Stress-strength reliability for doubly truncated random variables

• Published in: Communications in statistics. Theory and methods Vol. 54; no. 16; pp. 5146 - 5163
• Main Authors: K.R., Deepa, Mathew, Angel
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 18.08.2025
• Subjects: doubly truncated data; generalized failure rate; nonparametric estimation; Stress-strength reliability
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2024.2434563

In the context of reliability and survival analysis, the observed lifetimes are often subject to left, right, or double truncation. Doubly truncated data usually arises when information about the lifetime of a system is available only within a particular time interval. In this paper, we consider the stress-strength reliability measure for the doubly truncated data. Several properties of this measure, including bounds and the effect of monotonic transformations, are discussed. Further, we propose a nonparametric estimator for doubly truncated stress-strength reliability, and its asymptotic properties are studied. A simulation study is also carried out to evaluate the performance of the asymptotic confidence interval and the percentile bootstrap interval for doubly truncated stress-strength reliability. Finally, the proposed estimation procedure is applied to a real data set for illustration.