Side sensitive group runs t chart and its application in manufacturing

Abstract

A setback of the $\overline{X}$ type charts is that they signal out-of-control when the process standard deviation is not stable, i.e., they are not robust against estimation errors or changes in the process standard deviation. Thus, the t type charts were introduced to overcome this setback. In this study, the side sensitive group runs (SSGR) t chart is proposed for monitoring the process mean. The implementation, optimal designs and performance of the proposed SSGR t chart are discussed. The average run length (ARL) and expected ARL (EARL) criteria are used to evaluate and compare the performance of the proposed SSGR t chart with that of the existing synthetic (Syn) t, exponentially weighted moving average (EWMA) t and run sum (RS) t charts. Results show that the SSGR t chart outperforms the Syn t chart for all sizes of mean shifts, while the EWMA t and RS t charts are better for small shifts. A real manufacturing example is used to illustrate the implementation of the proposed SSGR t chart.

Keywords:

• Average run length
• expected average run length
• group runs
• side sensitive group runs
• t chart

Additional information

Funding

This work is supported by Miyan Research Institute, International University of Business Agriculture and Technology, Dhaka, Bangladesh.