Cumulative sum control charts for monitoring zero‐inflated COM‐Poisson processes

IF 2.2 3区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality and Reliability Engineering International Pub Date : 2024-04-04 DOI:10.1002/qre.3554

Konstantinos A. Tasias, Vasileios Alevizakos

引用次数: 0

Abstract

The zero‐inflated Conway‐Maxwell Poisson (ZICMP) distribution models count data with many zero observations. ZICMP model has been developed assuming that zero observations exist with probability and the number of non‐conformities in a product unit follows the Conway‐Maxwell Poisson (COM‐Poisson) distribution with location parameter and dispersion parameter . This article presents four kinds of cumulative sum (CUSUM) charts for monitoring upward shifts in a ZICMP process. Three CUSUM schemes, namely ‐CUSUM, ‐CUSUM, and ‐CUSUM, have been designed to detect shift only in one parameter assuming that the other two are fixed and one CUSUM scheme, namely ‐CUSUM, has been designed to detect shifts in all the parameters. The performance of the proposed charts has been evaluated in terms of the average run‐length (ARL). Finally, a numerical example is given to demonstrate the application of the proposed charts.

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用于监测零膨胀 COM-Poisson 过程的累积和控制图

零膨胀康威-麦克斯韦泊松（ZICMP）分布是对有许多零观测值的计数数据的建模。ZICMP 模型的建立是假定零观测值概率存在，且产品单位中的不符合项数量遵循带有位置参数和分散参数的康威-麦克斯韦泊松（COM-Poisson）分布。本文提出了四种用于监测 ZICMP 过程中向上移动的累积和（CUSUM）图表。三种 CUSUM 方案，即 -CUSUM、-CUSUM 和 -CUSUM，是在假设其他两个参数固定的情况下设计的，用于只检测一个参数的移动；一种 CUSUM 方案，即 -CUSUM，是设计的，用于检测所有参数的移动。根据平均运行长度（ARL）对所提出图表的性能进行了评估。最后，给出了一个数值示例，以演示所建议图表的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quality and Reliability Engineering International 管理科学-工程：工业

CiteScore

4.90

自引率

21.70%

发文量

181

审稿时长

6 months

期刊介绍： Quality and Reliability Engineering International is a journal devoted to practical engineering aspects of quality and reliability. A refereed technical journal published eight times per year, it covers the development and practical application of existing theoretical methods, research and industrial practices. Articles in the journal will be concerned with case studies, tutorial-type reviews and also with applications of new or well-known theory to the solution of actual quality and reliability problems in engineering. Papers describing the use of mathematical and statistical tools to solve real life industrial problems are encouraged, provided that the emphasis is placed on practical applications and demonstrated case studies. The scope of the journal is intended to include components, physics of failure, equipment and systems from the fields of electronic, electrical, mechanical and systems engineering. The areas of communications, aerospace, automotive, railways, shipboard equipment, control engineering and consumer products are all covered by the journal. Quality and reliability of hardware as well as software are covered. Papers on software engineering and its impact on product quality and reliability are encouraged. The journal will also cover the management of quality and reliability in the engineering industry. Special issues on a variety of key topics are published every year and contribute to the enhancement of Quality and Reliability Engineering International as a major reference in its field.