The Performance of Triple Sampling X Control Chart with Measurement Errors

ABSTRACT

The presence of measurement errors can seriously alter the statistical performance of Phase II control charts. Up today, no research on designing the triple sampling control charts taking into account the gauge measurement errors is reported in the existing literature. In this paper, we study the adverse effect of measurement errors on detecting performance of triple sampling (TS)-$\bar{X}$ control chart based on an additive covariate model. Three multiple measurement based triple sampling (MMBTS) schemes are developed to reduce the undesired impact of gauge inability on detecting performance of TS-$\bar{X}$ chart. Through simulation studies in terms of average run length (ARL) and standard deviation of run length (SDRL), it is indicated that the run length characteristics of the TS-$\bar{X}$ is significantly affected by the measurement errors. The results also confirm that all proposed remedial approaches can effectively reduce the undesired impact of imprecise measurements on performance of TS-$\bar{X}$ chart. A sensitivity analysis is also carried out to evaluate how the covariate model parameters affect the detection performance of the TS-$\bar{X}$ chart. Finally, using a real industrial data obtained from the spring production system, we demonstrate the performance of TS-$\bar{X}$ chart when the measurement errors exist.

KEYWORDS:

• Multiple measurement based remedial approach
• additive covariate model
• measurement errors
• triple sampling $\bar{X}$ chart
• Run length

Disclosure statement

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

Additional information

Notes on contributors

Mohammad Reza Maleki

Mohammad Reza Maleki is an Assistant Professor of Industrial Engineering at Golpayegan College of Engineering in Isfahan University of Technology. His research interests include statistical process monitoring, profile monitoring, and reliability engineering. He has been the author or co-author of many papers published in high-ranked journals such as Computers and Industrial Engineering, Quality and Reliability Engineering International, Journal of Statistical Computation and Simulation, Communications in Statistics–Simulation and Computation, Communications in Statistics–Theory and Methods, Transactions of the Institute of Measurement and Control, Journal of Industrial and Business Economics, Arabian Journal for Science and Engineering, Journal of Advanced Manufacturing Systems, International Journal of Modeling and Simulation and Scientia Iranica.

Ali Salmasnia

Ali Salmasnia is currently an Associate Professor of Industrial Engineering in University of Qom, Qom, Iran. His research interests include quality engineering, reliability, applied multivariate statistics and multi-criterion decision making. He is the author or co-author of various papers published in Journal of Manufacturing Systems, Computers and Industrial Engineering, Applied Soft Computing, Neurocomputing, Applied Mathematical Modelling, Expert Systems with Applications, Quality Technology and Quantitative Management, Journal of Information Science, Neural Computing and Applications, Applied Stochastic Models in Business and Industry, IEEE Transactions on Engineering Management, International Journal of Information Technology and Decision Making, Operational Research, TOP, Quality and Reliability Engineering International, Journal of Statistical Computation and Simulation, International Journal of Advanced Manufacturing Technology, Communications in Statistics-Simulation and Computation, Arabian Journal for Science and Engineering, Journal of Industrial and Business Economics, International Journal of Modeling and Simulation, and Scientia Iranica.

Shayesteh Yarmohammadi Saber

Shayesteh Yarmohammadi Saber has obtained her BS and MS degrees in Industrial Engineering from University of Eyvanekey. Her research interests are statistical process monitoring and multi-criteria decision making.