Enhanced distribution-free Cucconi schemes based on runs: An application to the surveillance of daily average customer service time

The measurement of daily average customer service times in a service centre holds paramount importance as it serves as a key metric for assessing service performance and quality. It is essential to ensure that the average service time (AST) aligns with predetermined quality standards. Hence, regular monitoring of service times is vital to uphold and enhance service quality. This study proposes two enhanced distribution-free Cucconi schemes integrated with runs rules (RR), i.e., the 2-of-3 (2/3) RR Cucconi and the synthetic Cucconi schemes. The practical utility of these proposed schemes is illustrated through an application in the surveillance of the daily average customer service time at an Australian service centre. The inherent nonparametric feature of these schemes renders them versatile in a wide range of applications, regardless of the underlying process distribution. In addition, these newly devised schemes possess the capability to surveil both process location and scale parameters simultaneously. Through comprehensive Monte-Carlo simulations, we demonstrate the superior performance of the 2/3 RR Cucconi scheme against four existing schemes, namely the Shewhart-Lepage, 2/3 RR Lepage, synthetic Lepage, and Shewhart-Cucconi schemes. Therefore, the 2/3 RR Cucconi scheme is recommended over all competing schemes considered in this paper due to its excellent performance and ease of use.