Adaptive Shewhart Control Charts Under Fuzzy Parameters with Tuned Particle Swarm Optimization Algorithm

In recent years, adaptive control charts in which the design parameters depend on the observed samples have been successfully used as efficient alternatives for traditional control charts with constant parameters. In crisp run control rules, the process state may change very sharply from in-control to out-of-control conditions which increase the rate of false alarms. To overcome this drawback, this paper presents an adaptive Shewhart-type control chart, where the design parameters (sample size ([Formula: see text]), sampling interval ([Formula: see text]), and control limit coefficients ([Formula: see text] and [Formula: see text])) are defined with linguistic variables. To accomplish that, the chart parameters are determined based on the location of eight previous chart statistics using a set of fuzzy rules in a continuous environment. In order to improve the sensitivity of the proposed control chart in detecting small shifts in both location and scale parameters, the adaptive procedure is designed by integration of fuzzy Western Electric rules and fuzzy adaptive sampling rules. After designing the control charts using a fuzzy inference system (FIS), in order to provide an economic design of the proposed control chart, a tuned Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal values corresponding to membership functions of the control chart parameters. Finally, using simulation studies, the capability of the proposed control chart is analyzed and compared with common charts in the literature. The results confirm that under different shifts in location and scale parameters, the proposed control chart outperforms other charts in terms of both economic and statistical criteria.

A New EWMA Loss Control Chart with Adaptive Control Scheme

A single chart, instead of and R charts or and S charts, to simultaneously monitor the process mean and variability would reduce the required time and effort. A number of studies have attempted to find such charts. Moreover, a number of studies demonstrated that the adaptive control charts may detect process shifts faster than the fixed control charts. This paper proposes the EWMA loss chart with variable sample sizes and sampling intervals (VSSI) to effectively monitor the difference of process measurements and target. An example is used to illustrate the application and performance of the proposed control chart in detecting the changes in the difference of the process measurements and target. Numerical analyses demonstrated that the VSSI EWMA loss chart outperforms the fixed sampling interval EWMA average loss chart and the Shewhart joint and S charts. Therefore, the VSSI EWMA loss chart is recommended.