USING NORMAL APPROXIMATION ON TESTING AND DETERMINING SAMPLE SIZE FOR C_pk

ABSTRACT

Process capability indices are widely used to measure the ability of the process to manufacture products meeting established specification limits. Simply reporting and then making decision from the calculated estimate of the capability index along is not reliable since sampling errors are ignored. However, a more appropriate estimate would be provided by a hypothesis testing. Using a Bayesian-like estimator of C _pk index, this paper presents a generalized approach for testing C _pk index and power computations determining whether a process meets the capability requirement. Applying Hamaker's approximation, the testing procedure can be adequately simplified as a normal approximation and that the more complicated use of the non-central t distribution can be avoided. It allows for testing at any α-level and any sample size. Additionally, an analysis is provided to offer the practitioner the sampling requirements to obtain a fixed power.

Keywords:

• process capability indices
• critical value
• power
• non-central t distribution
• Hamaker's approximation