Process Capability Index for Geometrically Distributed Quality Characteristics

Abstract

Process capability indices play a very important role in the control and the improvement of quality characteristics of products during the production process. Various process capability indices have been developed for quality characteristics which follow normal, Weibull, exponential and other distributions. Many researchers have also developed process capability indices for quality characteristics which follow bivariate normal and exponential distributions, respectively. Some of these indices are being used by industries for the quality improvement of products during the production process for competing in global markets. Some quality characteristics of the products should be treated as discrete random variables following distributions like geometric distribution rather than widely known continuous distribution like normal. Such situations are encountered while dealing with quality characteristics like number of operations before the failure of electrical, electronic or mechanical switches and components. The control and the improvement of such quality characteristics of such products during the production process, in order to ensure the conformity to the specification (usually one-sided), are quite important. No much work has been done so far to develop process capability index applicable to such quality characteristics following the geometric distribution. In this paper, the author proposes a process capability index for a number of successes or operations before the first failure of a component or product assumed to follow a geometric distribution and derives the expectation and variance of the estimated index. The optimal choice of process capability interval related to the said index has also been discussed. The said process capability index may be low for a highly capable process and for the minimum variation of the index, the percentage area lying outside natural tolerance limit may be low as 0.02, and the probability of successes or operations before the first failure may be high as 0.99.