Max chart and DS chart for monitoring high-quality processes

Article Type

Research Article

Publication Title

Communications in Statistics Simulation and Computation

Abstract

The defects data in the outputs of a high-quality process is commonly modeled by two-parameter zero-inflated Poisson (ZIP) distribution. Most often separate control charts are used for monitoring the two parameters and these charts are developed assuming that all the outputs are inspected one by one. In mass production processes, it is practicable if outputs are inspected online. However, high-quality processes without online inspection system are not uncommon in reality. Again, a one-chart scheme for joint monitoring of the two parameters allows the practitioners to focus on a single chart and thus, offers operational advantages. Simulation studies show that the MLEs of the two parameters ((Formula presented.) and (Formula presented.)) are asymptotically normally distributed if sample size (Formula presented.) and they are also independent if (Formula presented.) Based on these findings, two one-chart schemes (Max chart and DS chart) are proposed for joint monitoring of the two parameters using offline samples of large size. Simulation studies reveal that out-of-control (OOC) average run length (ARL) performances of the Max chart are better when there is shift in one parameter only. However, OOC ARL performances of DS chart are better if both the parameters shift simultaneously. The proposed charts are applied to an automobile industry.

DOI

10.1080/03610918.2025.2473441

Publication Date

1-1-2025

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