Generalized Burr-Hatke Equation as Generator of a Homographic Failure Rate
Journal Title: Journal of Applied Quantitative Methods - Year 2008, Vol 3, Issue 3
Abstract
Starting from a generalized form of Burr-Hatke differential equation namely dϕ / dx = u(x) ⋅ϕ [sup]a[/sup] + v(x) ⋅ϕ [sup]b[/sup] (see for details [18]), we obtain – for peculiar choices of u, v, a and b – as a solution, a reliability function ϕ (x) which provides a homographic failure rate (HFR) h(x) =θ +1/ x , where θ > 0 . Some statistical inferences on the variable X having such a hazard rate are performed. Main indicators are evaluated and it is proved that the maximum likelihood method of estimation cannot furnish a solution for the parameter involved. A moment estimator is deduced which is used in the construction of some special sampling plans for durability testing.
Authors and Affiliations
Alexandru ISAIC-MANIU, Viorel VODĂ
Keywords
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