Development of a fuzzy loss-based process capability index

Process capability indices are appropriate tools in order to measure the inherent capability of process, but most of these indices cannot take into account the losses of a process such as rejects, while in today’s competitive business environment, it is becoming more and more important for companies to evaluate and minimize their losses. Since most of process capability indices do not consider the losses, the process capability indices based on losses can help manufacturers to understand the real capability of their processes in order to improve them. Literature review showed two main gaps in loss-based process capability indices. The first gap is that there is not a loss-based process capability index, which has more features such as reject based, asymmetric, bounded, and target based. In order to overcome this problem, an appropriate loss function (asymmetric inverted normal loss function) was employed to propose a new loss-based process capability index. The methodology is to compare the standard loss for a capable process with other cases. The proposed process capability index is bounded, asymmetric and it is able to provide a more realistic metric to evaluate and predict the performance of processes. The second gap in literature review is that among all loss-based process capability indices, just Cpm has been fuzzificated, while literature review showed that the index Cpm is not an appropriate process capability index. Then fuzzy logic and operation research model were employed to fuzzificate the new proposed loss-based process capability index. The α-cuts of the fuzzy observation was the method employed to find the fuzzy membership function of the new loss-based process capability indices. The result of this study is a new loss-based index with more specifications such as mean-based, target- based, variation-based, bounded, and loss-based compared with other process capability indices. The new process capability index was fuzzificated using α-cut method. Therefore a fuzzy loss-based process capability index was developed that is useful for vague data. In order to validate the new loss-based method, the sensitivity of this index to process specifications was studied. Sensitivity analysis showed that this index is sensitive to the mean, variation, and target of data. The new index has 99.6% relationship with the loss especially asymmetric inverted normal loss function. This relationship with loss is the highest relationship compared with other process capability indices. Moreover a regression analysis showed that the new index has the most relationship with the value of loss compared with other process capability indices.

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