A nonparametric capability analysis incorporating quantile sampling in manufacturing processes

Process capability analysis is a series of tools used in industry to determine if a process is able to generate goods that are within the specification limits determine by the client. One of these tools is the process capability index (PCI); which is a ratio that measures the desired variability of a process against its real variability. These ratios were built under certain assumptions, being one of them the normality of the data. If these assumptions are not met, decisions based on them might lead to erroneous conclusions about the process. To address the problem of lack of normality, nonparametric techniques have been proposed, for instance, the Clements’ method. This method is based on fitting a series of known curves to the data understudy in order to estimate the extreme quantiles 0.99865 and 0.00135. It has been reported that when the skewness of the data is greater than 1.5, the method losses accuracy. In addition, all the information of the data is used to estimate quantiles that are located at the extreme of the distribution. During this dissertation a novel method, which takes into consideration only information on the tails of the distribution, is proposed. Monte Carlo simulations are conducted to evaluate its performance. On the second part of this dissertation, an extension of the methodology is proposed. The method is now expanded for its used on k homogenous samples. Results and discussions are presented.