Redesigning the Omnibus SPRT Control Chart for Simultaneous Monitoring of the Mean and Dispersion of Weibull Processes

Quality control charts play an important role in distinguishing between abnormal variations and normal variations of a manufacturing process. Generally, unusual variations in a process may arise due to a change in its mean or dispersion, or a simultaneous change in both parameters. In recent literature, the omnibus sequential probability ratio test (OSPRT) control chart has been proven effective for detecting joint shifts in both the process mean and variability. However, one limitation of the proposed scheme lies in its absolute dependence on the validity of the normality assumption, which may not apply to many quality data, such as machine failure times, the strength of plant fibres, etc. In this research, we critically analyze the performances of the OSPRT chart designed for the Normal distribution, in the case where quality data follow the well-known Weibull distribution. Our findings reveal that the in-control average run length and standard deviation of the run length of the OSPRT chart are significantly compromised due to the positive skewness of the Weibull distribution. As a means of tackling the problem, the skewness correction design has been proposed to correct the control limits of the OSPRT chart. The corrected OSPRT chart is found to produce a more satisfactory in-control performance, with an acceptable decline in its sensitivity towards small process shift sizes.