Determination of Bayesian optimal warranty length under Type-II unified hybrid censoring scheme

ABSTRACT

We consider determination of optimal warranty length for the combined free replacement and pro-rata warranty (FRW-PRW) policy based on the Type-II unified hybrid censored data by Bayesian approach. A non-linear pro-rata rebate cost function is proposed based on which warranty cost is computed. It is assumed that the lifetime follows log normal distribution. The optimal warranty length is obtained by maximizing an expected utility function consisting of three cost functions such as economic benefit function, warranty cost function and dissatisfaction cost function. The expectation is taken with respect to the posterior predictive model for the time-to-failure data. It is observed that the non-linear pro-rata rebate cost function gives a larger warranty length with maximum profit as compared to linear pro-rata rebate cost function. A real-data set is analyzed in order to illustrate the proposed methodology of finding optimal warranty length.

KEYWORDS:

• FRW-prw policy
• log-normal distribution
• prior distribution
• optimal warranty length

Acknowledgments

The authors thank an associate editor and four anonymous reviewers for his/her critical comments and helpful suggestions, which have resulted in an improvement over the earlier version of the manuscript.

Disclosure statement

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

Additional information

Notes on contributors

Tanmay Sen

Tanmay Sen is currently working as a data scientist at Ericsson Kolkata. He received his BSc (Hons) and MSc degrees in mathematics from the University of Calcutta in 2009 and 2011, respectively, and his MTech in mathematics and computing and PhD in statistics from the Indian Institute of Technology Patna in 2014 and 2019, respectively. His research interests are machine learning, deep learning, federated learning, optimization, and censored life testing experiments.

Ritwik Bhattacharya

Ritwik Bhattacharya is an assistant professor at Tecnologico de Monterrey, School of Engineering and Science, Mexico. He received the B.Sc. degree in mathematics from the University of Calcutta, India, in 2006, and the M.Sc. degree in mathematics from IIT Kharagpur, India, in 2008, and the Ph.D. degree in Quality, Reliability, and Operations Research (QROR) from the Indian Statistical Institute, Kolkata, India, in 2016.  His research interests include inference based on censored data, reliability, survival analysis, and statistical quality control.

Biswabrata Pradhan

Biswabrata Pradhanis currently a Professor at the Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, Kolkata. He received his BSc (Hons) and MSc degrees in Statistics from the University of Calcutta and his MTech in Quality, Reliability, and Operations Research (QROR) and PhD in statistics from the Indian Statistical Institute. His research interests include inference based on censored data, design of censored life testing experiments, reliability theory, and survival analysis.

Yogesh Mani Tripathi

Yogesh Mani Tripathi received his Ph.D. degree from the Department of Mathematics, IndianInstitute of Technology Kharagpur, India, under the guidance of Prof. Somesh Kumar. He was aPostdoctoral Fellow with Prof. Éric Marchand with the Department of Mathematics at Universityof Sherbrooke, Canada and with G. S. Shieh at Institute of Statistical Science, Academia Sinica,Taiwan. Currently, he is an Associate Professor with the Department of Mathematics, IndianInstitute of Technology Patna, India. His research interests are in decision theory, life-testing andreliability analysis.