The average run length of Shewhart style control chart under normal fuzzy random environments with trapezoidal membership function

Due to the globalization impacts modern manufacturing environments are inevitably complicating and evolving, which is random fuzzy in nature. Therefore, the mathematical treatments in statistical control charts have to deal with the coexisting random and fuzzy uncertainties. Fuzzy mathematics created by Zadeh [5], [6] is possibility measure theory based and the treatments are at fuzzy set level which is difficult to handle. The new fuzzy theory founded by Liu [2] is axiomatic based which convert fuzzy set variable into a scalar fuzzy variable and thus makes the fuzzy mathematical treatments behave similar to those in standard probability theory. In this paper, we introduce the new fuzzy theory-credibility measure theory into the analysis of the average run length (abbreviated as ARL) analysis of Shewhart style statistical control chart under normal fuzzy manufacture environments.