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A homogeneously weighted moving average control chart for Conway-Maxwell Poisson distribution.

Olatunde Adebayo Adeoti1, Jean-Claude Malela-Majika2, Sandile Charles Shongwe3

  • 1Department of Statistics, Federal University of Technology Akure, Akure, Nigeria.

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|August 29, 2022
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Summary

A new homogeneously weighted moving average (HWMA) control chart effectively monitors count data using the Conway-Maxwell distribution. This HWMA chart shows competitive performance against existing memory-type charts for detecting process shifts.

Keywords:
Attribute chartcount dataover-dispersed datarun-length characteristicsunder-dispersed data

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Area of Science:

  • Statistical Process Control
  • Quality Management
  • Industrial Engineering

Background:

  • Traditional control charts may not adequately monitor count data, especially when over-dispersed or under-dispersed.
  • Memory-type control charts incorporate past data, offering enhanced sensitivity to process variations.
  • The Conway-Maxwell (COM) distribution provides a flexible model for various count data types.

Purpose of the Study:

  • To introduce a new homogeneously weighted moving average (HWMA) control chart for monitoring count data.
  • To evaluate the performance of the proposed HWMA chart using the Conway-Maxwell distribution.
  • To compare the proposed HWMA chart's sensitivity against existing COM-Poisson memory-type control charts.

Main Methods:

  • Development of a HWMA control chart based on the COM distribution.
  • Performance evaluation using Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and Median Run Length (MRL).
  • Analysis of expected ARL, SDRL, and MRL for location and dispersion shifts.
  • Comparison of out-of-control ARL with existing memory-type control charts.

Main Results:

  • The proposed HWMA control chart demonstrates competitive performance in detecting shifts in location and dispersion parameters.
  • The chart effectively monitors count data, including under-spread and over-spread scenarios, using the COM distribution.
  • Numerical examples illustrate the practical application and effectiveness of the HWMA chart.

Conclusions:

  • The HWMA control chart is a viable and competitive option for monitoring count data quality.
  • The chart's flexibility, owing to the COM distribution, makes it suitable for diverse count data applications.
  • The study confirms the utility of the HWMA chart in enhancing statistical process control for count data.