Efficient monitoring of exponential processes using memory control charts for healthcare applications

Currently, assessing the efficiency of memory control charts both in zero-state (ZS) and steady-state (SS) contexts is a burning issue in the statistical process control (SPC). In certain cases, a memory control chart may demonstrate exceptional performance in the ZS while underperforming in the SS, and researchers assert the superiority of their proposed chart solely based on its ZS performance. Recent research indicates that a control chart receives priority over alternative control charts if it has both superior ZS and SS performances. Keeping in mind, this paper presents the design of two novel cumulative sums (CUSUM) and crosier CUSUM (CCUSUM) control charts termed $$\:{\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$ and $$\:{\text{C}\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$incorporating variable transformation based on the assumption of exponential distribution aimed at improving process monitoring in both ZS and SS conditions. The results of the study are derived using the Monte Carlo simulation approach. A number of different metrics are utilized using a variety of indicators. These metrics include the average and standard deviation of run length (RL) denoted by ARL and SDRL. Similarly, the performance comparison index (PCI), relative ARL (RARL), and extra quadratic loss (EQL) are also used as performance indicators. The suggested $$\:{\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$ and $$\:{\text{C}\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$ charts are contrasted with the rival charts using these performance metrics. According to the results, the suggested control charts are more effective than other control charts when it comes to detecting shifts quickly in ZS and SS. Breast cancer (BS) and urinary tract infection (UTI) are the burning issues in the healthcare monitoring and their early monitoring is very beneficial for treatment. As a last step towards putting the suggested $$\:{\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$ and$$\:\:{\text{C}\text{C}\text{U}\text{S}\text{U}\text{M}}_{\text{E}}$$ control chart into practice, two examples originating from breast cancer and urinary tract infection are also included.