Sample size determination for estimating process precision and process loss based on multiple samples with designated accuracy ratio

Abstract

Numerous process capability indices including Cp, Cpk, Cpm, and Cpmk have been proposed in the manufacturing industry providing numerical measures on process capability based on various criteria. The index Cp provides measures on process precision, which reflect the consistency of product quality. The index Cpm, also called the Taguchi index, essentially measures process loss. Lower confidence bounds estimate the minimum process capability conveying critical information regarding product quality, which is essential to quality assurance. Existing research works have focused on constructing lower confidence bounds, but investigation on the sample sizes required for specified accuracy ratio of the estimation has been comparatively neglected. The sample size determination is important directly related to the cost of data collection plan. Furthermore, existing researches considered solely one single sample. Current quality control practice, however, is to estimate process capability using multiple groups of control chart samples rather than one singl sample. In this paper, based on multiple samples collected from past in-control and S control chart data, the sampling distributions of the estimated Cp and Cpm are derived with efficient Matlab programs that can be used to determine the sample size required for given estimating accuracy ratio. We also provide tables of the sample size information for the engineers/practitioners to use for their in-plant applications.