Exponentially Weighted Moving Average Control Chart Based on Normal Fuzzy Random Variables
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Exponentially weighted moving average (EWMA) chart is an alternative to Shewhart control charts and can serve as an effective tool for detection of shifts in small persistent process. Notably, existing methods rely on induced imprecise observations of a normal distribution with fuzzy mean and variance. Such techniques did not investigate the statistical properties relevant to a fuzzy EWMA. To overcome this shortcoming, employing a common notion of normal fuzzy random variable with fuzzy mean and non-fuzzy variance could be helpful. This paper first developed a notion of fuzzy EWMA statistic as a natural extension to the classical counterpart. Then, the concept of fuzzy EWMA control limit was introduced and discussed in cases where fuzzy mean and/or non-fuzzy variance was unknown parameters. A degree of violence was also employed to monitor the proposed fuzzy EWMA control chart. Potential applications of the proposed fuzzy EWMA chart were also demonstrated based on a real-life example. The advantages of the proposed method were also discussed in comparison with other existing fuzzy EWMA methods.
KeywordsNormal fuzzy random variable Fuzzy EWMA statistic Fuzzy EWMA chart Consistent estimator Violence degree
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