In recent years, researchers introduced several distribution-free schemes for simultaneously monitoring the location and scale parameters of distribution in the literature related to process monitoring and control. To this end, the Shewhart-Lepage (SL) and Shewhart-Cucconi (SC) schemes are two fundamental distribution-free schemes. These schemes are primarily designed to monitor the location-scale family of densities. In practice, apart from the location and scale parameters, we often encounter the presence of a shape (or skewness) parameter. In this article, we investigate the performance of the SL and SC schemes in monitoring such models. We consider some skewed distributions in the location-scale family with one or two additional parameters, some three-parameter time-to-event processes, such as three-parameter Weibull and Gamma, which are very common in various measurement and control literature. First, we present the in-control performance of the two competing schemes and then carry out a comprehensive out-of-control performance study by considering different combinations of shifts. Several recent investigations showed that the SC scheme performs just as well or better than the SL scheme in joint monitoring of the location and scale parameters for a large number of process distributions. The current study shows that in the presence of an additional parameter, especially when the shift in the shape parameter is substantial, the SL scheme is better; for a small change in shape, the SC scheme is more competitive. In general, the SL scheme performs better in monitoring the three-parameter distributions for time-to-event processes. Finally, a real application and some concluding remarks are presented.

中文翻译：

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无分布的 Shewhart 型 Lepage 和 Cucconi 方案在监控复杂过程分布中的性能比较

近年来，研究人员在与过程监测和控制相关的文献中引入了几种用于同时监测分布的位置和尺度参数的无分布方案。为此，Shewhart-Lepage (SL) 和 Shewhart-Cucconi (SC) 方案是两种基本的无分配方案。这些方案主要设计用于监测位置尺度的密度族。在实践中，除了位置和尺度参数之外，我们经常会遇到形状（或偏度）参数的存在。在本文中，我们研究了 SL 和 SC 方案在监控此类模型方面的性能。我们考虑位置尺度系列中的一些偏态分布，带有一两个附加参数，一些三参数时间到事件过程，例如三参数 Weibull 和 Gamma，这在各种测量和控制文献中非常常见。首先，我们介绍了两种竞争方案的控制性能，然后通过考虑不同的班次组合进行全面的失控性能研究。最近的几项调查表明，在联合监测大量过程分布的位置和尺度参数方面，SC 方案的性能与 SL 方案一样好或更好。目前的研究表明，在存在附加参数的情况下，特别是当形状参数的变化很大时，SL 方案更好；对于形状的微小变化，SC方案更具竞争力。一般来说，SL 方案在监视时间到事件过程的三参数分布方面表现更好。最后，