Evaluation of Conditional Failure Density from Hazard Rate

Further to the recent discussion regarding the concepts of hazard rate and conditional failure density, it is shown that the latter may be expressed in terms of the former. Moreover, six functions, namely, failure time distribution function, failure time density, reliability function, hazard rate, conditional failure distribution, and conditional failure density, are shown to be equivalent to the extent that if one of them is known, the other five are completely determined. The results are summarized in a table.