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Minimum Loss Design of X Control Chart for Correlated Data Under Weibull In-Control Times with Multiple Assignable Causes | ||
| Journal of Data Science and Modeling | ||
| مقاله 8، دوره 1، شماره 1، اسفند 2022، صفحه 99-127 اصل مقاله (645.38 K) | ||
| نوع مقاله: Research Manuscript | ||
| شناسه دیجیتال (DOI): 10.22054/jcsm.2018.36532.1014 | ||
| نویسندگان | ||
| mohammad hossein naderi1؛ Mohammad Bameni Moghadam* 2؛ asghar Seif3 | ||
| 1PhD candidate in statistics, Allameh Tabataba'i University, Tehran, Iran. | ||
| 2Department of Statistics, Faculty of Mathematical Sciences and Computer, Allameh Tabataba'i University | ||
| 3Assistant professor of statistics, Bu-Ali Sina University, Hamedan, Iran. | ||
| چکیده | ||
| A proper method of monitoring a stochastic system is to use the control charts of statistical process control in which a drift in characteristics of output may be due to one or several assignable causes. In the establishment of X charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice, there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Using three di erent loss functions in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Although some research works have considered the economic design of control charts under single assignable cause and correlated data, the economic statistical design of X control chart for multiple assignable causes and correlated data under Weibull shock model with three di erent loss functions have not been presented yet. Based on the optimization of the average cost per unit of time and taking into account the di erent combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval and control limit coecient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling integrated with three di erent loss functions has a lower cost than the model with uniform sampling. | ||
| کلیدواژهها | ||
| Economic statistical design؛ X control chart؛ Multiple assignable causes | ||
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