A variable parameters auxiliary information based quality control chart with application in a spring manufacturing process: The Markov chain approach

Abstract

In this paper, a new variable parameters chart for the process mean with a statistic that integrates information from the study and auxiliary variables is proposed. The proposed variable parameters chart with auxiliary information (AI) (abbreviated as VP-AI) is optimally designed to minimize the out-of-control steady-state (i) average time to signal (ATS₁) and (ii) expected average time to signal (EATS₁) values when the mean shift sizes are known and unknown, respectively. The Markov chain approach is adopted to derive the formulae of the performance measures ATS₁, standard deviation of the time to signal (SDTS₁) and EATS₁. The VP-AI chart significantly outperforms the standard VP chart; thus, justifying the incorporation of auxiliary information to enhance the ability of the VP chart. The VP-AI chart is also compared with the Shewhart AI, synthetic AI, exponentially weighted moving average (EWMA) AI, run sum AI and variable sample size and sampling interval (VSSI) AI charts. The VP-AI chart significantly outperforms the Shewhart AI, synthetic AI and VSSI AI charts for all levels of shifts. Meanwhile, the VP-AI chart outperforms the EWMA AI and run sum AI charts for most shifts. The VP-AI chart is found to be more robust than the EWMA-AI chart when the correlation coefficient is misspecified or the bivariate normality assumption is violated as long as the size of the shift is moderate or large. A real application which monitors spring elasticity is used to illustrate the VP-AI chart’s implementation.

Keywords:

• control chart
• variable parameters
• auxiliary information
• average time to signal
• expected average time to signal

Acknowledgments

This research is supported by the Kementerian Pendidikan Malaysia, Fundamental Research Grant Scheme, number 203.PMATHS.6711603.

Additional information

Notes on contributors

Nger Ling Chong

Nger Ling Chong was a PhD student in Statistics in the School of Mathematical Sciences, Universiti Sains Malaysia (USM). She obtained her Bachelor of Applied Science (majoring in Applied Statistics) degree in 2015 and MSc in Statistics in 2016, both from USM. Her research interest is in Statistical Quality Control.

Michael B. C. Khoo

Michael B. C. Khoo is a professor in the School of Mathematical Sciences, USM. He received his PhD in Applied Statistics in 2001 from USM. His research interest is in Statistical Quality Control. He is a member of the American Society for Quality.

Philippe Castagliola

Philippe Castagliola graduated (PhD, 1991) from the UTC (Université de Technologie de Compiégne, France). He is currently a professor at the Université de Nantes, Nantes, France, and a member of the LS2N (Laboratoire des Sciences du Numérique de Nantes), UMR CNRS 6004. He is an Associate Editor for the Journal of Quality Technology, Communications in Statistics (LSTA, LSSP, UCAS), Quality Technology & Quantitative Management and International Journal of Reliability, Quality and Safety Engineering. His research activity includes developments of new Statistical Process Monitoring techniques.

Sajal Saha

Sajal Saha is an associate professor in the Department of Mathematics, International University of Business Agriculture and Technology, Dhaka, Bangladesh. He received his PhD in Applied Statistics from USM. He holds a Bachelor of Mathematics and Masters in Applied Mathematics from University of Dhaka, Bangladesh. His research interest is in Statistical Quality Control.

Faijun Nahar Mim

Faijun Nahar Mim is a PhD student in Statistics in the School of Mathematical Sciences, USM. She holds BSc and MSc degrees in Statistics from Jahangirnagar University, Dhaka, Bangladesh. Her research interest is in Statistical Quality Control.