Generalized Burr-Hatke Equation as Generator of a Homographic Failure Rates

Keywords

Burr-Hatke equation, HFR, homographic failure rate, exponential integral, moment estimator, log-likelihood equation, (n, 0) - sampling plan

Abstract

Starting from a generalized form of Burr-Hatke differential equation namely (see for details [18]), we obtain – for peculiar choices of u, v, a and b – as a solution, a reliability function which provides a homographic failure rate (HFR) , where . 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.

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