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For an exponentially distributed failure time, the interval giving a target reliability R is -MTBF x ln(R): 90% reliability needs an interval of about 0.105 x MTBF. The economic interval balances the cost of intervening against the expected cost of failure, and shrinks as failures become more expensive relative to planned work.
Reliability-based interval
Interval = -MTBF x ln(target reliability)
Economic interval
Interval = MTBF x sqrt(2 x PM cost / failure cost)
Only for components with an increasing failure rate. For random failures, replacing a good part does not reduce risk, so condition monitoring is the better strategy.
MTBF is the mean, and with exponential failures about 63% of items fail before it. Holding failure probability to 10% requires intervening at roughly a tenth of the MTBF.