A variable sampling interval multivariate exponentially weighted moving average control chart for monitoring the gumbel's bivariate exponential data

Document Type : Research Article

Authors

1 School of Automation, Nanjing University of Science and Technology, Nanjing, China

2 School of Management & Institute of High-Quality Development Evaluation, Nanjing University of Posts and Telecommunications, Nanjing, China

3 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

10.24200/sci.2022.56544.4780

Abstract

The general assumption in designing a multivariate control chart is that the multiple variables are independent and  normally distributed. This assumption may not be tenable in many practical situations, because multiple variables with dependency often need to be monitored simultaneously to ensure the process is in control. The Gumbel's Bivariate
Exponential (GBE) distribution is considered to be a better model for skewed data with dependency in reliability analysis. In this paper, a Multivariate Exponentially Weighted Moving Average (MEWMA) scheme with Variable Sampling Interval (VSI) feature is developed to monitor the mean vector of GBE model. The Monte Carlo simulation is used to evaluate the Average Time to Signal (ATS) performance of the proposed VSI MEWMA GBE scheme for three di erent types of shifts. Some tables are presented to show the ATS performance of the proposed scheme with different designed parameters.
Additionally, both the zero-state and the steady-state ATS performance of the proposed scheme is compared with that of the conventional MEWMA chart with FSI (Fix Sampling Interval) feature. Comparative results show that the suggested scheme works better than its FSI counterpart in monitoring GBE data. Finally, a simulation example is provided to show that the VSI MEWMA GBE scheme performs well in monitoring GBE data.

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Main Subjects

Scientia Iranica
Volume 32, Issue 8
Transactions on Industrial Engineering (E)
March and April 2025 Article ID:4780

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History

  • Receive Date: 04 August 2020
  • Revise Date: 29 October 2021
  • Accept Date: 03 January 2022

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