Phase-II monitoring of the lower truncated proportional hazard rate process based on progressive Type-II censoring

Abstract

The problem of monitoring statistical processes using complete data has been extensively studied by researchers. However, in fields such as reliability engineering and lifetime experiments, complete samples are often not available. To address this gap, we introduce four control charts designed for monitoring both parameters of a family of distributions known as the lower truncated proportional hazard rate model, specifically under progressively Type-II censoring. Three of these control charts are exponentially weighted moving average (EWMA) charts that utilize the likelihood ratio statistic and maximum likelihood estimators. The fourth chart is based on a novel weighted log-likelihood ratio statistic. We conduct a Monte Carlo simulation study to assess the performance of the proposed control charts. Finally, we present a practical example to illustrate the application of our methods.