AGEING NOTIONS AND CLASSES OF LIFE DISTRIBUTIONS

 BACKGROUND : 

    The concept of ageing is very important in reliability analysis. ‘No ageing’ means that the age of a component has no effect on the distribution of residual lifetime of the component. ‘Positive ageing’ (also known as ‘averse ageing’) describes the situation where residual lifetime tends to decrease, in some probabilistic sense, with increasing age of a component. This situation is common in reliability engineering as components tend to become worse with time due to increased wear and tear. On the other hand, ‘negative ageing’ has an opposite effect on the residual lifetime. ‘Negative ageing’ is also known as ‘beneficial ageing’. Although this is less common, when a system undergoes regular testing and improvement, there are cases for which we have reliability growth phenomenon. Though we concentrate on positive ageing, it is being understood that a parallel development of negative ageing can also be carried out.

     Concepts of ageing describe how a component or system improves or deteriorates with age. Many classes of life distributions are categorized or defined in the literature according to their ageing properties. An important aspect of such classifications is that the exponential distribution is nearly always a member of each class. The notion of stochastic ageing plays an important role in any reliability analysis and many test statistics have been developed in the literature for testing exponentiality against different ageing alternatives. Our aim in this chapter is to provide an overview of these developments.

    By ‘life distributions’ we mean those for which negative values do not occur, i.e., F(x) = 0 for x < 0. The nonnegative variate X is thought of as the time to failure (or death) of an electrical or mechanical component (or organism), but other interpretations may be possible – an inter-event time is normally necessarily positive.

 RECOMMENDED TEXT BOOKS: 

- Stochastic Ageing and Dependence for Reliability. By Chin-Diew Lai and  Min Xie (2006).

- Statistical Theory of Reliability and Life Testing: Probability Models. By Barlow, R. E., and Proschan, F. (1975

 LECTURE NOTES:   

- Ageing Notions   Second Chapter of Lai & Xie Book

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