Measuring capability of a binomial process

Abstract

Many product characteristics are qualitative in nature, e.g. colour, brightness, surface finish etc. The manufacturing process of such products is usually described in terms of fraction nonconforming or conforming which is assumed to follow binomial distribution. Measuring capability of a binomial process implies assessing to what extent the fraction nonconforming or conforming in the continuous stream of lots conform to the specification limits. The Cp or Cpl of a binomial process can be estimated using several approaches. However, these approaches generally give widely varying assessment about the capability of a given binomial process. Consequently, a user of the index may inadvertently be led to erroneous decision making based on an inaccurate estimate of the index. In this paper, a procedure is proposed for assessing accuracies of estimates of Cpu or Cpl obtained by different methods. Subsequently, the best method for evaluating capability of a binomial process is identified based on analysis of multiple case studies, and also the methods giving inaccurate estimates are highlighted.

Keywords: Process capability index, binomial process, fraction nonconforming, nonconforming lot (NL), predicted NL%, prediction error