Bootstrap confidence limits for the process capability index C_(pmk)

摘要

Process capability indices are widely used by quality professionals to determine whether a production process is capable of producing items within a specified tolerance. The capability index C_(pmk) is a generalised version of the basic process capability indices C_p, C_(pk) and C_(pm). Recently, techniques and tables were developed to construct confidence limits for each index. These techniques are based on the assumption that the underlying process is normally distributed. However, many processes can be frequently skewed or heavy tailed in practice and hence the interval estimation technique that is free from the assumption of distribution is desirable. In this article, the capability index C_(pmk) is considered and its confidence limits are estimated using the bootstrap technique. A simulation using three distributions (one normal and two non-normal) is conducted and a comparison is made to show the performances of the three bootstrap confidence intervals.