The Predicted Failure on A Two-Dimensional Warranty Using the Bayesian Approach

Authors

  • Valeriana Lukitosari Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia
  • Sentot Didik Surjanto Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia
  • Sena Safarina Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia
  • Komar Baihaqi Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia
  • Sri Irna Solihatun Ummah Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

DOI:

https://doi.org/10.13052/jrss0974-8024.1619

Keywords:

Warranty, failure, Bayesian, two-dimensional

Abstract

Traditionally, the warranty cost is assumed to be the cost of repairs based on the average cost that arises from a damage claim. Several studies have considered the Least Square and Maximum Likelihood Estimation methods in estimating the parameters of the failure distribution. However, this study uses the Bayesian method using the posterior distribution obtained from the prior distribution and the likelihood function. The Bayesian approach is more optimal to use in estimating parameters because it has the smallest value of Aikaike’s Information Criterion (AIC) compared to other methods. Failure expectations that are close to natural can be used to analyze survival to determine how long a product will last before the failure. The numerical example in this study, is the type of motorcycle with an engine capacity of 125 CC with the Weibull distribution, while the 150 CC and 160 CC with Exponential distribution. The novelty in this study is that the free repair approach in two-dimensional can be anticipated with failure considering the dimensions of age and mileage.

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Author Biographies

Valeriana Lukitosari, Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

Valeriana Lukitosari is a lecturer at the Department of Mathematics, Sepuluh Nopember Institute of Technology (ITS) – Indonesia. Having a history of work in industrial manufacturing, she also has professional certifications such as Quality Engineer in Manufacturing. The first education she took was Undergraduate Mathematics-ITS, Postgraduate Production-Materials Engineering – ITS, in 1994 and 2000 respectively, and her last one was a Doctorate in Industrial Engineering in 2019, at ITS, Indonesia. The topics she is interested in are Optimization and Operations Research and several research experiences such as spare parts inventory, product life cycle, reliability and growing product supplies. She served as Head of the Industrial and Financial Mathematics Laboratory.

Sentot Didik Surjanto, Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

Sentot Didik Surjanto holds a Bachelor’s Degree in Mathematics from the Sepuluh Nopember Institute of Technology, Indonesia and a Master of Science, from the Department of Mathematics, University of Gajah Mada, Indonesia. He currently works as a Lecturer in the Department of Mathematics since 1987 until now, Faculty of Science and Data Analysis Sepuluh Nopember Institute of Technology, Indonesia. Research areas include stability and persistence analysis on the epidemic model and the Performance of some numerical Laplace inversion methods. He is also an active member of The Indonesian Mathematical Society.

Sena Safarina, Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

Sena Safarina earned a Bachelor of Mathematics from the Bandung Institute of Technology (ITB) and a Master of Science and Doctoral Degree from the Department of Mathematical and Computing Science in 2019, Tokyo Institute of Technology, Japan. Currently working as a Lecturer in the Mathematics Department, Faculty of Science and Data Analysis, Sepuluh Nopember Institute of Technology, Indonesia. Research areas include Operation Research, Mathematical Optimization Convex Optimization Second-order Cone Programming Mixed-Integer Non-Linear Programming Applied Mathematics. She is also an active member of SIAM.

Komar Baihaqi, Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

Komar Baihaqi is a lecturer in the Department of Mathematics, Sepuluh Nopember Institute of Technology (ITS), Indonesia, since 1988. He graduated with a Bachelor of Mathematics from ITS and a Master of Mathematics from Gajah Mada University, with a research interest in Algebra.

Sri Irna Solihatun Ummah, Industrial and Financial Mathematics Laboratory, Department of Mathematics, Sepuluh Nopember Institute of Technology, Surabaya 60111, Indonesia

Sri Irna Solihatun Ummah is a research member at the Industrial and Financial Mathematics laboratory. She is active in student association organizations, namely the Mathematics Student Association, ITS – 2022 as Secretary of the Student Welfare Department.

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Published

2023-11-29

How to Cite

Lukitosari, V. ., Surjanto, S. D. ., Safarina, S. ., Baihaqi, K. ., & Ummah, S. I. S. . (2023). The Predicted Failure on A Two-Dimensional Warranty Using the Bayesian Approach. Journal of Reliability and Statistical Studies, 16(01), 171–196. https://doi.org/10.13052/jrss0974-8024.1619

Issue

2023: Vol 16 Iss 1

Section

Articles