Letter to the Editor—A Note on Conditional Probability of Failure When Hazards are Proportional

The following result is of some interest to people studying equipment failure models [Barlow, R. E., L. Hunter, F. Proschan. 1963. Optimum redundancy when components are subject to open and short circuit failures. J. Soc. Indust. Appl. Math.11 64–73.], and I shall state it in those terms. The result and the proof are of the type that make one think that this is probably a folk theorem but none of the folks I know, or that have reviewed the paper, seem to know the result.