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- W2527734553 abstract "In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set. The failure rate function r (t) is an important object of study in reliability theory and survival analysis. If T is the lifetime of an object, then r (t) At is the infinitesimal conditional probability that the object will fail in the next At units of time given that it has survived t units of time, i.e. given that T > t. Knowledge of its characteristics is thus an important tool in any statistical analysis. For example, if r(t) is increasing, then we know that the item is wearing out over time, while if r(t) is decreasing, the product is improving over time. Other behaviours are also important. For example, if a failure rate has a bathtub shape, then it is a candidate for bum-in. See Block and Savits (1997) for a discussion of bum-in. It is often difficult to determine the precise behaviour of the failure rate of objects that undergo various reliability operations such as mixtures or formation of systems. Thus, it might be useful to have information about its initial or asymptotic behaviour. The aim of this paper is to develop such knowledge since it is a first step in our overall goal of describing the complete shape characteristics. First we introduce some terminology that will be used throughout. Let T be the lifetime of an item with distribution function F(t) = P(T t) and density function f(t). The failure rate function (also called the hazard rate function) r(t) is defined as f(t) r(t)= F(t' t > 0. We say that F (or T) has an increasing failure rate (IFR) or a decreasing failure rate (DFR) distribution if r(t) is an increasing function of t or a decreasing function of t respectively. We" @default.
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- W2527734553 date "2003-01-01" @default.
- W2527734553 modified "2023-09-26" @default.
- W2527734553 title "RATE FUNCTIONS FOR MIXTURES AND SYSTEMS" @default.
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