How to measure Process capabilitiy (Cp/CpK) for non-normal distribution?

How is process capability (Cp, Cpk) estimated for non-normal data?

First, we should discuss some general requirements for Process Capability Indices (Cp, Cpk)

1. You need to know the underlying shape of the process distribution to calculate a meaningful Process Capability index. The standard calculations apply only to a process whose observations are normally distributed. To properly calculate a capability index for non-normal data, you either need to transform the data to normal, or use special case calculations for non-normal processes.

2. You should never do a transformation, or calculate Process Capability, until you have determined the process is in the state of statistical control. If the process is not in control, then it is not stable, and cannot be predicted using capability indices. Likewise, an out of control situation is evidence that multiple distributions are in place, so a single transformation for all the process data would be meaningless.

So how do you handle this data?

1. First investigate the process stability using a control chart. We could use an X-Bar chart with a subgroup size of5. Why five? The Central Limit Theorem tells us the average of five observations from even pretty non-normal processes will tend to be normally distributed. You can do a Normality test on these averages to verify. You might also go with a subgroup size3 if that works, which it often does. A better approach is to use a Moving Average chart (cell width of3 or5, for same reasons as above) or an EWMA chart with your original subgroup size of one (a lambda of0.4 works well). This chart should handle even non-normal data well.

2. If the process is out of control, stop there and improve the process. Do not bother with a capability analysis or with transformation, as they will be meaningless.

3. If the process is in control, then you can estimate capability. You could either transform the data to Normal and use the standard calculations for capability applied to the normalized data, or fit a distribution to the data and calculate the capability using the percentiles of the distribution. The Johnson technique applies this latter approach.

Process Capability enables you evaluate non-normal process capability using: 

1. Box-Cox power Transformation 
2. Johnson Transformation system 
3. Clements Method using Pearson Curves

these transformation can be easly done in MINTAB

OR 

find the which distribution the data is following

and then transfer the data to normal distribustion 

Actually you can't use Cp and Cpk on non-normal distribution. the forrmula is based on the assumption that the distribution is normal.

thats why when we explain process capapility we say do normal quantile plot, "Probability Plotting" or at least a simple Histogram first to understand the distribution u have

to answer your question:

Option1: transform the data, so that the new  metric has a normal distribution. there is many mathods to do the trick based on what distribution you have. For example: reciprocal transformation..

I do recommend this option

Option2: use the Luceno index Cpc = (USL-LSL)/6(Sqrt((pi/2)*E*abs(X-T)))

wehere T= Process Target value =0.5(USL+LSL)

but people are not familoiare with this, so you'll have trouble reporting it and training others on this concept

so, the first option is much easier. a little practice on excel sheet, and you can transform data into normal and use the good mighty Cp and Cpk

Hope that was helpful.

any how, if  u want  help in transfring data, just email  me one of the data and i'll see what i can do

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