Exponential cumulative sums chart for detecting shifts in time-between-events |
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Authors: | Liang Qu Michael B.C. Khoo Philippe Castagliola Zhen He |
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Affiliation: | 1. College of Management and Economics, Tianjin University, Tianjin, China;2. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia;3. Department of Quality and Logistics, Université de Nantes, IRCCyN UMR CNRS 6597, Nantes, France |
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Abstract: | Time-between-events (TBE) charts use the time interval T between events to monitor process shifts (or failure rates λ). This paper presents a two-sided TBE cumulative sums (CUSUM) chart called a weighted CUSUM(WCUSUM)chart for detecting either a deterioration (decrease in T) or an improvement (increase in T) in the condition of a process. A new kind of WCUSUM chart that has an additional charting power parameter w is proposed here. A WCUSUM chart’s efficiency can be improved by using the parameter w, based on an estimated value of the mean shift. In addition, a methodology and optimal design are presented for minimising the average loss. Construction of the WCUSUM chart is illustrated by considering a random shift δ in λ (including both increasing and decreasing shifts) in the design. |
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Keywords: | time-between-events CUSUM chart exponential of the sample mean shift increasing and decreasing shifts average loss |
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