WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
Asymptotic Properties of the Hazard Function and the Mean Residual Life Function
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Abstract: The memoryless or non-aging property of systems is of special relevance in reliability theory, which implies that the hazard function is constant in time, and the corresponding mean residual life function takes a reciprocal value. The only known continuous distribution with that property is the exponential distribution. However, many other distributions exist whose asymptotic behavior of underlying hazard functions approaches a constant, while the mean residual life function approaches a reciprocally constant value. Here we provide an analysis which enables us to study a class of distributions that asymptotically approach the memoryless property, and which include gamma, Erlangian, exponential resilience, exponential geometric, hyper exponential, logistic exponential and the inverse Gaussian distribution.
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Pages: 275-279
DOI: 10.37394/23206.2020.19.27