Double exponentially weighted moving average control chart with supplementary runs-rules

ABSTRACT

Enhancing the sensitivity of control charts for detecting small process shift is desirable and may be done in different ways. In this paper, we propose the double exponentially weighted moving average (DEWMA) control chart using the 2-of-2 and 1-of-1 or 2-of-2 runs-rules schemes for monitoring process mean shifts. The performances of the resulting control schemes are investigated in terms of the average run-length ($ARL$), standard deviation of the run-length ($SDRL$) and selective percentiles of the run-length ($PRL$). In addition, the overall performance of the proposed runs-rules charts are examined and compared with those of the existing charts in terms of the $ARL$, average extra quadratic loss ($AEQL$), average ratio of the average run-length ($ARARL$) and performance comparison index ($PCI$) values. It is observed that the proposed control schemes are more efficient in many situations and improve the ability of the existing DEWMA schemes in detecting small, moderate and large mean shifts.

KEYWORDS:

• Runs-rules
• DEWMA ͞X control chart
• enhanced scheme
• asymptotic control limits
• exact control limits
• quality loss function

Nomenclature

Table

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Olatunde A. Adeoti

Olatunde A. Adeoti obtained his B.Sc (Hons) degree (First class honours) in Mathematics from the University of Ilorin, M.Sc. (Statistics) from the University of Lagos and PhD in Statistics from the University of Ilorin, Ilorin, Nigeria. He has articles that have been published or accepted for publication in Quality Engineering, Quality and Reliability Engineering International, Communications in Statistics—Theory and Methods, International Journal of Quality and Reliability Management. He is a member of the Nigerian Statistical Association, American Society for Qualityand the American Statistical Association. His research interest include Statistical Process Control, StatisticalQuality Control and Management in Healthcare, and Artificial Neural Network in Statistical Process Control. He is currently a Senior Lecturer at the Department of Statistics, Federal University of Technology, Akure, Nigeria.

Jean-Claude Malela-Majika

Jean-Claude Malela-Majika has a PhD in Statistics from the University of South Africa, South Africa. He is a member of the South African Statistical Association, the International Statistical Institute (ISI) and the High Education Learning and Teaching Association of South Africa (HELTASA). His principal research interests include Statistical Process / Quality Control, Distribution Theory and Statistical Inference.