Control chart for generalized exponential distribution based on modified chain sampling

In recent years, modern statistical process control has established higher concentration, and this approach is reinforced by new control charts to efficiently monitor the process. The goal of this article is to create a control chart based on a modified chain sampling plan (MchSP) when product quality dimensions are followed by a generalized exponential distribution. There was a brief overview of the generalized exponential distribution (GED) and the modified chain sampling strategy. The chart parameters were presented for several sample sizes at various average run length (ARL) values. A variety of tables were provided for the actual application of the produced control chart in industrial applications at various shift values of scale and form parameters. The real data set was used to demonstrate the application of the created MchSP control chart process. In addition, the proposed MchSP control chart process was developed using simulated data. The average run length (ARL) results of the established control chart for shifting both scale and shape parameters were computed for various sample sizes. The results show that when the shift constant (both scale and form) increases, the ARL values decrease. Also, it was discovered that ARL1 values tend to decrease as the shape parameter value increases.