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Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Author

Listed:
  • Muhammad Farhan Akram
  • Sajid Ali
  • Ismail Shah
  • Giulia Marcon

Abstract

Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit‐interval data. To this end, maximum exponentially weighted moving average (Max‐EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max‐EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium‐sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift.

Suggested Citation

  • Muhammad Farhan Akram & Sajid Ali & Ismail Shah & Giulia Marcon, 2022. "Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7951748
    DOI: 10.1155/2022/7951748
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    References listed on IDEAS

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    1. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
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    Cited by:

    1. Muhammad Farhan Akram & Sajid Ali & Ismail Shah & Syed Muhammad Muslim Raza, 2022. "Max‐EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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