Computing Average & Standard deviation for Run Lengths For Non normal Cumulative Sum Schemes

Abstract

In this study, we investigate about the run length properties of cumulative sum control charts. By generalization, the homogenous markov chain approach to detect positive shifts in the mean of the process for the proposed Logistic distribution with known standard deviation. And also to detect a positive shifts in the median of the process for the proposed Laplace distribution with known standard deviation .To compute the average and the standard deviation for run length for Cusum charts, when the variable under control follows the normal distribution. And we compared it with the average and the standard deviation for run length for the same control charts, when the variable under control follows the Logistic distribution and Laplace distribution, which were proposed in this study. The experiments executed for different combinations of the Cusum parameters, and several state numbers for markov chains. The results were obtained by using Programs written using MATLAB-R2008a program .The results shown that Cusum control charts for Logistic distribution and Laplace distribution were more sensitive than the Cusum control charts for normal distribution.