Efficient failure detection in industrial applications: Enhanced monitoring framework for modified Weibull model

Abstract

This paper explores a statistical approach to propose a new monitoring framework (control chart) for the Modified Weibull model’s (MWM) failure rate function (FRF), based on type I-censored data under Step-Stress accelerated life test (SSALT) (MISS will be used hereafter). Specifically, we focus on SSALT model under type I censoring, where testing stress increases in steps. This scheme utilizes FRF of the MWM and a Shewhart-type control chart approach. Special cases of the proposed scheme can be obtained for other specific distributions, including Weibull, generalized exponential, Rayleigh, and exponential, under type I censoring. To develop the Shewhart-type scheme, the article first derives the maximum likelihood estimators (MLE) for the MWM under type I censoring. It then discusses the asymptotic properties of these estimators. An in-depth simulation study evaluates the in-control (IC) performance of the scheme. The study analyzes average run length (ARL) for various combinations of model parameters. The study also investigates the out-of-control (OOC) performance for different parameter shifts in the chosen density function. Finally, we illustrate the application of the proposed monitoring scheme with a real-world data example from industrial sector, demonstrating how the obtained results can be used in practice. The comparison reveals that the proposed schemes effectively detect OOC signals, both in terms of frequency and speed.