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Fuzzy development of mean and range control charts using statistical properties of different representative values. (English) Zbl 1303.62113

Summary: This paper develops Mean and Range control charts in fuzzy environment using different transformation methods. It is assumed that the observations of each sample are fuzzy random variables, which have triangular membership functions. After calculating fuzzy mean and fuzzy range of each sample using fuzzy arithmetic, their representative values are calculated exploiting the transformation methods. Then, using statistical properties of the obtained representative values and basic structure of Shewhart control charts, new Mean and Range control charts are constructed to monitor the process mean and variation. After that, the power of control charts constructed based on different transformation methods are examined applying average run length (ARL) criterion. According to this criterion, it is concluded that, contrary to the previous claim, these different transformation methods lead to mean and rang control charts with various performances. Moreover, it is represented that the value of \(\alpha\)-level has significant influence on the performance of obtained control charts. Finally, it is derived that incorporating fuzziness into observations results in less powerful control charts.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
93C42 Fuzzy control/observation systems
93E03 Stochastic systems in control theory (general)
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