| ON EVALUATING THE RUN LENGTH PROPERTIES OF CHARTS WITH ESTIMATED CONTROL LIMITS |
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| 作者姓名： | LI Guoying |
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| 作者单位： | LI Guoying(Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China)YANG Chunyan Siu-Keung TSE (Department of Management Sciences，City University of Hong Kong) |
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| 基金项目： | This research is is partially supported by the National Natural Science Foundation of China. |
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| 摘 要： | (?) charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the (?) charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.
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ON EVALUATING THE RUN LENGTH PROPERTIES OF (?) CHARTS WITH ESTIMATED CONTROL LIMITS |
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| LI Guoying.ON EVALUATING THE RUN LENGTH PROPERTIES OF (?) CHARTS WITH ESTIMATED CONTROL LIMITS[J].Journal of Systems Science and Complexity,2002(4). |
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| Authors: | LI Guoying |
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| Abstract: | X charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the X charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen. |
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| Keywords: | Average run length uniform integrability numerical integration number theory method |
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