Adaptive Estimators of Process Capability Indices Using Preliminary Test

• Activity Number: 600
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 AM
• Sponsor: Quality and Productivity Section
• Author(s): Chien-Pai Han*+ and Choudur K. Lakshminarayan
• Companies: Univ of Texas Department of Mathematics and HP Labs
• Keywords: Process capability ; preliminary test estimator ; weight function estimator ; mean square error

Abstract

A process capability index is a statistical measure of a process to produce output within pre specified limits known as specification limits. Process capability indices measure natural variations in processes relative to specification limits determined a priori. They allow detection of shifts in the processes. Common process capability indices are C_p and C_pk . If LSL and USL are the lower specification limit and upper specification limits of a process, the midpoint of the specification interval is given by m=(USL+LSL)/2. It is well known that when the process mean equals m, C_pk reduces to C_p. However the process mean is usually unknown. This makes it difficult to determine whether to use C_p or C_pk without any guideline in practice. In this paper, we introduce new estimators of process capability based on a preliminary test of statistical hypothesis. The estimators are known as the preliminary test estimator (PTE) and the weighting function estimator (WFE). Based on mathematical derivations and Monte Carlo experiments, we demonstrate that the PTE and WFE outperform the C_p and C_pk indices under the mean square error criterion.