The use of the Extended Generalized Lambda Distribution for controlling the statistical process in individual measurements

Abstract

In quality control (QC) of the individual pieces tested, the distribution of the intended variable is not normal in many cases. Therefore, the use of conventional statistical methods to design the control charts (X chart) can lead to misleading and inaccurate results, and hence, it can cause problems to users; because in such a situation it would not be expected that the failure in the production line will be detected in a timely manner. Therefore, in this study, the use of Extended Generalized Lambda distribution (XGLD) has been proposed for approximating the statistical distribution of data and finding a quality control chart based on it. For this purpose, the distribution function of data was firstly estimated by the XGLD, and then, based on this distribution, the control limits were calculated. The research data consists of the tensile strength of 149 aluminum plates categorized into 22 classes. For the goodness of fit test, Chi-square test was utilized and to evaluate the effectiveness of the proposed model, the average run length (ARL) method was used. The results showed that the ARL values in the proposed method are lower than that in the conventional method. Since this is true at all points, it can be concluded that the use of the new method can lead to the faster detection of the systems failure and consequently, the subsequent costs can be reduced. In addition, since the XGLD is a highly flexible distribution and can estimate many conventional (and even unconventional) distributions with high precision, the use of the proposed method instead of using other cases which are based on distributions other than normal, will increase the accuracy of the systems failure detection.