Building a Cpk control chart – A novel and practical method for practitioners

Abstract

This paper covers a hitherto unresolved problem, the search for a practical method for the Cpk^ control chart. The simplicity of the proposed method facilitates its immediate application. This control chart method reduces the complexity of the current paradigm for capability and quality control studies, while increasing sensitivity to out-of-control signals and improving the early detection aspect, as the ARL results show. The concept of distance implicit in Cpk definition is used to derive a new method based on chi-square distribution. The goodness of fit of the derived expression, which approximates the distribution of the Cpk^ statistic of the proposed method to the reference distribution of the simulated values and to the exact probability density function, was confirmed graphically, through the comparison of the histograms and the probability density functions, and analytically, using the F-test.