Control Charts for Percentiles of Truncated Beta Distributed Environmental Data Using Studentized Bootstrap Method

TL;DR

This paper develops a control chart for monitoring percentiles of environmental data modeled by a truncated beta distribution, using a studentized bootstrap method to handle unknown parameters, validated through simulations and real data examples.

Contribution

It introduces a novel control chart for truncated beta distributed data employing a studentized bootstrap approach to estimate unknown parameters.

Findings

The proposed chart maintains good in-control performance across various scenarios.

It outperforms traditional beta-based charts in detecting distribution shifts.

Real-world environmental data demonstrate the chart's practical utility.

Abstract

This paper proposes a control chart for monitoring percentiles of a process that follows a truncated beta distribution, utilizing a studentized parametric bootstrap method to account for the case when in-control parameters are unknown. To evaluate the in-control performance, extensive Monte Carlo simulations are conducted across various combinations of percentiles, false alarm rates, and sample sizes, with performance measured in terms of the average run length. The out-of-control performance is thoroughly assessed by introducing shifts in the distributional parameters and comparing the proposed chart with the conventional beta-based chart. The effectiveness and practical applicability of the proposed chart is illustrated through real-world examples from environmental data.