The additive Perks distribution and its applications in reliability analysis

ABSTRACT

In this paper, the Additive Perks Distribution (ADP) is presented; this distribution describes the behavior of the bathtub curve, which is one of the most deeply rooted concepts in reliability analysis. The proposed distribution is based on the sum of the positive and negative hazard rate functions of the Perks distribution. ADP’s statistical properties include Measures of Central Tendency, moments, moment generating function, statistical order, residual lifetime, reversed residual lifetime, Rényi entropy, time-varying, and life-stress relationship modeling presented. For estimating the ADP parameters, the Maximum Likelihood Method is used. On the other hand, the APD is tested in three case studies and compared with other distributions that can describe the failure rates in a bathtub curve. The results from the case studies showed that the APD is a good choice for describing the failure times in the shape of a bathtub curve.

KEYWORDS:

• Additive perks distribution
• bathtub distributions
• non-monotone failure rate
• Perks distribution
• reliability analysis

Disclosure statement

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

Additional information

Notes on contributors

Luis Carlos Méndez-González

Luis Carlos Méndez González Ph.D. is currently a full-time professor at the Department of Industrial Engineering and Manufacturing at the Autonomous University of Ciudad Juárez, México. He received his Ph.D. in Science in Engineering in 2015. He received his M.S in Industrial Engineering from the Technological Institute of Ciudad Juarez in 2011 and his B.S in Electronics Engineering in 2007. He has more than fifteen years in software, hardware design, Applied Statistics, Measurement System Analysis, Reliability Engineering, and Quality Engineering. He is currently a member of the National Researchers System from México as Level 1. His research interests include reliability and degradation modeling, stochastic modeling, hardware, and software design, and Machine Learning.

Luis Alberto Rodríguez-Picón

Luis Alberto Rodríguez-Picón Ph.D. is currently a full-time professor at the Department of Industrial Engineering and Manufacturing at the Autonomous University of Ciudad Juárez, México. He received his Ph.D. in Science in Engineering in 2015. He received his B.S. and M.S. degrees in Industrial Engineering from the Technological Institute of Ciudad Juárez, México, in 2010 and 2012, respectively. He has worked as a professor in industrial engineering, statistics, and mathematics and has several years of professional experience in the automotive industry. He is currently a member of the National Researchers System from México as Level 1. His research interests include reliability and degradation modeling, stochastic modeling, multivariate statistical modeling, and design of experiments.

Ivan Juan Carlos Pérez Olguín

Iván JC Pérez-Olguín received a Doctor of Science degree in industrial engineering from the Technological Institute of Ciudad Juarez, Mexico. He is currently a full-time Professor and a Researcher with the Autonomous University of Ciudad Juarez, Mexico. He has published in journals, conference proceedings, and books more than 50 articles; he also contributed to the automotive industry with two patents and four utility models. His research interests include robust optimization, reliability tests, product optimization, process optimization, and lean manufacturing.

Vicente García

Vicente García PhD. received the B.Eng. degree in computer systems from the Technological Institute of Villahermosa, México, in 1995, the M.Sc. degree in computer science from the Technological Institute of Toluca, México, in 2000 and the Ph.D. degree in computer science from the Universitat Jaume I, Castellon, Spain, in 2010. From 2010 to 2013, he was a research fellow with the Institute of New Imaging Technologies, Castellón, Spain. From September 2013 to July 2014, he was a post-doc at the Department of Ingeniería Eléctrica y Computación of the Universidad Autónoma de Ciudad Juárez, Chihuahua, México. Since 2014 serves as a Full Professor of Computer Science, Master and Ph.D. area advisor at the Universidad Autónoma de Ciudad Juárez. His research interest includes classification, performance evaluation metrics, data mining, and medical imaging.

David Luviano-Cruz

David Luviano-Cruz PhD. received the Ph.D. degree in sciences from the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV) using artificial neural networks (ANN) to improve path recognition. He is currently an Active Researcher at the Universidad Autónoma de Ciudad Juárez, where he also performs full-time Professor activities. He has published and published more than 23 scientific works with more than 138 citations. His research interests include optimization using artificial neural network algorithms, Pythagorean fuzzy sets, and machine learning.