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A Simple Method for Computing the Arl of [ILM0001]-Charts with Zone Tests |
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| Authors: | Jain Chung Terry Obert Pittman |
| Affiliation: | 1. Department of Research Statistics , 07110–1199 , Nutley , NJ , Hoffmann-La Roche Inc. 340 Kingsland Street;2. Department of Business Information Systems and Quantitative Analysis , Mississippi State University , 39762–6107 , MS , Mississippi State |
| Abstract: | In practice the [ILM0002]-chart has been augmented with one or more zone tests to improve the sensitivity of detecting small shifts in the process mean. The average run length (ARL) is one of the indices used to evaluate the performance of control chart procedures. Two unified patterns of transition probability matrices and four closed form expressions of the ARL are found based on the Markov Chain approach. These closed form expressions can be used for computing the ARL for both one-sided and two-sided [ILM0003]-charts with zone tests. |
| Keywords: | Average Run Length Markov Chain Zone Test Transition Probability Matrix |