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AbstractThe mean time to failure (MTTF) function in age replacement is used to evaluate the performance and effectiveness of the age replacement policy. In this paper, based on the MTTF function, we introduce two new nonparametric classes of lifetime distributions with nonmonotonic mean time to failure in age replacement; increasing then decreasing MTTF (IDMTTF) and decreasing then increasing MTTF (DIMTTF). The implications between these classes of distributions and some existing classes of nonmonotonic ageing classes are studied. The characterizations of IDMTTF and DIMTTF in terms of the scaled total time on test transform are also obtained.

Stochastic ordering problems in weighted- k -out-of- n systems are considered. The influence of component lifetimes and weights on the total capacity is studied. When it is allowed to allocate lifetimes to the weights, an optimal allocation to attain maximum total capacity is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the testing problem whether burn-in is required based on the long-run average cost for a population with bathtub-shaped failure rate function. We propose a test based on kernel density estimation. We then apply our proposed test to two real data sets in the context of reliability. [ABSTRACT FROM AUTHOR]

Abstract: We propose a new reliability model which is a generalization of the logistic frailty model first considered by for fitting human mortality data. Essentially, a shape parameter is added to the existing model providing more flexibility in modeling lifetime data. Several model properties such as the survival function, density and the hazard rate are investigated. In particular, we show that the model is very versatile; able to take a variety of non-monotonic hazard rate shapes. Parameters estimation is also considered. Two well known survival data sets are satisfactorily fitted by the proposed distribution and its goodness-of-fit is compared. [Copyright &y& Elsevier]