Control charts for processes with variable mean

  • Mohammad Saber Fallahnezhad Department of Industrial Engineering, Yazd University
  • Farideh Sadeghi Department of Industrial Engineering, Science and Art University
  • Amir Ghalichehbaf Department of Industrial Engineering, Yazd University
Keywords: variable mean, Shewhart control chart, control limits, first type error


Despite of strong ability and performance of control charts to control and monitor processes, they have some problems in practical applications. If control chart’s limits are not properly designed then we receive false alarms. For example, several observations may be outside the control limits when the mean of process is in-control. Not considering the variation of the process mean at each sampling time may lead to this error. The process may be adjusted at specific mean but different working conditions and different operators may change mean of the process and it may have a small deviation from its predetermined value and this problem can lead to wrong implementation of control charts. In this paper, the effects of variable mean on control charts are analyzed. It is assumed that the mean of observation varies over time but its probability distribution is normal probability distribution function. It is observed that long-term process mean control chart generates false alarms.


Montgomery DC. Introduction to Statistical Quality Control, 5th ed. Wiley; 2004. 776p.

Shewhart WA. Economic Control of Quality of Manufactured Product. D. van Nostrand Company, Inc.; 1931.

Ryan TP. Statistical Methods for Quality Improvement, 2nd ed. Wiley-Interscience; 2000. 592p.

Brown TD. Determining lumber target size and monitoring sawing accuracy. Forest Products Journal 1979; 29(4): 48–54.

Senturk S, Erginel N. Development of fuzzy -R and -S control charts using α-cut. Information Sciences 2009; 179(10): 1542–1551. doi: 10.1016/j.ins.2008.09.022

Lee PH. Adaptive R charts with variable parameters. Computational Statistics & Data Analysis 2011; 55(5): 2003–2010. doi: 10.1016/j.csda.2010.11.026

Torng CC, Lee PH, Liao NY. An economic-statistical design of double sampling control chart. International Journal of Production Economics 2009; 120(2): 495–500. doi: 10.1016/j.ijpe.2009.03.013

Schilling EG, Nelson PR. The effect of non-normality on the control limits of charts. Journal of Quality Technology 1976; 8(4): l83–188. doi: 10.1080/00224065.1976.11980743

Fallah Nezhad MS, Akhavan Niaki ST. A new monitoring design for uni-variate statistical quality control charts. Information Sciences 2010; 180(6): 1051–1059. doi: 10.1016/j.ins.2009.11.033

Malindzakova M, Culková K, Trpcevská J. Shewhart control charts implementation for quality and production management. Processes 2023; 11(4): 1246. doi: 10.3390/pr11041246

Nagar H. A review on statistical quality control. NeuroQuantology 2022; 20(9): 637–642. doi: 10.14704/nq.2022.20.9.NQ440070

Triantafyllou IS, Ram M. Distribution-free CUSUM-type control charts for monitoring industrial processes: An overview. International Journal of Mathematical, Engineering and Management Sciences 2021; 6(4): 975–1008. doi: 10.33889/IJMEMS.2021.6.4.058

Brown AR. The alternative distribution of the non-parametric extended median test CUSUM chart for multiple stream processes. Communications in Statistics—Theory and Methods 2022; 51(16): 5750–5761. doi: 10.1080/03610926.2020.1850792

Original Research Article