Developing the Sign and Signed Rank Non-parametric Control Charts by Using Interval Type-2 Fuzzy Sets

Considering the high flexibility of type-2 fuzzy sets to represent uncertainty, their applications in different scopes included control charts are extended. In this paper, to control the centrality of non-normal and ambiguous processes, two non parametric control charts included sign and signed-rank charts have been developed using interval type-2 fuzzy sets. In the type-2 fuzzy sign chart and type-2 fuzzy signed-rank chart, the observations of each sample are compared with the centrality of the process in the control state, which for this purpose it used two different methods. To describe the applicability of the proposed charts, they are used in an example with real data and it is showed their correctness performance. Also, to evaluate the performance of type-2 fuzzy sign chart and type-2 fuzzy signed rank chart, simulation programs have been used in which type-2 fuzzy random variables with three different density functions are generated and in each distribution and both methods, the average run length (ARL) of the charts are calculated. The numerical results show the appropriate performance and applicability of the type-2 fuzzy sign chart and type-2 fuzzy signed-rank chart to control the centrality of non-normal fuzzy random variables.