Testing capability index C_pk with its application in automobile engine manufacturing industry

Abstract

Hypotheses testing is an effective technique for making a decision about the process capability. The adversity to test $C_{pk}$ based on determining the distribution of its natural estimator is very complex, even under the Normal distribution. Thus, the Monte Carlo simulation approach is an executable procedure for the hypotheses testing of $C_{pk}$ based on the natural estimator. The proposed approach is a testing technique to evaluate whether products quality meets the preset specification limits. This procedure implies a Monte Carlo statistical test, which is applicable to Normal processes. A case study in an automobile factory is presented to check out the products, and numerical computations are presented to show the effect of the Monte Carlo critical values for making a reliable decision on the hypotheses testing of $C_{pk}.$

Keywords:

• capability analysis
• critical value
• hypotheses testing
• Monte Carlo simulation

Acknowledgments

The authors would like to thank anonymous referees for their constructive comments which significantly improved the presentation of this paper.

Additional information

Funding

This research was supported by a grant from Ferdowsi University of Mashhad 10.13039/501100003121; No. 2/57565.

Notes on contributors

Hamideh Iranmanesh

Hamideh Iranmanesh was born at Kerman in the south part of Iran in 1989. She received his BSc (2011), MSc (2014) in Statistics from Shahid Bahonar University of Kerman (SBUK). Currently, she is a PhD student at Ferdowsi University of Mashhad in Iran. Her current research focuses on Statistical Quality Control, Fuzzy Quality, Process Capability Indices, Statistical Testing of Hypotheses, etc. [email protected]

Abbas Parchami

Dr. Abbas Parchami was born at Mashhad in the north-eastern part of Iran in 1977. He received his BSc (2001), MSc (2004) and PhD (2015) in Statistics from Ferdowsi University of Mashhad, Shahid Bahonar University of Kerman (SBUK) and Ferdowsi University of Mashhad, respectively. He is currently working as an Associate Professor of Statistics at the Department of Statistics of SBUK. His research interests include Statistical Simulation, Fuzzy Statistics, Data Mining, Decision Making and Quality Control. [email protected]

Mehdi Jabbari Nooghabi

Dr. Mehdi Jabbari Nooghabi obtained his master's degree in mathematical statistics at Ferdowsi University of Mashhad in 2002 and he received his Ph.D. from university of Mumbai in 2011. Currently, he is Associate Professor at Ferdowsi University of Mashhad. His current research focuses on, Inference in the presence of Outliers, Applied Statistics, Statistical Quality Control, Data Science, etc. [email protected]