The Really Reliable Company produces roller bearings used in a high-wear application in diesel locomotives. The exponentially distributed mean time to failure for these roller bearings has been determined to be 10,000 hours of operation. Really Reliable wants to determine an appropriate warranty period (in hours) such that it will have to provide warranty service for no more than 0.04% of the roller bearings it produces.

Appropriate warranty period = 4 hours

Explanation:

According to the scenario, computation of the given data are as follows:

Here, mean = 10,000 = 1/λ

Let appropriate warranty period = t

Hence, 0.0004 = 1-e^-λt

0.0004 = 1-e^(t/10,000)

e^(t/10,000) = 0.9996

Taking ln on both the sides and then solving,

t/10,000 = 0.0004

t = 4 hours

Hence, Appropriate warranty period = 4 hours

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