Comparing Residual Lives and Inactivity Times by Transform Stochastic Orders

• Published in: IEEE transactions on reliability Vol. 66; no. 2; pp. 366 - 372
• Main Authors: Arriaza, Antonio, Sordo, Miguel A., Suarez-Llorens, Alfonso
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aging; Aging notions; Distribution functions; Economic models; Hazards; inactivity time; Probability theory; Quantiles; Random variables; Reliability; residual life; Stochastic processes; transform stochastic orders; Transforms
• ISSN: 0018-9529; 1558-1721
• DOI: 10.1109/TR.2017.2679158

Comparison of residual lives and inactivity times is an important topic in reliability. In this framework, our purpose is twofold. First, we interpret a family of stochastic orders, known in the literature as transform stochastic orderings, in terms of stochastic comparisons among residual lives and inactivity times at quantiles. Second, we introduce a new stochastic order that occupies an intermediate position between two of these transform orderings, namely the convex order and the star order. As an application, we introduce a new aging class intermediate between the aging classes increasing hazard rate and increasing hazard rate average and show its usefulness.