Optimal repetitive reliability inspection of manufactured lots for lifetime models using prior information

Abstract

Repetitive group inspection of production lots is considered to develop the failure censored plan with minimal expected sampling effort using prior information. Optimal reliability test plans are derived for the family of log-location-scale lifetime distributions, whereas a limited beta distribution is assumed to model the proportion nonconforming, p. A highly efficient and quick step-by-step algorithm is proposed to solve the underlying mixed nonlinear programming problem. Conventional repetitive group plans are often very effective in reducing the average sample number with respect to other inspection schemes, but sample sizes may increase under certain conditions such as high censoring. The inclusion of previous knowledge from past empirical results contributes to drastically reduce the amount of sampling required in life testing. Moreover, the use of expected sampling risks significantly improves the assessment of the actual producer and consumer sampling risks. Several tables and figures are presented to analyse the effect of the available prior evidence about p. The results show that the proposed lot inspection scheme clearly outperforms the standard repetitive group plans obtained under the traditional approach based on conventional risks. Finally, an application to the manufacture of integrated circuits is included for illustrative purposes.

Keywords:

• Expected producer and consumer risks
• expected average sample number
• log-location-scale lifetime distribution
• limited beta prior model
• repetitive lot inspection

Acknowledgments

The authors would like to thank Associate Editor and two anonymous referees for their valuable comments and suggestions, which have significantly improved this paper.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported under the grant number PID2019-110442GB-I00 funded by MCIN/AEI/10.13039/501100011033.

Notes on contributors

Carlos J. Pérez-González

Carlos J. Pérez-González is an Associate Professor in the Department of Mathematics, Statistics and Operational Research and is a member of the Institute of Mathematics and Applications of the University of La Laguna (ULL) in Spain. He received his Ph.D. in 2009 and he has worked with several businesses and public sectors. His main areas of expertise include reliability analysis and acceptance sampling in quality control with a special emphasis on optimisation problems in designing inspection plans. Other research interests are in the fields of biostatistics and computation.

Arturo J. Fernández

Arturo J. Fernández is currently the coordinator of the consolidated research group ‘Statistics’ of the University of La Laguna (Tenerife, Canary Islands, Spain), as well as a member of the Department of Mathematics, Statistics and Operational Research and the Institute of Mathematics and Applications. Prof. Fernández is the principal investigator of a national research project on statistical inference, quality control and industrial reliability. He is an academic editor of the journal Mathematical Problems in Engineering (Hindawi, Wiley) and has also served as reviewer for over fifty international journals. His major research interests include reliability and quality control, survival analysis, Bayesian inference, statistical decision theory, and censoring methodology. He is the author and co-author of more than 60 articles published in major journals, including, among others, IEEE Transactions on Reliability, Computers & Industrial Engineering, Journal of Computational and Applied Mathematics, European Journal of Operational Research, Applied Mathematical Modelling, International Journal of Advanced Manufacturing Technology and Computational Statistics & Data Analysis.

Vicent Giner-Bosch

Vicent Giner-Bosch holds a Ph.D. in Statistics, Operational Research and Quality. He works as an Assistant Professor at the Universitat Politècnica de València, Spain, and he is also an invited lecturer at the École Supérieure d'Ingénieurs en Génie Électrique, France. He has taken part in several research projects with national and European funding. Furthermore, he has published and has also acted as a reviewer for some high-impact scientific journals. His current research is focused on optimisation in quality control and engineering and on clinical biostatistics.

Andrés Carrión-García

Andrés Carrión is Ph.D. in Industrial Engineering, and associate professor at the Department of Applied Statistics, OR and Quality in the Universitat Politècnica de València (Spain). He has been head of this Department during 2001–2010, and now he is Director of the research Centre for Quality and Change Management. His research has been oriented mainly to the use of statistical tools in different fields of knowledge (education, quality control, reliability …) and quality management, including quality and management in higher education institutions. He has participated in different international projects related to higher education. He is a senior member of the American Society for Quality (ASQ).