Control Charts for new Reflected Pareto Distribution

Abstract

Pareto distribution has vast application in different fields of medical and engineering sciences. In this thesis, we have proposed a new Reflected Pareto Distribution (RPD) using Cohen (1973) to reflect the parameter of distribution. We derive different mathematical properties such as mean, variance, rth moment. Reliability measures are also discussed including Survival Function, Hazard function and reversed hazard function. The method of Maximum Likelihood Estimator and Modified maximum likelihood estimator is used to estimate the model parameters. We used three different data sets to show the performance of Reflected Pareto distribution over already existing probability distributions. We also construct the control charts to monitor the shape parameter for reliability processes using Shewhart control chart and Exponentially weighted moving averages control chart. We compare the performance of maximum likelihood estimator and modified maximum likelihood estimator for the shape parameter of Reflected Pareto distribution.