A re-evaluation of the run rules xbar chart when the process parameters are unknown

ABSTRACT

Run Rules $\bar{X}$ chart are often implemented for process monitoring. The process observations are usually assumed normally distributed, and the process parameters are assumed known. In fact, a very limited number of Phase I samples may only be available to the practitioners to estimate the process parameters, the control chart's properties will vary among different practitioners. Considering this variability, the performance of the Run Rules $\bar{X}$ chart with estimated parameters is investigated. To measure this variability, the standard deviation of average run length (SDARL) is used to evaluate the performance of control chart. The results show that the Run Rules $\bar{X}$ chart requires a much larger amount of Phase I data to sufficiently reduce the between-practitioners variability. Moreover, we also investigate the properties of Run Rules $\bar{X}$ chart with estimated parameters under the non-normal distributed data. Due to the limitation of the amount of Phase I data set in practice, a bootstrap method is applied to design the Run Rules $\bar{X}$ chart. Finally, an example is provided to illustrate the application of the Run Rules $\bar{X}$ chart with estimated parameters.

KEYWORDS:

• Average average run length
• estimated parameters
• Run Rules chart
• standard deviation of average run length
• the bootstrap method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by  National Natural Science Foundation of China[71802110]; Natural Science Foundation of JiangSu Province[BK20170894]; Humanity and Social Science Youth foundation of Ministry of Education of China[17YJC630043]; Nanjing University of Posts and Telecommunications [NYY217007;NY218041];

Notes on contributors

XueLong Hu

Xuelong Hu is currently an assisant professor  in the School of Management, Nanjing University of Posts and Telecommunications.He received his PhD in Nanjing University of Science and Technology. His research interests are maily focused on the new statistical quality monitoring and active queue management.

Philippe Castagliola

Philippe Castagliola is currently a professor at the Université de Nantes, Institut Universitaire de Technologie deNantes, France, and he is also a member of the LS2N (Laboratoire des Sciences du Numérique de Nantes), UMR CNRS6004. His research activity includes developments of new SPC techniques.