A New Approach to Production Process Capability Assessment for Non-Normal Data

Abstract

The process quality capability indicators Cp and Cpk are widely used to measure process capability. Traditional metric estimation methods require process data to be explicit and normally distributed. Often, the actual data obtained from the production process regarding the measurements of quality features are incomplete and do not have a normal distribution. This means that the use of traditional methods of estimating Cp and Cpk indicators may lead to erroneous results. Moreover, in the case of qualitative characteristics where a two-sided tolerance limit is specified, it should not be very difficult. The problem arises when the data do not meet the postulate of normality distribution and/or a one-sided tolerance limit has been defined for the process. Therefore, the purpose of this article was to present the possibility of using the Six Sigma method in relation to numerical data that do not meet the postulate of normality of distribution. The paper proposes a power transformation method using multiple-criteria decision analysis (MCDA) for the asymmetry coefficient and kurtosis coefficient. The task was to minimize the Jarque–Bera statistic, which we used to test the normality of the distribution. An appropriate methodology was developed for this purpose and presented on an empirical example. In addition, for the variable after transformation, for which the one-sided tolerance limit was determined, selected process quality evaluation indices were calculated.