Capability indexes, like defects counts, appeal to 'carrot and stick' managers. They are never a substitute for a Process Behavior Chart and Histogram.
When a process is not in control, capability indexes are meaningless. A capability index used alone, gives no indication as to the nature of the process that generated it. Used alone it is useless. Process capability indexes may complement a Process Behavior Chart and Histogram but should never be presented without them.
The idea of a capability index is to indicate whether a process is capable of producing good product. However, this can only be done with a Process Behavior Chart. The aim should be to have worker teams who understand Quality, working with Process Behavior Charts and Histograms to reduce variation.
Many authors such as Mr Pyzdek, Mr Breyfogle incorrectly claim that process capability indexes can only be used "when the data follows a normal distribution". This is utter nonsense. These authors also claim that Process Behavior Charts require data to be normally distributed. This is also nonsense.
Authors promoting the Six Sigma Scam do not understand Dr Shewhart and the control charts he devised. They do not understand the basics of Quality. Dr Shewhart created a massive departure from traditional statistics, where the nature of the underlying distribution needed to be known. Shewhart charts work for ANY process data distribution. You should never waste time checking for normality.
Similarly, you should NEVER draw normal distributions over histograms for a process. Not only are they irrelevant nonsense, but they hide the information contained in the histogram. One should develop skill in interpreting raw histogram shapes.
Professor Deming's protégé, Dr Wheeler, not only understood Dr Shewhart, but at great length, validated Dr Shewhart's assumptions, by testing 1143 different distributions. He proved conclusively that Process Behavior Charts and hence Process Capability indexes, do NOT depend on normality.
Dr Wheeler also showed that the most simple Process Behavior Charts based on ranges, are best. XmR should be used unless there are multiple data points for each point in time.
Process Capability indexes are statistics. That is, they vary over time. If a process is stable, process capability values will converge. If the process is not stable, the value will not converge. The problem is that a capability index alone gives no indication as to stability and whether or not it is meaningful.
Anyone using Capability indexes should read Dr Wheeler's detailed papers on Capability and Performance Ratios here:
https://lnkd.in/gnY27VHT
https://lnkd.in/g2q9TYtQ
https://lnkd.in/gBt5-gSs
by Dr Tony Burns BE (Hon 1) PhD (Chem Eng)