Joint statistical design of double sampling X¯ and s charts

In statistical quality control, usually the mean and variance of a manufacturing process are monitored jointly by two statistical control charts, e.g., a X¯ chart and a R   chart. Because of the efficiency of double sampling (DS) X¯ charts in detecting shifts in process mean and DS s   charts in process standard deviation it seems reasonable to investigate the joint DS X¯ and s   charts for statistical quality control. In this paper, a joint DS X¯ and s   chart scheme is proposed. The statistical design of the joint DS X¯ and s   charts is defined and formulated as an optimization problem and solved using a genetic algorithm. The performance of the joint DS X¯ and s   charts is also investigated. The results of the investigation indicate that the joint DS X¯ and s   charts offer a better statistical efficiency in terms of average run length (ARL) than combined EWMA and CUSUM schemes, omnibus EWMA scheme over certain shift ranges when all schemes are optimized to detect certain shifts. In comparison with the joint standard, two-stage samplings and variable sampling size X¯ and R charts, the joint DS charts offer a better statistical efficiency for all ranges of the shifts.