Ages in Reliability and Bio Systems, Interpretations, Control, and Applications

Document Type

Book Chapter

Publication Date


Publication Title

Mathematical and statistical models and methods in reliability. Applications to medicine, finance, and quality control.


In this article, we define age and compare ages for objects from two populations by making use of their lifetime distributions. The main purposes of this talk are to propose various definitions, based on relationships between important different but equivalent probability components, which allow tractable use in engineering and humane practice. These definitions admit different meaning important in numerous applications. Respectively, there are various areas of use. Most of the statements and Examples are straightforward consequences of the Definitions. For instance, there are several ways for evaluation of the true age of an object on the background of its population. An approach to the time scaling in the age evaluation based on accelerated testing is offered, using the concept of accumulated total stress. Examples with biological age control similar to reliability age-correcting factor illustrate the theory. We generalize this approach to two-dimensional and multi-dimensional distributions that also may represent life, and sketch areas where this knowledge can be applied.

First Page


Last Page





Part III: Applications, Chapter 25. Edited by V.V. Rykov, N. Balakrishnan, and M.S. Nikulin. Invited papers based on the presentation at the 6th international conference (MMR 2009), Moscow, Russia, June 22–26, 2009.


© 2019 Springer Science+Business Media, LLC 2010