Revised triple sampling X̄ control charts for the mean with known and estimated process parameters

ABSTRACT

The primary aim of this research is to propose a revised triple sampling (TS) $\overline{X}$ chart, where the derivations of new formulae for computing the average run length of the triple sampling (TS) $\overline{X}$ chart correctly are provided. The secondary aim is to develop the revised TS $\overline{X}$ chart with estimated process parameters. The revised TS $\overline{X}$ charts are compared with the double sampling (DS) $\overline{X}$, two stage adaptive sample size (AS₂) $\overline{X}$ and three stage adaptive sample size (AS₃) $\overline{X}$ charts when process parameters are known and estimated using the average run length (ARL), average number of observations to signal (ANOS), average of the average run lengths (AARL), standard deviation of the average run lengths (SDARL), average of the average number of observations to signal (AANOS) and standard deviation of the average number of observations to signal (SDANOS) criteria, where the revised TS $\overline{X}$ charts are found to be superior. Additionally, a table giving the minimum number of Phase-I samples for estimating the process mean so that the revised TS $\overline{X}$ chart with estimated process parameters has the desired in-control AARL and AANOS performances is provided.

KEYWORDS:

• Control charts
• triple sampling
• double sampling
• known process parameters
• estimated process parameters

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the Universiti Sains Malaysia, Research University [grant number 1001.PMATHS.8011039].

Notes on contributors

Faijun Nahar Mim

Faijun Nahar Mim is a Ph.D. student in Statistics in the School of Mathematical Sciences, Universiti Sains Malaysia (USM). She holds a B.Sc. and M. Sc. in Statistics from Jahangirnagar University, Dhaka, Bangladesh. 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, Universiti Sains Malaysia. He specialises in Statistical Quality Control. He has published numerous papers in International journals indexed in the Web of Science (WoS) database. He has also reviewed numerous papers for journals indexed in the WoS database. He is a member of the American Society for Quality.

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 Ph.D. in Applied Statistics from Universiti Sains Malaysia (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.

Philippe Castagliola

Philippe Castagliola graduated (Ph.D. 1991) from UTC (Université de Technologie de Compiègne, France). He is currently a professor at the Université de Nantes, Nantes, France, and he is also 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.