Cumulative hazard rate

[peppe bambina]

I've read in an article about preventive maintenance that the hazard rate, integrated over a time interval and multiplicated by the cost of a substitution, gives the average cost of substitution over the same period.
I can't explain it, since I've ever thought that, in order to obtain the expected number of failures over a time interval,I must consider renewal fuction.Could anybody solve this question? Thanx.

[RS Support]

The hazard rate (or failure rate) integrated over a time interval provides the expected number of failures per part.
(For more details see Ref. [10] http://www.reliasoft.com/Books/index.html Page 193)

[kcarr]

This works well when the time for repairs are small compaired to the typical interval between failures. Also note that the assumption of no rejuvenation following repair is required for beta other than 1. This is a "Good-as-old" approximation and is frequently valid for complex equipment where repairs are of many independent parts.