Control Charts for Exponentially Distributed Characteristics: SD, ED, ESD with Taguchi’s Loss Function

Abstract

ABSTRACTThis paper addresses the challenge of quality characteristics that follow an exponential distribution, which can significantly impact decision-making in various fields. Existing approaches rely on approximations to convert exponential distributions to normal distributions, upon which control charts are constructed. However, such conversions introduce errors that can lead to incorrect outcomes, particularly for highly sensitive characteristics. To address this limitation, we propose the development of control charts specifically designed for exponential characteristics, without relying on approximations. Our objective is to introduce four different schemes for constructing these control charts: a statistical scheme, an economic scheme, an economic-statistical scheme combined with Taguchi’s loss function, and an economic-statistical scheme without the application of a loss function. To determine optimal design parameter values for each scheme, we employ the artificial bee colony algorithm. Additionally, we conduct a sensitivity analysis to investigate the impact of design parameters on each proposed design. To illustrate the practical implementation of these control charts, we provide a numerical example that demonstrates their effectiveness. By addressing the limitations of existing approaches and offering novel control chart designs, this paper contributes to enhancing decision-making accuracy and reliability in scenarios involving exponentially distributed quality characteristics.