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Activity Number:
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238
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Quality & Productivity
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| Abstract - #300932 |
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Title:
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Attribute Charts for Monitoring a Markov Process
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Author(s):
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Deborah K. Shepherd*+ and Charles W. Champ
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Companies:
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Louisiana State University, Shreveport and Georgia Southern University
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Address:
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5605 Mirador Cir., Shreveport, LA, 71119-4009,
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Keywords:
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control chart ; ARL ; Markov chain
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Abstract:
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A tool commonly used for monitoring the quality of a process is the control chart. Generally, a control charting procedure uses a sequence of measures to make a decision about the quality of the process. Often the sequence is modeled as independent and identically distributed (iid) random variables. In this paper a sequence of attribute random variables is used to classify an item as conforming or nonconforming under a stationary Markov chain model with 100% sequential sampling. Two different control charting schemes are investigated. Both schemes plot a sequence of measures that count the number of conforming items before a nonconforming item. The first scheme signals as out-of-control if a measure falls below a certain lower limit, while the second signals if two out of two measures fall below a certain lower limit. The efficiency of both control charts is evaluated by the average run length (ARL) of the chart and the power of the chart to detect a shift in the process. The two out of two scheme is shown to have high power and a large ARL given certain parameter values of the process. A simulation study is provided to support the theoretical models discussed.
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