Wortham and Baker proposed the MDS sampling in quality control charts. Recently, researchers focused on multiple dependent state (MDS) sampling in the creation of a control chart. Several researchers have developed diversified sampling designs to obtain more efficient control charts. Mohammed, Mohammed and Laney, and Aslam et al. Santiago and Smith used transformation given by Johnson and Kotz and Nelson. The works on the control charts for the gamma distribution are presented by Al-Oraini and Rahim, Jearkpaporn et al. For skewed data, the gamma distribution is widely used. Numerous researchers concentrate on quality characteristic understudy which follows a nonnormal distribution or transformed into normality to apply Shewhart type control charts. The waiting time of an event, for example, can be represented by a gamma distribution as in. Nevertheless, these assumptions may not be true for various realistic situations and other distributions away from normality had been considered and discussed by many authors in the literature (e.g., see ). Usually, control charts are being designed and operating under the assumption of the normality for the variable of interest. More details about Shewhart control charts can be seen in Montgomery. This control charting helps to avoid nonconforming products from being manufactured by the company. The main feature of control charting is to identify the amount of assignable cause(s) and hence rectify it by taking necessary action on the production process before sending the outcome of the products into the market. Walter during 1920s in Bell Telephone Laboratories, wide varieties of control chart techniques have been constructed and extensively implemented in SQC. One of the important techniques for improving manufactured product quality and for reducing the manufacturing costs is statistical quality control (SQC). A case study with real-life data from ICU intake to death caused by COVID-19 has been incorporated for the realistic handling of the proposed control chart design. The proposed gamma control chart performs better than the existing multiple dependent state sampling (MDS) based on gamma distribution and traditional Shewhart control charts in terms of average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS sampling is explored using simulation for various shift size changes in scale parameters to study the performance of the control chart. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions.
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