Control Chart for Generalized Weibull Quantiles under Hybrid Censoring

TL;DR

This paper develops bootstrap and Shewhart control schemes for monitoring generalized Weibull distribution quantiles under hybrid censoring, with applications to healthcare and comparisons to existing methods.

Contribution

It introduces new control schemes for generalized Weibull quantiles under hybrid censoring, including derivation of MLEs via EM algorithm and performance evaluation.

Findings

Schemes effectively detect out-of-control signals.

Performance depends on quantile choice, false-alarm rate, and sample size.

Out-of-control detection is rapid and reliable.

Abstract

In this article, bootstrap and Shewhart type process control monitoring schemes are proposed for the quantiles of generalized Weibull distribution under hybrid censoring. Monitoring schemes for the quantiles of Weibull, generalized exponential, Rayleigh, and Burr type $X$ distributions for type I, type II and hybrid censoring can be obtained as the special cases of the proposed schemes. The maximum likelihood estimators are derived under hybrid censoring using EM algorithm and the asymptotic properties of the estimators are discussed in order to develop the Shewhart type scheme. The in-control performance of the schemes is examined in a simulation study on the basis of the average run length for different choices of quantiles, false-alarm rates and sample sizes. Behavior of the out-of-control performance of the schemes is studied for several choices of shifts in the parameters of the chosen density function. The proposed monitoring schemes are illustrated with an example from healthcare and compared with similar schemes under type I and type II censoring. The schemes are found to detect out-of-control signals effectively in terms of frequency and speed both.