One‐sided capability indices <i>C</i>_PU and <i>C</i>_PL: decision making with sample information

TLDR

Process capability indices quantify manufacturing potential and performance, but conventional use ignores sampling error, making conclusions unreliable. This study seeks to derive unbiased estimators for the one‑sided indices C PU and C PL and to formulate a testing procedure for them. The authors construct unbiased estimators and develop a procedure analogous to the two‑sided indices C p, C pk, and C pm for the one‑sided indices. Practitioners can apply the proposed procedure to determine whether their processes satisfy capability requirements.

Abstract

Process capability indices have been used in the manufacturing industry to provide quantitative measures on process potential and performance. The formulae for these indices are easy to understand and straightforward to apply. But, since sample data must be collected in order to calculate these indices, a great degree of uncertainty may be introduced into capability assessments due to sampling errors. Currently, most practitioners simply look at the value of the index calculated from the sample data and then make a conclusion on whether their processes meet the capability requirement. This approach is not reliable since sampling errors are ignored. Procedures for two‐sided capability indices, C p , C pk , and C pm have been developed to assist practitioners to determine whether their processes meet the capability requirement based on sample information. In this paper, we first obtain unbiased estimators of C PU and C PL . We then develop a procedure similar to those of C p , C pk , and C pm , for the one‐sided capability indices C PU and C PL . Practitioners can use the procedure to test whether their processes meet the capability requirement.