Re-evaluating the process capability indices for non-normal distributions

Classical process capability indices (PCIs) C_p, C_pu, C_pl and C_pk can indicate the potential process capability accurately when the quality characteristic of the product is normally distributed. When the process has a non-normal distribution, classical PCIs will be inappropriate and can misled the assessment of process capability. Zwick (1995), Schneider and Pruett (1995-96) and Tong and Chen (1998) proposed various PCIs for non-normal distributions. This paper compares the accuracy of these indices for several selected non-normal distributions based on the proportion of non-conformity of manufactured product. The results indicate that these PCIs lead to a larger number of errors in various combinations of shape parameters and specification limits. Therefore, this paper proposes three indices, S_pu, S_pl and S_pk, which can reflect accurately the proportion of nonconformity in either normal or non-normal distributions.