International Journal of Performability Engineering 

Volume 6, Number 1, January 2010

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Paper 3 - pp. 35 - 52 Rational Polynomial Hazard Functions M. BEBBINGTON1, C. D. LAI1, D. N.P. MURTHY2 and R. ZITIKIS3 1 Institute of Fundamental Sciences - Statistics, Massey University, Private Bag 11222,          Palmerston North New Zealand 2 Division of Mechanical Engineering, University of Queensland, Q 4072, Australia 3 Department of Statistical and Actuarial Sciences, University of Western Ontario,     London, Ontario N6A 5B7, Canada Abstract: Lifetime modeling of physical systems and biological organisms involves the use of failure distribution functions. The shape of the hazard rate (HR) function associated with the distribution function characterizes the effect of age (and other factors) on the failure. Examples of failure (and survival) data indicate that the shapes are many and varied, due to many underlying reasons. In this paper we investigate a model where the HR function is a rational function, which is by definition the ratio of two polynomials. The different possible shapes (increasing, decreasing, bathtub, inverted bathtub, modified bathtub, roller-coaster, etc.) of the HR rational functions are identified, and necessary and sufficient conditions on the parameters to ensure their existence derived.           Click "Add to Cart" to purchase the full article