Process Monitoring Using Truncated Gamma Distribution

Sajid Ali, Shayaan Rajput, Ismail Shah () and Hassan Houmani ()
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Sajid Ali: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Shayaan Rajput: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Ismail Shah: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Hassan Houmani: Department of Economics, School of Business, Lebanese International University-LIU, Beirut 146404, Lebanon

Stats, 2023, vol. 6, issue 4, 1-25

Abstract: The time-between-events idea is commonly used for monitoring high-quality processes. This study aims to monitor the increase and/or decrease in the process mean rapidly using a one-sided exponentially weighted moving average (EWMA) chart for the detection of upward or downward mean shifts using a truncated gamma distribution. The use of the truncation method helps to enhance and improve the sensitivity of the proposed chart. The performance of the proposed chart with known and estimated parameters is analyzed by using the run length properties, including the average run length (ARL) and standard deviation run length (SDRL), through extensive Monte Carlo simulation. The numerical results show that the proposed scheme is more sensitive than the existing ones. Finally, the chart is implemented in real-world situations to highlight the significance of the proposed chart.

Keywords: average run length; exponentially weighted moving average; standard deviation of run length; time-between-events; truncated gamma distribution (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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