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Bayesian enhanced EWMA scheme for shape parameter surveillance in Inverse Gaussian models

Published: 01 November 2024 Publication History

Highlights

Bayesian EWMA charts (BE_CCs) tailored for monitoring the shape parameter in Inverse Gaussian (IG) models.
BE_CCs superior ability to detect small and gradual shifts in the shape parameter of IG models.
Simulation studies validate the effectiveness and reliability of the proposed scheme.
Effectively applied BE_CCs in industrial and environmental monitoring.
Prior knowledge enhanced the detectability of the BE_CCs for process monitoring.

Abstract

Bayesian control charts (BCC) are increasingly recognized as highly effective statistical schemes to investigate manufacturing processes and effectively control process variability. This technique is mainly adept at handling uncertain parameters in the manufacturing sector. This study sets the surveillance threshold for the Inverse Gaussian Distribution (IGD) shape parameter. It develops several non-informative exponentially-weighted moving averages (EWMA) control charts (CCs) using different loss functions (LFs). The proposal and existing charts are assessed using different individual performance measures. The non-informative Bayesian (NIB) charts developed in this study are evaluated across various sample sizes. The simulation study determines that the proposed non-informative Bayesian EWMA CCs are more effective than conventional classical EWMA charts. These proposed EWMA chart techniques excel in identifying faults in the shape parameter and perform better than their classical counterpart in swiftly identifying shifts. Additionally, the procedure is applied to real data from the manufacturing industry, and the results validate the conclusions drawn from the simulation outcomes.

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Published In

cover image Computers and Industrial Engineering
Computers and Industrial Engineering  Volume 197, Issue C
Nov 2024
1591 pages

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 01 November 2024

Author Tags

  1. Average run length (ARL)
  2. Bayesian estimation
  3. Uniform prior
  4. Jeffreys’ prior
  5. Loss functions
  6. EWMA control chart

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