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- Title
GENERALIZED BURR-HATKE EQUATION AS GENERATOR OF A HOMOGRAPHIC FAILURE RATE.
- Authors
Isaic-Maniu, Alexandru; Vodӑ, Viorel Gh.
- Abstract
Starting from a generalized form of Burr-Hatke differential equation namely dϕ/dx = u(x)· ϕa + v(x)·ϕb(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.
- Subjects
DIFFERENTIAL equations; CALCULUS; BESSEL functions; TRANSCENDENTAL functions; HARMONIC analysis (Mathematics)
- Publication
Journal of Applied Quantitative Methods, 2008, Vol 3, Issue 3, p215
- ISSN
1842-4562
- Publication type
Article