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.

Products & Services
Opacity Sensors and Instruments
Opacity sensors and instruments measure the amount of light transmitted through a sample.
Sanitary Fittings
Sanitary fittings are designed and constructed for use in food, beverage, medical, pharmaceutical and biological applications where cleanliness and sterility are required.
Pneumatic Fittings
Pneumatic fittings are parts used to connect sections of pipe, tube, and hose in pneumatic (pressurized gas) lines and systems.
Tube Fittings
Tube fittings connect runs of tubing for in-line, offset, multi-port, and mounting configurations to other tubing sections, pipe, hose, and other fluid transfer components.
Statistical Process Control Software (SPC)
Statistical process control software (SPC) is used to measure, control, monitor or manage industrial processes without human intervention. SPC software uses statistical functions and techniques to provide continuous monitoring.

Topics of Interest

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