Monitoring Reliability for Three-Parameter Frechet Distribution Using Control Charts

Control Charts for attributes have been widely adopted for examining the fraction non-conforming or non-conformities in a process. However, Shewhart control charts may face some practical problems when the process fraction of non-conformities is very low. While dealing with high quality parameters (low defects), a precise solution is to use time between events (TBE) charts. In the present study, control charts for time between failures have been developed considering that the inter-failure time follows Frechet distribution. Maximum likelihood estimation method (MLE) and Probability weighted moment method (PWMM) are taken into account for estimation purposes. We have also used cumulative sums for inter-failure times to monitor the reliability of three-parameter Frechet distribution. The distribution of sum of Frechet random variates has been obtained with the help of moment approximation. Control limits of cumulative chart for different values of shape parameter have been obtained. Two real data sets are analyzed for illustrative purposes.