- Published 2011

The use of capability indices such as Cp, Cpk, and “Sigma” values is widespread in industry. It is important to emphasize that there are certain crucial assumptions, which allow the use of such values to have a meaningful interpretation, which are frequently overlooked. It is the aim of the author to address such issues by the use of discussion and case studies, and to provide some useful guidelines and insights when performing capability analysis using Minitab®. Procedures when dealing with non-Normal data will be considered in the following edition of EXTRAOrdinary Sense. Assumptions There are two critical assumptions to consider when performing process capability analyses with continuous data, namely: 1. The process is in statistical control. 2. The distribution of the process considered is Normal. If these assumptions are not met, the resulting statistics may be highly unreliable. One finds in practice that, typically, one or both of these assumptions are disregarded. 1. Control Status If the process is not in statistical control we are unable to reliably use our estimates for spread and location, hence our formulae are redundant. In order to assess whether or not a process is in statistical control, quality practitioners use control charts. The most frequently used form of control charts in operation today are those which have their derivation from the pioneering work of Dr. Walter Shewhart in the early 1920’s. In their basic form, these charts (e.g. Xbar–R, Xbar-S) are sensitive to detecting relatively large shifts in the process, i.e. of the order of 1.5 standard deviations or above. Two types of charts are primarily used to detect smaller shifts, namely Cumulative Sum (CUSUM) charts and Exponentially Weighted Moving Average (EWMA) charts. For more information on these charts, the interested reader is referred to Montgomery1 and an example by Bower2. 1 Montgomery, D.C. (1996). Introduction to Statistical Quality Control, 3rd Edition. John Wiley & Sons. 2 Bower, K.M. (October, 2000). “Using Exponentially Weighted Moving Average (EWMA) Charts”, Asia-Pacific Engineer. Process Capability Analysis Using MINITAB (I) By Keith M. Bower, M.S. 2. The Normal Distribution One should note that there are an infinite number of distributions which may show the familiar bell-shaped curve, but are not Normally distributed. This is particularly important to remember when performing capability analyses. We therefore need to determine whether the underlying distribution can indeed be modeled well by a Normal distribution. If the Normal distribution assumption is not appropriate, yet capability indices are recorded, one may seriously misrepresent the true capability of a process. Example Consider the following simulation. Suppose the LSL = 37, the USL = 43, and our target for this process is midway between the specs, i.e. at 40. Firstly, considering the X-R charts in Figure 1, we see that the distribution is stable over the period of study (this may also be reported via Minitab’s Capability SixpackTM).

@inproceedings{Bower2011ProcessCA,
title={Process Capability Analysis Using MINITAB ( I )},
author={Keith M . Bower},
year={2011}
}