Modified Shewhart Control Chart Based on CEV for Gamma Distributed Lifetimes in the Presence of Type-I Censored Data

Abstract

This article explains the modified version of Shewhart control charts for monitoring the mean level of the Gamma lifetimes under the Type-I censored data. Shewhart control chart based on the conditional expected values (CEV) is developed which can efficiently monitor the Type-I censored. The results of the proposed control chart are compared with simple/traditional Shewhart control chart using different censoring rates (P_c). The main focus is the stability of the mean level for which we have considered the specified parameter(s) as well as the unspecified parameter(s) cases (where Maximum Likelihood Estimates (MLE) has been considered). It is observed that in the presence of Type-I censored observation the CEV Shewhart  Control chart outperforms traditional Shewhart control chart. The proposed censoring control charts always outperform when known parameters are used rather than the MLE estimate cases. The proposed charting methodology is also illustrated by an example.