Modern and emerging techniques of technology have brought a revolution in quality inspection of products. When events in highly efficient production processes occur rarely, it requires to inspect and monitor the time between occurrence of these events (TBE). The exponential and gamma distributions are commonly used models for time between events (TBE) data. In this article, a new monitoring scheme has been established for TBE data based on exponential and gamma distributions. In a previous research, transformation‐based control charts have been developed for TBE. The proposed study is aimed to use the exact probability distribution of charting statistic rather than applying transformations to data and this has remained still unaddressed. Average run length (ARL) and percentage decrease in ARL (ΔARL) have been calculated using Monte Carlo simulations and the proposed monitoring method has been compared with existing techniques applied to transformed data. The proposed scheme provides a simpler design structure and better performance on different sample sizes in identifying annoying process variations. Further, the technique has been applied to simulated and real‐life data sets of time between manufacturing plant accidents to highlight the worth and particle applicability of the proposed work.

中文翻译：

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事件之间的时间控制图以进行伽玛分布

现代和新兴的技术带来了产品质量检查的一场革命。当高效生产过程中的事件很少发生时，它需要检查和监视这些事件发生之间的时间（TBE）。指数分布和伽马分布是事件之间时间（TBE）数据的常用模型。在本文中，已经针对基于指数和伽马分布的TBE数据建立了新的监视方案。在先前的研究中，已经为TBE开发了基于转换的控制图。拟议的研究旨在使用制图统计的确切概率分布，而不是对数据进行转换，而这一问题仍未解决。已使用蒙特卡罗模拟计算了平均行程长度（ARL）和ARL降低百分比（ΔARL），并将拟议的监测方法与应用于转换数据的现有技术进行了比较。所提出的方案提供了更简单的设计结构，并在识别烦人的过程变化时对不同样本量提供了更好的性能。此外，该技术已应用于制造工厂事故之间的模拟时间和实际数据集，以突出所提议工作的价值和适用性。