Improved Memory-Type Control Charts for Censored Data

Abstract

Statistical Process Control (SPC) is an industrial methodology used for measuring and controlling quality of manufacturing processes. Data on the manufactured products or processes are obtained in real-time during the manufacturing process. Therefore, manufacturing industries consistently use the control charts for monitoring the stability of their productions. The commonly used control charts to monitor complete data are Shewhart, Exponentially Weighted Moving Average (EWMA), and Cumulative Sum (CUSUM) control charts. Initially, these charts were developed assuming normal distribution, but now have been generalized to non-normal distributions such as Weibull, Rayleigh, Poisson-Exponential distributions, etc. These charts, however, are designed to monitor the complete data and perform very poor when the observed data are censored or incomplete. Thus, to overcome this research gap, we purpose some new control charts in this thesis for monitoring the censored data, especially type-I censored data, assuming Weibull, Rayleigh, and Poisson-Exponential distributions. The reason for focusing these distributions is their usage in reliability studies. In particular, we construct EWMA and CUSUM control charts using Conditional Expected Value (CEV) and Conditional Median (CM) approaches. The performance of the control charts is assessed using the Average Run Length (ARL) as a performance measure. Furthermore, the CEV and CM based Double EWMA control charts are also discussed in this study. The CEV and CM based Hybrid DEWMA control charts are also proposed and compared with some existing charts to monitor the type-I right censored data. Since, in practice, usually the parameters are unknown and to be estimated from the observed data, the proposed charts are also evaluated using estimated parameters, where the Maximum Likelihood Estimator (MLE) is considered to estimate the unknown parameter. It is observed that the proposed control charts outperform the existing charts. Furthermore, a large Phase-I data is required to overcome the estimation error.The real data examples of each chapters supplement the conclusion drawn from the simulation study.