important that all input
variables are kept consistent to get a baseline for the
process capability.
Machine material inputs should be consistant.
Machine settings should stay the same, etc.

20. The Data
LearnLeanSigma.com - Your Path To Operational Excellence
2.35, 2.76, 2.30, 2.10, 1.90, 2.75, 2.40, 1.85, 2.10, 2.24, 2.74, 2.15,
2.65, 2.56, 2.66, 2.55, 2.33, 2.67, 1.84, 2.80, 2.70, 2.65, 2.89, 2.38,
2.31, 2.41, 2.05, 2.59, 2.47, 2.61, 2.69, 2.19, 2.62, 2.31, 2.08, 2.85,
1.99, 2.54, 2.57, 2.41
Below are the data points we collected
So now we have the data we need to do 6 steps to
understand the Cp and Cpk for this data:
Calculate the Mean (average) of the Data1.
Calculate the Standard Deviation (σ) of the Data2.
Determine the Specification Limits3.
Calculate Cp (Process Capability)4.
Calculate Cpk (Process Capability Index)5.
Interpret the Results6.

21. Calculating the Mean
LearnLeanSigma.com - Your Path To Operational Excellence
2.35, 2.76, 2.30, 2.10, 1.90, 2.75, 2.40, 1.85, 2.10, 2.24, 2.74, 2.15,
2.65, 2.56, 2.66, 2.55, 2.33, 2.67, 1.84, 2.80, 2.70, 2.65, 2.89, 2.38,
2.31, 2.41, 2.05, 2.59, 2.47, 2.61, 2.69, 2.19, 2.62, 2.31, 2.08, 2.85,
1.99, 2.54, 2.57, 2.41
To calculate the mean for the data below, you need to:
Add all the data points together
Divided the total by the number of data points.
Mean =
∑xi​​
n
Eg. 2.35 + 2.76 + 2.30 + 2.10 + 1.90 + 2.75 + 2.40... etc = 97.009999
Number of data points = 40
Mean =
97.01
40
2.425

22. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Calculating the Standard deivation is a multi step process
which we recommend you do in a software such as Excel:
Step 1: Subtract the mean from each data point
Column A = Data points collected
Column B = Mean
Column C = =Sum(A2-B2)
You now have the difference from the mean for each result,
this will be a range of positive and negative numbers.
Now we have the mean of 2.425 we can calculate the standard deivation of the data.
Download Excel sheet
to follow along
*Formula will be different if using your own data set with a different number of data points.

23. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Step 2: Square the result of difference from mean (A-B column)
This is done by multipling the number by its self.
in Column D type “=C2^2” (Power of formula)
Drag formula down row D to cover all data points
Now we have the difference of our data points from the mean
Download updated
Excel example
To recap:
We have the difference of data points from mean1.
We then squared the differences (multipled the number by
its self).
2.
*Formula will be different if using your own data set with a different number of data points.

24. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Step 3: Sum all the squared differences
At the bottom of Column D type =SUM(D2:D41)
The result should be 3.22
Now we have the difference to the mean squared.
Download updated
Excel example
*Formula will be different if using your own data set with a different number of data points.

25. Step 4: We need to calculate the Variance
This is done by dividing “sum of squared differneces” (3.22)
by n-1 “sample size minus 1” (39)
In excel you can type = sum(D42/39)*
Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Now we have the sum of all squared differences
Download updated
Excel example
Variance=
∑(xi​−Mean)
n−1
2
3.22
39
= 0.0825=
*Formula will be different if using your own data set with a different number of data points.

26. σ = 0.0825 ​≈ 0.287
Step 5: We calculate the square root of the variance and this will give us
the standard deivation
In Excel type =SQRT(E44) to get the square root of the variance
Or on calculator do 0.0825 then press the square root button
Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Now we have the variance
Download updated
Excel example
*Formula will be different if using your own data set with a different number of data points.
The standard deviation of our example data is 0.287
Now you understand how to fully manually calculate
standard deivation, you can consider the short cut.
At the bottom of Column A type “=STDEV.S(A2:A41)”

27. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
Now you you understand how to calculate standard deivation.
In our example the standard deivation is 0.287, but what does this mean?
We can now make more sense of the Bell curve from earlier
At the bottom of the curve we have μ which mean the
mean and σ which means standard deivation.
From the mean μ we have μ+σ this is the Mean + 1
Standard deviation
Therefore between -1σ and +1σ from the mean
statistically 68.26% of all data points will fall.

28. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
In our example the mean was 2.425 and the
standard deviation was 0.287 meaning:
+1σ = 2.712
-1σ = 2.138
2.425 2.7122.138
= 68.26% of data points were
between 2.138 and 2.712
On a smaller data set this may be a couple of
percentages out. Our example data set has 65%
of data points that are +/- 1 standard deviation
These results carry on through +/- 2 σ and +/-3σ

29. Calculating Standard Deviation σ
LearnLeanSigma.com - Your Path To Operational Excellence
In the 6 Steps you now know how to calculate the Mean
and standard deviation:
Calculate the Mean (average) of the Data1.
Calculate the Standard Deviation (σ) of the Data2.
Determine the Specification Limits3.
Calculate Cp (Process Capability)4.
Calculate Cpk (Process Capability Index)5.
Interpret the Results6.
Next step is to determin the Specification Limits

30. Determining the Spec Limits
LearnLeanSigma.com - Your Path To Operational Excellence
Upper Specification Limit (USL): The USL is the maximum value a process
output can take while remaining acceptable. Outputs exceeding this limit are
considered defective. It controls the upper boundary of acceptable
performance. For example, in the production of plastic bottles, if the
maximum acceptable bottle weight is 50 grams, the USL is set at 50 grams.
Any bottle weighing more than 50 grams would be rejected as it might indicate
excess material usage or potential structural issues.
Lower Specification Limit (LSL): The LSL is the minimum acceptable value for
a process output. Outputs below this limit are also deemed defective. It
controls the lower boundary of acceptable performance. Using the same
plastic bottle example, if the minimum acceptable weight is 45 grams, the LSL
is set at 45 grams. Any bottle weighing less than 45 grams would be rejected as
it might indicate insufficient material, leading to possible weaknesses or failure
in use.
47g

31. Determining the Spec Limits
LearnLeanSigma.com - Your Path To Operational Excellence
47g44g
How Specification Limits Are Set:
Based on Process Requirements: The USL and LSL are
typically determined by the functional or performance
requirements of the product.
Industry Standards: In many industries, specification limits
are guided by standards set by regulatory bodies or
industry organizations. These standards ensure
consistency and safety across the industry.
Customer Requirements: Sometimes, specification limits are set based on customer
requirements. For custom products or specialized orders, the customer may specify tighter or
looser limits based on their needs.
Historical Data: Past performance data can also help in setting realistic and achievable
specification limits. This data reflects what the process has been capable of producing
consistently.

32. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
Cp is a measure of how well a process can produce output within
the specified limits. It specifically looks at the potential capability
of the process assuming it is perfectly centered between the
upper and lower specification limits.
Continuing with the material thickness example
So now we have the data and have calculated the standard
deivation (σ). We need to following information to calculate
the Cp:
Specification limits (USL) and (LSL)
The standard deviation (σ)

33. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
Our customer has set the specification for the material they need
to be between 2mm and 2.6mm thick.
Based on the data we collected we need to see if our process is
capable of meeting that in its current set up.
As a reminder our standard deivation (σ) is 0.287mm
Cp Calculation therefore is
I need this material to
be between 2mm and
2.6mm thick
Cp =
USL - LSL
6σ
Cp =
2.6 - 2
6 x 0.287

34. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
The output number of Cp and Cpk is a ratio.
In simple terms a score of:
1 = process is just capable
<1 = process is not capable and will likely
product outside of the spec limits, the lower the
number the higher the number of defects.
>1 = process is more than capable and the higher
the number the more capable the process is and
the lower the risk of the process drifting and
producing defects.
LSL USL

35. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
In the Chart there are 3 bell curves, we can see the
higher the Cp the the taller and narrower the bell
curve.
The red bell curve has a Cp of 0.5, showing it is
not capable as much of the bell curve falls outside
of the specification limits
The green bell curve has a Cp of 1, showing it is
just about capable and almost all of the bell curve
is inside ths specification limits. Statistically this
will produce 3.4 defects in 1 million opportunities.
The blue bell curve a Cp of 1.5, showing it is more
than capable and should produce outputs well
within the specification limits.
LSL USL

36. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
Tell me when you have
improved your
processes..
To make the customer happy we would need to reduce out
process variation to meet the required specification limits to
achive a Cp of at least 1.
If we do not we will either send our customer product outside
the specification limits which will be rejects or end up with
internal reject or rework material which would be a cost of
poor quality and impact profitability.
Untill then our customer wont buy from us.

37. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
The new data collection produced the following outputs:
2.40, 2.53, 2.39, 2.32, 2.26, 2.53, 2.42, 2.24, 2.32, 2.37, 2.53, 2.34,
2.50, 2.47, 2.50, 2.47, 2.39, 2.50, 2.24, 2.55, 2.51, 2.50, 2.57, 2.41,
2.39, 2.42, 2.31, 2.48, 2.44, 2.48, 2.51, 2.35, 2.49, 2.39, 2.31, 2.56,
2.29, 2.46, 2.47, 2.42
To improve the process capability meet the customers needs
the production team did some analysis and optimized the
settings using Design of Experiments (DOE).
They managed to reduce the variation and collected more data
to verify this.

38. Calculate Process Capability (Cp)
LearnLeanSigma.com - Your Path To Operational Excellence
Based on this data we need to run the same calculations as
before:
2.40, 2.53, 2.39, 2.32, 2.26, 2.53, 2.42, 2.24, 2.32, 2.37, 2.53, 2.34,
2.50, 2.47, 2.50, 2.47, 2.39, 2.50, 2.24, 2.55, 2.51, 2.50, 2.57, 2.41,
2.39, 2.42, 2.31, 2.48, 2.44, 2.48, 2.51, 2.35, 2.49, 2.39, 2.31, 2.56,
2.29, 2.46, 2.47, 2.42
They find out the standard deviation for this data is 0.09 and run
the Cp Calculation
Cp =
USL - LSL
6σ
Cp =
2.6 - 2 = 0.6
6 x 0.092 = 0.552
= 0.6 divded by 0.552 = 1.086Cp

39. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
The Cp tells us if the process is capable with a Cp of 1 or higher means
the process is capable of meeting the customers specifcation needs,
but does not tell us if the process is producing on target.
For this we need to do one final calculation, Cpk.
Cpk considers how centered the process is within the specification
limits. It is calculated as the minimum of two values:
One considering the mean and the lower specification limit (LSL).
One considering the mean and the upper specification limit (USL).
Im glad you reduced
the variation, but is the
process on target?
Cpk = min
USL - μ
3σ
The Formula is
μ - LSL
3σ
( )
,

40. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
The Cpk helps us to understand if our process is on target
which means is it performing its output within the
specification limits.
It is possible for a process to have a Cp of 1 or higher but
produce defects (outside the spec limit) by being off-
centre.
This can be seen in the example. The process has a Cp of 1.2
but it will produce some outputs outside of the upper spec
limit as the process is not centered between the USL and
LSL.
The Cpk calculations will tell us if the process is producing
outside of either spec limit.
Defects

41. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
There are 4 Steps to using Process Capability
Step 1: Identify the process capability index (Cp) using (USL-LSL)/6 x standard deviation (σ).
Step 2: Identify Cpu* relative to upper specification limit using (USL-Mean)/3 x standard deviation (σ).
Step 3: Identify Cpl** relative to lower specification limits using (Mean-LSL)/3 x standard deviation (σ).
Step 4: Identify the Cpk which is the distance between (Mean) and the closest Cpu or Cpl to the
specification limit.
*Cpu = Process Capability in relation to upper spec limit.
**Cpl = Process Capability in relation to the lower spec limit.

42. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
Step 1: Calculate the process capability (Cp) we already did with the improved
data below:
2.40, 2.53, 2.39, 2.32, 2.26, 2.53, 2.42, 2.24, 2.32, 2.37, 2.53, 2.34, 2.50, 2.47, 2.50,
2.47, 2.39, 2.50, 2.24, 2.55, 2.51, 2.50, 2.57, 2.41, 2.39, 2.42, 2.31, 2.48, 2.44, 2.48,
2.51, 2.35, 2.49, 2.39, 2.31, 2.56, 2.29, 2.46, 2.47, 2.42
A reminder of the calculation and Cp Result:
Cp =
USL - LSL
6σ
Cp =
2.6 - 2 = 0.6
6 x 0.092 = 0.552
= 0.6 divded by 0.552 = 1.086Cp

43. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
Step 2: Identify Cpu relative to the upper specification limit using (USL-Mean) / 3 x standard deviation (σ).
A reminder of our calculations and input information:
USL: 2.6
LSL: 2
Mean: 2.425
Cp: 1.086
σ: 0.092
Cpu =
USL - Mean
3 x σ
2.6 - 2.425
3 x 0.092
=
0.3575
0.276
=
Cpu =1.295

44. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
Step 3: Identify Cpl relative to lower specification limits using (Mean-LSL)/3 x standard deviation (σ).
A reminder of our calculations and input information:
USL: 2.6
LSL: 2
Mean: 2.425
Cp: 1.086
σ: 0.092
Cpl =
Mean - LSL
3 x σ
2.425 - 2
3 x 0.092
=
0.425
0.276
=
Cpl =1.539

45. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
Step 4: Identify the Cpk which is the distance between (Mean) and the closest Cpu or Cpl to the
specification limit.
Cpl =
Mean - LSL
3 x σ
2.425 - 2
3 x 0.092
=
0.425
0.276
=
Cpl =1.539
Cpu =
USL - Mean
3 x σ
2.6 - 2.425
3 x 0.092
=
0.3575
0.276
=
Cpu =1.295
As the Cpu is the lowest number out of Cpu and Cpl, the Cpu becomes
the Cpk value.
Cpk = 1.295

46. Calculate Process Capability (Cpk)
LearnLeanSigma.com - Your Path To Operational Excellence
If you followed these calculations carefully you should now be able to
calculate the Cp and Cpk for any process data using the same calculations.
Success
Next, we will cover how to display these results in a graphical representation

47. 04 Graphical Representation
Histograms and Capability Plots
LearnLeanSigma.com - Your Path To Operational Excellence

48. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
Now that you can calculate Cp and Cpk it is important to understand how to graphically display
these results to help interpret results.
In process capability Histograms are the main method of displaying data.
45 50 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25

49. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
A Histogram is a graphical representation of the
distribution of data points across specified ranges
(bins).
It shows how frequently data points occur within
each range, providing a visual summary of the data's
spread and central tendency.
45 50 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
The example Histogram on the right shows data in bins
of 5 from 45 up to 95.
All of the data falls between these two points.
We can see the volume of data points in each interval:
e.g. there are 5 data points between 50 and 55

50. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
Histograms are powerful tools for understanding the
distribution of process data.
They help identify patterns, such as whether data is
skewed, normally distributed, or has outliers.
45 50 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25

51. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
Histograms are simple and quick to make using
modern versions of Microsoft Excel making them a
simple statistical analysis method.
If you have not done this before, you can download
our dummy data set and follow the steps
45 50 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
Example Histogram
Data

52. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
Step 1: Gather data or use our example data and input it
into Excel.
Step 2: Go to, Insert > Recommended Charts > Histogram
Step 3: Right-click Histogram Axis > Format Axis >
Manually adjust bid width as needed for the use case.
Example Histogram
Data

53. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
45 50 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
We can now interpret our Histogram for process capability by
overlaying the Upper spec limits (USL) and Lower Spec limit
(LSL).
We need the output
between 60 and 90
Out of our sample data, we
can see 6 outputs were
produced below the LSL
and 5 outputs were
produced outside the USL

54. Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
Histograms can also tell us if the data is symmetrical, skewed or
does it have multiple peaks?
30 35 40 45 50 55 60 65 70
0
100
200
300
400
40 50 60 70 80 90 100
0
10
20
30
40
50
60
34 38 424446 50 54 58 62 66
0
50
100
150
200
Symetrical Skewed (Right) Multiple Peaks (Bimodal)
For the full guide to Histograms, review our Histograms Guide

55. 44 45 46 47 48 49 50 51 52 53 54
0
5
10
15
20
25
30 35 40 45 50 55 60 65 70 75 80
0
5
10
15
20
25
30
Graphical Representation
LearnLeanSigma.com - Your Path To Operational Excellence
We can also use Histograms to identify how wide or narrow the distributions are.
We can also identify if the data has any outliers, which are data points that are distant from the rest
of the data and could be a statistical anomaly
Narrow Distribution
Wide Distribution
For the full guide to Histograms, review our Histograms Guide
Outlier

56. 05 Interpreting Results
What Do the Cp and Cpk Values Mean?
LearnLeanSigma.com - Your Path To Operational Excellence

57. 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
Interpreting Results
LearnLeanSigma.com - Your Path To Operational Excellence
Earlier in this lesson we briefly touched on what the Cp
values mean, but it's important to cover this topic in must
more detail.
Cp = 1: Just Capable
The process meets the specification limits exactly.
Risks:
No margin for variability or unexpected shifts.
High risk of defects if the process variability
increases or the mean shifts.
Example: Bell Curve fits just inside the LSL and USL
LSL
USL
Cp 1 Bell Curve

58. 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
Interpreting Results
LearnLeanSigma.com - Your Path To Operational Excellence
Cp > 1: Capable Process
The process is more capable, with lower variability
relative to the specification limits.
Importance of Higher Cp:
Strive for Cp > 1.33 or 1.5 for added robustness and
reliability.
Higher Cp values mean the process can handle
more variation without producing defects.
Example: A Bell Curve Cp > 1.33 would lead to
consistent quality outputs over time with the outputs
well within the specification limits. LSL USL
Cp 1.33 Bell Curve

59. 55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
Interpreting Results
LearnLeanSigma.com - Your Path To Operational Excellence
Cp < 1: Not Capable
The process variability exceeds the specification limits.
The Problem:
Variation is wider than the specification limits
meaning the process is not capable of producing
outputs to what the customer wants
Example: a process with Cp < 1 this process is
producing defects as outputs are outside the
specification limits as shown in the illustation
LSL USL
Cp 0.8 Bell Curve

60. Common Pitfalls
LearnLeanSigma.com - Your Path To Operational Excellence
Misinterpreting Cp and Cpk:
Cp vs. Cpk:
Cp: Measures only the spread of the process relative
to the specification limits.
Cpk: Accounts for both the spread and the centering
of the process mean.
Key Point: A high Cp with a low Cpk indicates that
the process is not well-centered, which can lead to
issues even if the variability is low.
55 60 65 70 75 80 85 90 95
0
5
10
15
20
25
LSL
USL
Example

61. Common Pitfalls
LearnLeanSigma.com - Your Path To Operational Excellence
Ignoring Process Stability:
Assumption: Cp and Cpk calculations assume the process is stable.
Pitfall: Calculating Cp and Cpk without confirming process stability can lead to incorrect
conclusions.
Action: Always verify process stability with control charts before interpreting Cp and Cpk.
Summary:
Understanding and interpreting Cp and Cpk is crucial for assessing process capability.
Adjusting process mean and reducing variability are key strategies for improvement.
Avoid common pitfalls by considering both Cp and Cpk, ensuring process stability, and using
a combination of tools.

62. 06 Improving
Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence

63. Improving Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
The aim of Process capability to
understand how capable your
process is in meeting the
customer's specification and to
identify when it is not.
When it is not meeting the
specifications it is important to
know what kind of process
capability issue you have. In
general, these fall into 4 instances:
On Target & Capable Off Target but Capable
On Target not Capable
Off Target not Capable
A
B
D
C

64. Improving Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
If your process capability curve looks similar to A
where the process is on target and capable, in
general, the process is performing well and is not
likely to produce any defects unless something
changes.
On Target & Capable
A

65. Improving Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
If your process capability curve looks similar to B
where the process is off target but capable, this
shows the process that the variation is controlled
enough to not produce defects, but the process is off
target.
Action: look at machine inputs and calibrations to
make adjustments to bring the process to the centre
of the specification limits.
This could be done with Design of Experiments (DOE)
or One Factor as a Time (OFAT) experiments to make
adjustments and record the changes to outputs.
Off Target but Capable
B

66. Improving Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
If your process capability curve looks similar to C
where the process is on target but not capable, this
shows the process that the process is centered in the
specification limits but the process has too much
variation
Action: Look to improve control of the process inputs
which could be contributing to excess output
variation, such more consistent input raw materials,
conditions or settings.
On Target not Capable
C

67. Improving Process Capability
LearnLeanSigma.com - Your Path To Operational Excellence
If your process capability curve looks similar to D
where the process is off target and also not capable,
this shows the process that the process needs to
recentered in the specification limits and aim to
reduce variation
Action: Action for this would be a combination of
suggested actions of B and C.
We suggest first aim to reduce the variation to ensure
the process can be made capable of meeting
specification limits then take action to re-centre the
process.
Off Target not Capable
D

68. 07 Resources
Supporting Material
LearnLeanSigma.com - Your Path To Operational Excellence

69. Resources
LearnLeanSigma.com - Your Path To Operational Excellence
Process Capability Analyzer
Our tool is designed to streamline and simplify
the Process Capability Analysis process. It
leverages computational algorithms and an
intuitive user interface to deliver instant,
accurate results. In fact, our tool can provide
comprehensive process capability metrics
faster than you can type “How to Create a
Process Capability Chart in Excel” into Google
Try it now

70. Resources
LearnLeanSigma.com - Your Path To Operational Excellence
Process Capability Calculator
The Process Capability CP and CPK Index
Calculator is a useful tool for assessing the
performance and stability of business processes.
Our calculator generates accurate Capability
Indices (Cp and Cpk) by analyzing data on
process variations and target specifications. You
can optimize production, improve quality, and
reduce defects with actionable insights. Using
our easy-to-use Process Capability Index
Calculator, you can simplify your decision-
making process and achieve significant efficiency
gains.
Try it now