The Decreasing Hazard Rate Phenomenon: A Review of Different Models, with a Discussion of the Rationale behind Their Choice

Abstract

It is well known that, especially in the field of electronic components reliability studies and applications, the Exponential reliability model is by far the most adopted, although the data fostering it are few. This appears to be due partly to its simplicity (also in view of estimation, since it is characterized by a unique parameter), and partly because most components seem to be well represented, at least in their “useful life” time interval, by the Exponential model. This adoption is basically due to its peculiar “memory-less” property, i.e., the fact that such model possesses a constant hazard rate function, meaning that stochastic “accidents” cause the failure of the component, independently of its service time. This theoretical reason behind the choice of the Exponential model is largely prevailing over the classical statistical “goodness of fit” tests, since the high-reliability values attained by such devices does not allow the availability of an adequate number of lifetime values to be observed and analyzed in a statistical data analysis procedure. A second model also widely adopted is the Weibull model, especially if characterized by a shape parameter greater than unity, so implying an increasing hazard rate function. However, there are many cases—which can be also justified on a theoretical basis, as reviewed in this paper—in which a decreasing hazard rate function (at least for relatively large mission times) may be the best suited to describe the true model behind a given failure mechanism. The afore-mentioned theoretical basis of these apparently peculiar models is the main core of the present review article, whose aim also includes the illustration of the basic features of the main reliability models featuring an hazard rate function diminishing with time. The paper also discusses, resorting to graphical and numerical case-studies relevant to both field and simulated data, the consequences of mistaken model identification in terms of the hazard rate function behaviour, which may imply wrong maintenance actions.