Control Monitoring Schemes for Monitoring Percentiles of Generalized Exponential Distribution with Hybrid Censoring

Abstract

In this article, a parametric bootstrap control monitoring scheme equivalently known as control chart, is proposed for process monitoring of percentiles of the generalized exponential distribution for type-I hybrid censored data assuming in-control parameters to be unknown. Similar schemes can be derived for type-I and type-II censored data as a special case of the proposed censoring scheme. Monte Carlo simulations are carried out for various combinations of percentiles, false-alarm rates and sample sizes to evaluate the in-control performance of the proposed scheme in terms of average run lengths. The out-of-control behavior and performance of the scheme is thoroughly investigated for several choices of shifts in the parameters of the distribution. Conventional Shewhart-type scheme is also proposed under the same set-up asymptotically and compared with bootstrap scheme using a skewed data set. The chart under hybrid censoring scheme is found to be more effective than the same under type-I and type-II censoring schemes in terms of magnitude and speed of detection of out-of-control signals. Finally, an application of the proposed scheme is shown from clinical practice.