A Nonconformity Ratio Based Desirability Function for Capability Assessment

Abstract

The objective of this paper is to provide a process capability index structure, which respects “the higher the better” rule even when the underlying distribution of the quality characteristic not the normal distribution. An estimator of the univariate capability index is proposed and its statistical properties are studied using Taylor series expansion to monitor an exponential and a lognormal distribution. The used approximation shows that the estimator is unbiased and convergent when the underlying distribution is the exponential one. However, like classical indices, the estimator is biased for the lognormal distribution. A comparative study is carried out with some process capability indices from the literature designed to deal with non- normality. The proposed index performs better than existing indices considering “the higher the better” rule as a benchmark. Finally, a bootstrap confidence interval is implemented for capability judgement and a multivariate extension of the index is introduced.