control chart contoh materi untuk mengontrol

control chart contoh materi untuk mengontrol

1. Tools of Quality
Start-Tech Academy
Control chart
•A control chart is a time-ordered plot of sample st atistics.
•Each point is a sample statistics
Lower control
Limit
Upper control
Limit

2. Tools of Quality
Start-Tech Academy
Control chart
•A control chart is a time-ordered plot of sample st atistics.
•It is used to distinguish between random variabilit y and nonrandom variability.
•It has upper and lower limits, called control limits , that define the range of
acceptable (i.e., random) variation for the sample s tatistic.
Lower control Limit
Upper control Limit

3. Tools of Quality
Start-Tech Academy
Mean
Mean is the average of a data set. It is denoted by µ (mu) or To
S.no Observation 1 12
2 11
3 10
4 9
5 8
To l
s f ss f sQ f u f a
5
To l
50
5
To l sQ

4. Tools of Quality
Start-Tech Academy
Standard
Deviation
Standard deviation is a measure of dispersement in s tatistics. “Dispersement” tells you
how much your data is spread out. It is denoted by (sigma)
S.no Observation 1 12
2 11
3 10
4 9
5 8
ys S sQc
I
fyss S sQc
I
fysQ S sQc
I
fyu S sQc
I
fya S sQc
I
5
l
nerePeren
p
&&&&&&&&l&
&&l sm1s
S.no Observation 1 14
2 12
3 10
4 8
5 6
ys1 S sQc
I
fys S sQc
I
fysQ S sQc
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fya S sQc
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fy0 S sQc
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a&&l ma

5. Statistical Inference
Population &
Sample
Population
10,000 hammers
Sample
50 Hammers

6. Statistical Inference
Population &
Sample
Population parameter
–
Numerical measure of interest related to the popula tion
Population Proportion
-
Number of elements in the category of interest/ Tot al
number of elements
Population mean h
Standard deviation
Population proportion
p

7. Statistical Inference
Population &
Sample
Population
10,000 Houses
Sample
50 Houses
Sample Mean To
Sample Standard
deviation s
Sample Proportion 5o
Sample
Statistics

8. Statistical Inference
Population &
Sample
Sample
50 Houses
Sample Mean To l
∑–
N
d
l&
I-b,nbIg,
pP
l ii aim/
Sample Standard deviation s
l
∑yT
$SToc
I
%1
l 0Q0um&
Sample Proportion 5o l&
–
d
l
'P
pP
l Qm0
h

p
*Why (n-1) for sample standard deviation - https://en.wikipedia.org/wiki/Bessel%27s_correctio n

9. Tools of Quality
Start-Tech Academy
Control chart
•A control chart is a time-ordered plot of sample st atistics.
•It is used to distinguish between random variabilit y and nonrandom variability.
•It has upper and lower limits, called control limits , that define the range of
acceptable (i.e., random) variation for the sample s tatistic.
Lower control Limit
Upper control Limit

10. Tools of Quality
Start-Tech Academy
Mean Control
chart
•Control chart used to monitor the central tendency of a process.
Upper control limit (UCL): =
Lower control limit (LCL): =
Standard deviation of distribution of sample means
Estimate of the process standard deviation
Sample size
The number of standard deviations that control limits are base d on
Average of sample means
Observation
1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Sample

11. Tools of Quality
Start-Tech Academy
Mean Control
chart
•Control chart used to monitor the central tendency of a process.
Upper control limit (UCL): =
Lower control limit (LCL): =
= A factor from table
= Average of sample ranges
Reference:
https://web.mit.edu/2.810/www/files/readings/Contro lChartConstantsAndFormulae.pdf
Observation
1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample

12. Tools of Quality
Start-Tech Academy
Range Control
chart
•Control chart used to monitor the dispersion of a p rocess.
Observation
1 2 3 4 5
1 12.11 12.16 12.07 12.17 12.03
2 12.1 12.13 12.06 12.13 12.2
3 12.11 12.09 12.14 12.03 12.13
4 12.08 12.1 12.17 12.07 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.07 0.11 0.14 0.17
Sample
Observation
1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample

13. Tools of Quality
Start-Tech Academy
Range Control
chart
•Control chart used to monitor the dispersion of a p rocess.
Observation
1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample
Mean of sample ranges

14. Tools of Quality
Start-Tech Academy
Control Charts
for Attributes
Used when the process characteristic is counted rat her than measured.
1. p-chartis used when the data consist of two categories of items.
a. Good or bad
b. Pass or fail
2. c-chartis used, when the goal is to control the number of o ccurrences (e.g.,
defects) per unit, For Example
a. Scratches, chips, dents, or errors per item
b. Cracks or faults per unit of distance (e.g., meter s, miles)
c. Breaks or tears, per unit of area (e.g., square yar d, square meter)
d. Bacteria or pollutants per unit of volume (e.g., g allon, cubic foot, cubic yard)
e. Calls, complaints, failures, equipment breakdowns, or crimes per unit of time

15. Tools of Quality
Start-Tech Academy
p Chart
A p-chartis used to monitor the proportion of defective item s generated by a process.
•The centerline on a p-chart is the average fraction defective in the population, p.
•The standard deviation of the sampling distribution when p is known is
•Control limits
•If p is unknown, which is generally the case,
it can be estimated from samples as ()

16. Tools of Quality
Start-Tech Academy
c Chart
Control chart for attributes, used to monitor the nu mber of defects per unit.
•The mean number of defects per unit is c.
•the standard deviation is
*
•Control limits
•If the value of c is unknown, as is generally the ca se, the sample estimate, *̅, is used
in place of c, using
•*̅= Number of defects ÷ Number of samples.