The Effect of Pooled and Un-Pooled Variance Estimators on C_pm When Using Subsamples

Abstract

The vast majority of research on capability indices has assumed that the data consists of one large, representative sample. In practice, and in much of the quality control literature, process data are collected over time in subsamples representing rational subgroups. In this paper we examine the statistical behavior of two Cpm estimators based on this more realistic data structure. The estimators correspond to pooled and un-pooled variance estimators. The theoretical findings are applied to hypothesis testing and power calculations. The power functions of the tests based on the two estimators are used to determine the minimum number of subsamples needed to meet a threshold requirement that power exceeds 0.80. Extensive tables of the recommended number of subsamples are provided with comments on their usage.

• Capability Indices
• Hypothesis Testing
• Power
• Sample Size

Additional information

Notes on contributors

Norma Faris Hubele

Dr. Hubele is a Professor in the Department of Industrial Engineering. Her email address is [email protected].

Kerstin Vännman

Dr. Vannman is a Professor in the Department of Mathematics. Her email address is [email protected].