Developing x-R and x-S Control Charts with Fuzzy Median and Fuzzy Average Approaches

Control charts are the main statistical process control (SPC) tool in monitoring mean and variation of process to perform certain corrective action processes in which data represent quality-related characteristics of the products. If these characteristics are illustrated on numerical scales, we can use variable as soon as possible. The x  R and x  S are viewed as control charts, which are designed to monitor a process most commonly applied control charts. In these charts, the center line, upper and lower control limits are represented as numerical values. Control limits usually do not have an exact amount because of existence imprecise data in the manufacturing process. Also, if a sample mean is very close to the control limits and the used measurement system is not so sensitive, the decisions have low reliability. In this regard, fuzzy control limits provide more accurate and flexible evaluation. So, in this paper, we construct x  R and for detecting shifts in mean and variance of quality- associated characteristic. In an in-control state, the samples locate between the upper and the lower control limits, otherwise control chart alarms an out-of-control state, so preventive or corrective actions should be done to remove the assignable causes. Although data may be come from human judgment, evaluations and measurement errors and so on, usually, traditional control charts are based on assumption of precise data. In fact, x  S with new approach in which control limits the inspector assesses the quality of the inspected item on transformed to fuzzy control limits by utilizing methods of fuzzy average and fuzzy median. Then, the Monte Carlo simulation results are compared based on the Average Run Length (ARL) criterion to appraise performance of proposed approach. Comparing these results with classical charts and developed α-level fuzzy midrange charts shows that the proposed approach has better performance