Chapter 14: Distribution Shape and Stability


In Chapter 12, we addressed the issue of capability in general terms, and we showed some calculations for deriving the appropriate capability index. However, because the issue of capability is very important in any improvement endeavor, in this chapter the issues of shape and stability are discussed in a more detailed manner.

OVERVIEW

A process must be stable and in control before process capability may be determined. Stability is needed for a confident description of the distribution location (mean), spread (range or standard deviation), and shape (normal or other probability function). Each of these descriptions is used as part of the procedure for calculating the capability level of a process. If a manufacturing operation is out of control, one or more of the distribution descriptions (mean, standard deviation, or shape) are changing and unpredictable. Changes in these descriptions change the conclusions concerning the level of capability.

A non-normal data set may be changing and out of control. The shape of the data set may be the result of combining several different distributions (a process stream effect or changes over time). When this is done, the total data set does not describe any of the smaller distributions. The data illustrated in Figure 14.1 show the curves that result when data are not stable. The data included in the figure were collected as part of a process potential study. Thirty pieces were produced and measured in sequence. The first 15 parts are to the left of the center vertical line and are summarized with the histogram at the left axis. These data are stable and follow the normal distribution. Only one mean (Xbar), one range ( r ) and standard deviation ( s ), and one curve are needed to describe these data. As long as the process is stable, additional data do not make major changes to the location, spread, or shape of the summarizing histogram. The sample of 15 measurements estimates a single population that may be studied, analyzed , and interpreted for capability.

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Figure 14.1: Data from a process that is not stable.

A downward trend begins after the bold vertical line. This instability has a dramatic influence on the shape, spread, and location of the operation. The 30 measurements are summarized by the histogram at the right vertical axis. This distribution does not follow the normal curve and does not adequately describe the production operation. The mean, spread, and distribution shape are changing as more data are collected. The degree of asymmetry will change as most data are collected. The skewed distribution describes only the observed data. This is very different from what happens when the data are stable. An out-of-control operation cannot be described with a single distribution. The changing nature of the operation makes the data set unpredictable and impossible to describe with sample data. For this reason, a capability study can be performed only with data that are stable and in control.




Six Sigma and Beyond. Statistical Process Control (Vol. 4)
Six Sigma and Beyond: Statistical Process Control, Volume IV
ISBN: 1574443135
EAN: 2147483647
Year: 2003
Pages: 181
Authors: D.H. Stamatis

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