Reliability for lifetime distributions

✍ Scribed by S. Nadarajah

• Book ID: 104351197
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 448 KB
• Volume: 37
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(03)00074-8

✦ Synopsis

In

the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr (X2 < Xl) when Xi and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr (X2 < Xi) has been worked out for the majority of the well-known distributions including normal, uniform, exponential, gamma, Weibull, and Pareto.

However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper, we consider the class of lift-time distributions (in particular, exponential and gamma) and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.