Eur. Phys. J. Plus (2016) 131: 379
https://doi.org/10.1140/epjp/i2016-16379-8

Regular Article

Tsallis statistics in reliability analysis: Theory and methods

¹ Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Shaanxi, China
² Department of Statistical Science, Southern Methodist University Dallas, 75275-0332, Dallas, TX, USA

^* e-mail: lnsz-zfd@163.com

Received: 15 August 2016
Accepted: 6 October 2016
Published online: 31 October 2016

Abstract

Tsallis statistics, which is based on a non-additive entropy characterized by an index q, is a very useful tool in physics and statistical mechanics. This paper presents an application of Tsallis statistics in reliability analysis. We first show that the q-gamma and incomplete q-gamma functions are q-generalized. Then, three commonly used statistical distributions in reliability analysis are introduced in Tsallis statistics, and the corresponding reliability characteristics including the reliability function, hazard function, cumulative hazard function and mean time to failure are investigated. In addition, we study the statistical inference based on censored reliability data. Specifically, we investigate the point and interval estimation of the model parameters of the q-exponential distribution based on the maximum likelihood method. Simulated and real-life datasets are used to illustrate the methodologies discussed in this paper. Finally, some concluding remarks are provided.