A study on average run length of fuzzy EWMA control chart

Quality control charts are one of the main features of statistical process control. The performance of control charts is assessed on the basis of the average run length (Shepherd and Shi (1998) IFAC Proc Vol 31(16):435-440. https://doi.org/10.1016/S1474-6670(17)40518-0). ARL is the average number of sample points that must be plotted before a point shows an out-of-control condition. In-control average run length (ARL(0)) and out-of-control average run length (ARL(1)) are two types of ARLs. These values of ARL(0) show the false alarm when the process is in control, and ARL(1) indicates the true alarm when the process is out of control. The control chart that generates fewer ARL is considered more efficient. The exponentiated weighted moving average (EWMA) is used to detect small shifts in the process In this article comparative performance of one of the exponentially weighted moving average (EWMA) control charts are evaluated using ARLs in conventional and fuzzy environments. The novelty of the study is that the comparison between Fuzzy EWMA and conventional EWMA was made. The fuzzy EWMA chart detects a shift at the 20th sample, while the conventional EWMA chart detects the same shift at the 25th sample. A conventional and fuzzy EWMA control chart based on the real-life example of a measurement of food color is presented.