Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated

This is the authors' abstract. We don't add key points for this paper.

Many organizations use a single estimate of C p and/or C pk for process benchmarking, without considering the sampling variability of the estimators and how that impacts the probability of meeting minimum index requirements. Lower confidence limits have previously been determined for the C p and C pk indices under the standard assumption of independent data, which are based on the sampling distributions of the index estimators. In this paper, lower 100(1‐α)% confidence limits for C p and C pk were developed for autocorrelated processes. Simulation was used to generate the empirical sampling distribution of each estimator for various combinations of sample size (n), autoregressive parameter (ϕ), true index value (C p or C pk ), and confidence level. In addition, the minimum values of the estimators required in order to meet quality requirements with 100(1‐α)% certainty were also determined from these empirical sampling distributions. These tables may be used by practitioners to set minimum capability requirements for index estimators, rather than true values, for the autocorrelated case. The implications of these results for practitioners will be discussed.