From Response Modeling Methodology: Empirical Modeling for Engineering and Science

10.1. Introduction

A fitting procedure assigns values to the parameters of a fitted distribution so that it delivers the best possible representation for the approximated distribution. For example, in statistical process control, the p control chart (most often used to monitor the percentage nonconformance of a process) is the result of fitting a normal distribution to the binomial distribution. The former is the fitted distribution, which is the platform on which all of Shewhart control charts are based. The latter (the binomial) is the true distribution of the monitoring statistic, that is, the percentage observed in a sample of items.

The use of the normal distribution in all of Shewhart control charts provides a uniformity of practice that enables practitioners to use the same routine for constructing control charts even though they use monitoring statistics with differently shaped distributions, like the Poisson, the binomial or some continuous distributions that are not extremely asymmetrical (skewed).

In other scenarios, one may wish to use distribution fitting because the true underlying distribution is unknown and there is a need to use one that would represent well the unknown distribution. It is common practice in such cases to approximate the latter by fitting a parameter-rich distribution, which is flexible enough to represent a wide spectrum of diversely-shaped distributions. This is the case, for example, with Clements' method (1989) for process capability analysis, which attempts to represent the true (often unknown) process distribution by a member of the Pearson family of distributions.

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Topics of Interest

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