Using normal approximation for calculating the p-value in assessing process capability index Cpk

Abstract

When a process is in a perfect state of statistical control, the process capability indices are widely used to measure the capability of the process to manufacture items within the required tolerance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. The index Cpk has been used in various manufacturing industries to provide a quantitative measurement of the performance of the manufacturing. In this paper, based on the theory of statistical hypothesis testing, we propose a procedure on assessing Cpk index for practitioners to use in determining whether a given process as capable. Applying Hamaker’s approximation, the testing procedure can be adequately derived from a normal distribution approximation, which avoids the more complicated non-central t-distribution. The provided approach is easy to use and the decision making is more reliable.