A note on monitoring ratios of two Weibull percentiles

TL;DR

This paper proposes a Bayesian control chart for monitoring the ratio of Weibull percentiles in two processes, directly analyzing sampling data without normality transformation, and demonstrates its application in industry settings.

Contribution

It introduces a novel Bayesian control chart that compares Weibull percentiles without data transformation, utilizing accumulated knowledge for process monitoring.

Findings

Effective in industry case studies

Handles unknown Weibull parameters

Utilizes all past data for improved monitoring

Abstract

This note introduces a new Bayesian control chart to compare two processes by monitoring the ratio of their percentiles under Weibull assumption. Both in-control and out-of-control parameters are supposed unknown. The chart analyses the sampling data directly, instead of transforming them in order to comply with the usual normality assumption, as most charts do. The chart uses the whole accumulated knowledge, resulting from the current and all the past samples, to monitor the current value of the ratio. Two real applications in the wood industry and in the concrete industry give a first picture of the features of the chart.