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Max-EWMA Chart Using Beta and Simplex Distributions for Time and Magnitude Monitoring

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  • Sajid Ali
  • Muhammad Farhan Akram
  • Ismail Shah
  • Kauko Leiviskä

Abstract

Control charts are used to detect assignable causes in different manufacturing and nonmanufacturing processes. This study presents a new maximum exponentially weighted moving average (Max-EWMA) chart for joint unit interval time and magnitude monitoring. To this end, beta distribution is considered for time whereas simplex distribution is used for magnitude. Average run length (ARL), standard deviation of run length (SDRL), and different quantiles are used to evaluate the performance of the Max-EWMA chart. A real data example is also included in the study to show the application of the proposed chart. The results provide evidences that the Max-EWMA chart is efficient in detecting small- to medium-sized shifts.

Suggested Citation

  • Sajid Ali & Muhammad Farhan Akram & Ismail Shah & Kauko Leiviskä, 2022. "Max-EWMA Chart Using Beta and Simplex Distributions for Time and Magnitude Monitoring," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, July.
    • Handle: RePEc:hin:jnlmpe:7306775
    DOI: 10.1155/2022/7306775
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