1. Process Capability
1, Jatco Requirements
2, Cmk, Cpk, Ppk Explanation
3, Control Charts and Capability Ratio`s
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2. SPC Jatco Requirements
When calculating process capability Jatco requires a 90% confidence level.
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3. Process Capability Capability Studies
A process capability study is performed for a new or changed production process (including assembly) in order to verify the (preliminary) process capability or performance and to obtain additional inputs for controlling the process.
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4. Process Capability Machine Capability Study
The machine capability study is a short-term study with the sole aim of discovering the　machine-specific effects on the production process. 
Process Capability Study
The process capability study is a longer-term study. In addition to variation arising from the　machine, all other external factors that influence the production process over a longer operating　time must be taken into account.
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5. Process Capability Stable Process
A stable (in statistical control) process is only subject to random influences. In particular, the　location and variation of the product characteristic are stable over time.
Quality-Capable Process
A process is quality-capable when it can meet all the specified requirements without exception.
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6. Process Capability
Capability Indices Cmk, Cpk and Performance Index Ppk
The term Cpk must only be used for a stable process. A process is stable if the following synonymous statements apply to it: 
• Mean and variance are constant.
• No systematic variations of the mean such as trend, batch-to-batch variation, etc., occur.
• There is no significant difference between sample variation and total variation.
• Every sample represents the location and variation of the total process.
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7. Process Capability
If the process is not stable, one speaks of “process performance”, and the index is called the process performance index, Ppk .
This applies to all processes with systematic variation of the mean such as trend or batch-to-batch variation.
It is, therefore, the process behaviour which determines whether the index is named Cpk or Ppk .
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8. Process Capability
 In a machine capability study (“initial process study” or “short term study” ), the index is always called Cmk ,
Cmk is understood to be an index for a short-term capability study.
Only when sufficient data has been collected over a longer term (e.g., as the result of a process capability study, pre-production run with at least 125 values or evaluation of several control charts) it is possible to calculate and distinguish between Cpk and Ppk on the basis of the process behaviour.
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9. Process Capability Flow Chart for Machine and Process Capability Study
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10. Process Capability Flow Chart for Machine Capability
Manual Calculation Procedure
If no special software is available, m C and Cmk also can be calculated as follows. The
mean x and the overall standard deviation s total are calculated from the n measured values x i :
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11. Process Capability Machine Capability Study with Reduced Expense
As specified at least fifty ( n = 50 ) parts should be manufactured for a machine capability study, but use of one hundred ( n =100 ) parts is preferred. In practice, capability studies often incur high costs due to expensive measurements. In such cases, the following, two-stage procedure may be used to minimize cost:
1. Of the 50 parts produced consecutively, begin the study by measuring only every second part, i.e., parts 2, 4, 6, ..., 50. This step yields 25 measured values per characteristic. The machine is considered capable if the capability index calculated from the 25 values is Cmk ≥ 2.0 .
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12. Process Capability Machine Capability Study with Reduced Expense
2. If 1.67 < Cmk < 2.0 , the remaining 25 parts must also be measured. These results are combined with the original 25 measurements and the capability index is re-calculated. The machine is considered capable if a capability index Cmk ≥1.67 is achieved using all 50 values.
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13. Process Capability Machine Capability Study with Reduced Expense
In special cases, it may be unavoidable to reduce the sample size even further (regardless of the capability requirement). This may be the case if the measurement procedure is very expensive or the test is destructive.
Naturally, the smaller the sample size, the less accurate the conclusions (larger confidence interval of the characteristic calculated from the sample). The Jatco SQA engineer must be consulted before the sample size is reduced.
In such cases, the machine or process parameters should be given priority instead of the product parameters.
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14. Process Capability Process Capability Study
The process capability study is a long-term study that is conducted over an extended operating time and includes sources of variation external to a machine.
These sources are typically summarized under the headings of Man, Machine, Material, Method and Environment.
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15. Process Capability Process Capability Study
A process capability study includes the following steps:
• Select parts from series production in “rational” samples (not sorted); at least 25 subgroups　should be evaluated. The preferred sample size is n = 5. Overall, at least 125 parts should be　examined.
• Measure part characteristics and record the results along with production sequence.
• Statistical evaluation of the data: Evaluate temporal stability and statistical distribution.
Calculate capability indices.
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16. Process Capability Process Capability Study
Note: In special cases, use of fewer than 125 parts may be unavoidable due to time or cost of　making the necessary measurements, or if the test is destructive.
Smaller sample sizes lead to　larger confidence intervals of the characteristic(s) being studied. In turn, this reduces the accuracy of the conclusions that may be drawn from the data.
The Jatco SQA Engineer must　be consulted before the sample size is reduced.
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17. Process Capability Process Capability Study
The random samples shall be taken from on-going production under standard production conditions (i.e. with machine broken in and cycle time and machine adjusting parameter values as in standard production) at regular intervals in the same size each time.
In this case, in contrast to the MCS, all effects that result from changes in machine parameter values, tooling changes and machine malfunctions shall be taken into consideration.
However, the measurements that are necessary for machine setup or for a corrective measure are not taken into consideration in the PCS
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18. Process Capability Process Capability Study
When taking random samples, the measurement of the parts should be carried out as promptly as possible. However, if an accumulation of several random samples before the measurement recording cannot be prevented, an assignment of the parts to the random samples in their time sequence is to be made possible.
In contrast, the sampling sequence of the individual parts of a random sample does not have to be considered.
The form of sampling sometimes carried out in practice, in which each nth part, e.g. each 10th part, is taken from the on-going standard production, is not suitable for the process capability investigation.
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19. Process Capability Process Capability Study
The random sample size n must be at least 3 (recommended size n = 5)
The random sample quantity m must be at least 6
The total random sample size should generally be m × n >125. 
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20. Process Capability Process Capability Study
If this random sample size is difficult to obtain for economic or technical reasons, a smaller one is also permissible. Then the corresponding higher limit values calculated using a 90% confidence level using the equation below must be complied with.
However, the effective total random sample size (without outliers) must be at least 30.
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21. Process Capability Process Capability Study
The random sample frequency must be high enough so that at least once, a sampling of the specified size n is carried out within a time interval in which no systematic influences on the process are expected, i.e. at least one random sample per
– shift and employee
– change of the machine parameter values
– tool life and
– material batch
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22. Process Capability Process Capability Study
The testing period, over which the sampling of the m random samples extends, must contain at least the following influences (recommended period 1 to 2 weeks):
– 3 changes of shift
– 3 changes of employees
– a change of the tooling or change of the machine parameter values and
– a change of the material batch
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23. Process Capability Process Capability Study
Studying the Process Stability
 For the stability test, “control limits” based on the normal distribution are calculated for the means and the standard deviations
If the control limits for the means are exceeded, this shows that the process is not stable and that its position has changed systematically.
i.e. Make a control chart with the data and confirm stability.
If the process can be shown as stable then use Cp/Cpk if the process cannot be shown to be stable then use Pp/Ppk .
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24. Process Capability Process Capability Study
Studying the Statistical Distribution
A qualitative evaluation can be made and a distribution assigned using graphic representations such as an individual value plot, a histogram, probability plots etc. Calculating the shape parameters (skewness, kurtosis) or performing distribution tests can act as quantitative methods.
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25. Process Capability Process Capability Study
Calculating Process Capability Indices
If no special software is available, capability and performance values can also be calculated as follows.
Normal distribution:
Estimating the process average.
Total Mean ( Mean of the sample means)
Mean of a sample with size n (e.g. n=5)
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26. Process Capability Process Capability Study
Estimating the standard deviation of the process.
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27. Process Capability Process Capability Study
If the Process Cannot be Shown to be Stable:
From the n measured values x i , the total mean x and the overall standard deviation s total are calculated:
and with T = USL - LSL finally
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28. Process Capability Process Capability Study
6.1 Relation Between Capability Index and Fraction Nonconforming
Most of the literature on process capability shows that there is a direct relation between a calculated Cpk value and a fraction nonconforming,
e.g.: Cpk =1.33 corresponds to 32 ppm　(one-sided).
This relation is based on the normal distribution model. If the real characteristic distribution deviates from the normal distribution, different fractions nonconforming normally arise.
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29. Process Capability Process Capability Study
6.1 Relation Between Capability Index and Fraction Nonconforming
Most of the literature on process capability shows that there is a direct relation between a calculated Cpk value and a fraction nonconforming,
e.g.: Cpk =1.33 corresponds to 32 ppm　(one-sided).
This relation is based on the normal distribution model. If the real characteristic distribution deviates from the normal distribution, different fractions nonconforming normally arise.
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30. Process Capability Process Capability Study
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31. Process Capability Process Capability Study
Effect of the Measurement System
The measuring device and measuring procedure used to measure the parts in the random sample　are very important for evaluating the process later on.
If the measuring device is not accurate　enough or if the measuring procedure is unsuitable, the tolerance for the production process is　reduced unnecessarily.
A large %GRR value will impair the machine and process capability indices.
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32. Process Capability Process Capability Study
Capability ratios are statistics. All statistics will vary from sample to sample, even when the underlying process doesn't change.
We will use the data in Table below to illustrate the manner in which capability ratios vary over time.
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33. Process Capability
For the data of Table 1, the grand average is , and the average range is Thus, the limits for an average and range chart for these data would be:
For subgroup averages: X= ± A2 R-  =    ±  (0.577)(4.11) = 7.71 to 12.46
For subgroup ranges:
D4 R-  =  (2.114)(4.11)  =  8.69
As may be seen in graph below the data displays a reasonable degree of statistical control. There are no indications of anything other than routine, common-cause variation.
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34. Process Capability The Specifications are 3 to 17.
With these specification limits and the summary statistics from the control chart, the capability ratio for this bead board process would be:
Cp  =  (USL-LSL)/6Sigma(X)  =  (17-3)/(6.0)(1.767)  =  1.32
With a grand average of , the centered capability ratio is:
Cpk   =  (USL-X=)/3Sigma(X)  =  ( )/(3.0)(1.767)  =  1.30
Today, many customers ask for Cpk of 1.33 or greater. While this process is close, it does not quite meet this magic value.
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35. Process Capability
The calculations were are based on 500 data, and we seldom wait until we have so much data to compute the capability ratios. In most cases, capabilities are computed occasionally, or periodically, using 50 or fewer values. So we shall divide our 100 subgroups into blocks of 10 subgroups each and compute the Cpk value for each block.
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36. Process Capability Subgroups 1 to 10: Grand average = 10.08,
average range = 4.0, and Sigma(X) = 4.0/2.326  =  1.720
The centered capability ratio is:  
Cpk =  ( )/(3.0)(1.720)  =  1.34
A good capability ratio -- our customer will be pleased with this.
Subgroups 11 to 20: Grand average = 9.98, average range = 3.9, and Sigma(X) = 3.9/2.326  =  1.677
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.677)  =  1.39
Congratulations, the capability ratio got better.
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37. Process Capability Subgroups 21 to 30: Grand average = 10.12,
average range = 4.5, and Sigma(X) = 4.5/2.326  =  1.935
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.935)  =  1.19
What happened to cause the capability ratio to drop?
Subgroups 31 to 40: Grand average = 10.24,
average range = 4.2, and Sigma(X) = 4.2/2.326  =  1.806
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.806)  =  1.25
This capability ratio is still not good enough -- we must do better.
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38. Process Capability Subgroups 41 to 50: Grand average = 10.10,
average range = 4.9, and Sigma(X) = 4.9/2.326  =  2.107
The centered capability ratio is:   
Cpk =  ( )/(3.0)(2.107)  =  1.09
This is worse than before.
Subgroups 51 to 60: Grand average = 10.42,
average range = 3.9, and Sigma(X) = 3.9/2.326  =  1.677
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.677)  =  1.31
Well, this is better, but our customer is asking for 1.33 or greater.
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39. Process Capability Subgroups 61 to 70: Grand average = 10.30,
average range = 4.7, and Sigma(X) = 4.7/2.326  =  2.021
The centered capability ratio is:   
Cpk =  ( )/(3.0)(2.021)  =  1.11
You were supposed to be improving -- what is going on here?
Subgroups 71 to 80: Grand average = 10.06,
average range = 3.8, and Sigma(X) = 3.8/2.326  =  1.634
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.634)  =  1.42
At last – we`ll send this data to our customer.
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40. Process Capability Subgroups 81 to 90: Grand average = 9.88,
average range = 3.5, and Sigma(X) = 3.5/2.326  =  1.505
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.505)  =  1.52
Excellent capability ratio. Good work.
Subgroups 91 to 100: Grand average = 9.66,
average range = 3.7, and Sigma(X) = 3.7/2.326  =  1.591
The centered capability ratio is:   
Cpk =  ( )/(3.0)(1.591)  =  1.40
Why is this value slipping?
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41. Process Capability
    Of course, the real answer is that we are not slipping. The process was not getting worse, nor was it getting better. But our statistics were changing from block to block even though the process remained the same, and these changes were reflected in the centered capability ratio values computed. If we placed these 10 centered capability ratios on an XmR chart.
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42. Process Capability
   Figure 2 shows that the routine amount of variation in capability ratios, based upon 50 values each, will allow them to go as low as 0.88 or as high as 1.72, while the process is unchanging with an average capability ratio of 1.30.
So how can you make sense of the capability ratios? Put them on a control chart. If this chart is out of control, you can be sure that your process is also out of control. However, the converse is not true -- your process can be out of control and still yield a control chart for capability ratios that is in control.
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43. Data Driven Decision Making
Why SPC
Data Driven Decision Making
However it is not always practical to have the amount of data that will allow us to have this in depth analysis of the process capability before SOP
Therefore this analysis needs to be done after we have enough data over a reasonable time period.
The Jatco Safe Launch Plan allows us to make this analysis.
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