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

## TL;DR

This paper introduces new control charts for monitoring processes with censored data, useful in reliability engineering and lifetime experiments.

## Contribution

Four new control charts are proposed for monitoring a lower truncated proportional hazard rate model under progressive Type-II censoring.

## Key findings

- Three EWMA charts using likelihood ratio and maximum likelihood estimators were developed.
- A novel weighted log-likelihood ratio chart was introduced and evaluated.
- A simulation study and practical example demonstrated the effectiveness of the proposed methods.

## 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.