ABSTRACT

Advancement in technology brings a revolutionary change in the quality of the final product or items. Most of the manufacturing processes produce a large number of conforming items along with a few non-conforming items. For real-time monitoring of these highly efficient processes, monitoring of time-between-events is a well-known approach adopted in the literature of statistical process control. Usually, it is assumed that the time-between-events follows an exponential or gamma distribution. However, the generalized gamma distribution is the most popular choice for modelling skewed data. In this article, we consider a two-sided monitoring scheme based on the generalized gamma distribution. Two-sided monitoring schemes for skewed distributions often encounter bias in its run length properties. Therefore, we address this problem with modified control limits in a more general distributional setup. A Monte Carlo simulation-based study is designed, and results showed encouraging performance properties. A couple of practical applications in connection to monitoring renewable energy and coal mine explosions have been discussed.

摘要

技术的进步给最终产品或物品的质量带来了革命性的变化。大多数制造过程会产生大量合格品和少量不合格品。对于这些高效过程的实时监控，事件间隔时间的监控是统计过程控制文献中采用的一种众所周知的方法。通常，假设事件之间的时间遵循指数或伽马分布。然而，广义 Gamma 分布是对偏斜数据建模的最流行选择。在本文中，我们考虑基于广义伽马分布的两侧监测方案。偏斜分布的两侧监测方案在其运行长度属性中经常遇到偏差。所以，我们在更一般的分布设置中通过修改控制限制来解决这个问题。设计了一项基于蒙特卡罗模拟的研究，结果显示出令人鼓舞的性能特性。讨论了与监测可再生能源和煤矿爆炸有关的几个实际应用。