A GENERAL FORMULA FOR THE FAILURE-RATE FUNCTION WHEN DISTRIBUTION INFORMATION IS PARTIALLY SPECIFIED

This paper presents a new formula for the failure-rate function (FRF), derived from a recently-introduced 4-parameter family of distribution s. The new formula can be expressed in terms of its Cdf, is characteri zed by algebraic simplicity, and can replace more-complex hazard funct ions by using routine distribution fitting. When the actual Cdf is unk nown and partial distribution-information is available (or can be extr acted from sample data), new fitting procedures that use only first-de gree or first- & second-degree moments are used to approximate the unk nown FRF. This new approach is demonstrated for some commonly used Cdf 's and shown to yield highly accurate values for the FRF. Relative to current practice, the new FRF has 4 major advantages: It does not requ ire specification of an exact distribution, thus avoiding errors incur red by the use of a wrong model; Since estimates of only low-degree (a t most first- or second-degree) moments are required to determine the parameters of the FRF, the associated mean-square-deviations are relat ively small; The new FRF can be easily adapted for use with censored d ata; Simple maximum likelihood estimates can be developed.