Triple sampling X̄ control chart for gamma process

Monitoring production processes to provide potential customers with quality products while utilising fewer resources and reducing the cost of inspection is a challenge to quality and industrial engineers. Aiming at developing an improved design using reduced sample sizes, this study proposes a triple sampling (TS) $ \bar{X} $ X¯ chart to monitor shifts in the process mean when the quality characteristic of interest follows the gamma distribution. Optimal parameters are determined by employing three optimisation procedures. The detection ability of the TS $ \bar{X} $ X¯ chart is evaluated and contrasted with competing charts via the average number of observations to signal (ANOS), average run length (ARL) and expected ANOS (EANOS) criteria. When the TS $ \bar{X} $ X¯ chart is designed for detecting small and large shifts, it is noticed that the sample sizes at the first, second and third sampling stages are larger for detecting small shifts. Compared to its competitors, the TS $ \bar{X} $ X¯ chart requires fewer observations on the average to signal a shift; hence, it uses resources more efficiently and incurs lower inspection costs. To aid in the implementation of the TS $ \bar{X} $ X¯ chart, an illustrative example of monitoring the wafer process is provided. Overwhelming evidence based on reported results supports the TS $ \bar{X} $ X¯ chart.