Effect of Testing Normality on Estimating Process Capability Indices

Abstract

Process capability indices are used to measure whether a manufacturing process meets the specifications. The studies of these indices are usually based on the assumption that the process follows a normal distribution. These include the indices C _p , C _pk , C _pm , and C _pmk . When the investigator is uncertain whether the process follows a normal distribution, a test of normality may be used to resolve the uncertainty. If the test accepts the null hypothesis that the process follows a normal distribution, the investigator uses C _p , C _pk , C _pm , or C _pmk . If the test rejects the null hypothesis, the investigator uses indices under non-normal distributions. Therefore the test of normality is a preliminary test that determines the form of the distribution and the index to use. In this paper we study the effect of the preliminary test of normality on the estimation of the four process capability indices mentioned above.

Keywords:

• Non-normal distribution
• Preliminary test estimator
• Process capability index
• Relative efficiency

Notes

Note: The standard deviation is given in the parenthesis.