By M. J. Crowder, A. C. Kimber, R. L. Smith, T. J. Sweeting (auth.)

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Analysis of Reliability and Quality Control: Fracture Mechanics 1

This primary publication of a 3-volume set on Fracture Mechanics is especially based at the massive diversity of the legislation of statistical distributions encountered in a variety of clinical and technical fields. those legislation are vital in knowing the chance habit of elements and mechanical constructions which are exploited within the different volumes of this sequence, that are devoted to reliability and quality controls.

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Ir, at the first check after one hour, the unit is found to have failed, then one knows only that its lifetime was less than one hour. Ir, in this scenario, the unit was found to have failed between the second and third checks (that is, the unit was working at the second check, but had failed by the third check) then one would know that the unit had lifetime of between two and three hours. This is an example of interval censoring. We shall see later that censored observations may be dealt with, at least in principle, in a straightforward way provided that the mechanism of censoring is independent of the lifetimes of the units.

If () is known then there are no new problems sinee all that is being done is to work with T- () in plaee of T itself. However, if () is unknown we shall see in Chapter 3 that complieations may oeeur. Mixtures A seeond generalization is via mixtures. Suppose that the population eonsists of two types of unit, one with lifetime density fl and the other with lifetime density f2 . For example, one type of unit may be inherently weaker than the Some other lifetime distributions 33 other type. Thus, the mean lifetime corresponding to density fl may be much lower than that corresponding to density f2' Ir P is the proportion of type one units in the population, then the density of a randomly selected lifetime is f(t) = Pfl(t) + (1- P)f2(t), for t>O.

L. 534 respectively. As we shall see shortly, it turns out that the Weibull and lognormal distributions provide satisfactory fits to these data. Rather than work with sampie moments, a different approach is to estimate Simple data analytic methods: no censoring 39 the survivor function. 13) This is a non-increasing step function with steps at the observed lifetimes. It is a non-parametric estimator of S(t) in the sense that it does not depend on assumptions relating to any specific probability model.

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