A study on the performances of the run sum X̄ chart under the gamma process

¹ School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, 62200 Putrajaya, Malaysia
² Department of Electronic Engineering, Faculty of Engineering and Green Technology, Universiti Tunku Abdul Rahman, 31900 Perak, Malaysia
³ School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, Currie EH14 4AP, United Kingdom

^* Corresponding author: wei_lin.teoh@hw.ac.uk

Abstract

The run sum (RS) X̄ chart is known as a simple and powerful tool for monitoring the mean of a process. Most developments of the RS X̄ chart assume that the underlying process comes from a normal distribution. However, in practice, many processes tend to follow a non-normal distribution. These non-normal processes affect the performances of control charts under the design of normal distribution. In this paper, we present a detailed analysis on the performances of the RS X̄ chart when the underlying data come from a gamma distribution. By using Monte Carlo simulation approach, the run-length properties, namely the average run length and the standard deviation of the run length will be computed. Particularly, the 4 and 7 regions RS X̄ charts under both distributions are considered. When the charts’ parameters specifically designed for the normal distribution are used to monitor the data from a gamma distribution, simulated results show that RS X̄ charts’ performances are significantly deteriorated. The RS X̄ chart has higher false alarm rates when the underlying distribution is gamma.