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Activity Number:
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343
- Advances in Statistical Process Control and Capability
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Type:
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Contributed
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Date/Time:
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Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
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Sponsor:
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Quality and Productivity Section
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Abstract #324861
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View Presentation
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Title:
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CUSUM for Counts: Power Considerations and the Low-Count Regime
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Author(s):
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James Lucas* and Darwin Davis and Erwin M. Saniga and Thomas P. McWilliams
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Companies:
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J M Lucas & Associates and Dept of Business Admin. Lerner College of B & E and University of Delaware and Drexel University
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Keywords:
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Average Run Length (ARL), ;
CUSUM chart ;
Shewhart chart ;
Markov Chain ;
Bernoulli, Binomial, Poisson distributions
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Abstract:
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In this talk we discuss the power needs of CUSUM and Shewhart control schemes and emphasize the problems in the low-count regime. We show that the power needed by control procedures is often less than the power required by other applications. The low count regime has the complication in that only large proportional shifts in level can be detected. We discuss the ability to detect order of magnitude (OOM) shifts, OOM/2 shifts and a doubling in the low-count regime. We show that it is important to consider not only the size of the shift but also the "data richness" so that the amount of data needed to detect the shift with high power will be obtained. A CUSUM is an optimum detector of a change in distribution. For shift detection, a CUSUM will detect a specified shift faster than any other control procedure that has the same in-control ARL (false alarm frequency). The implementation statements show that a CUSUM is a Markov chain because the CUSUM state depends on the current observation and the previous state. Our automatic design procedure sets up a tentative Markov chain and iterates to find the appropriate Markov Chain for the control situation.
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Authors who are presenting talks have a * after their name.
