Where Ti is the mean time to failure for components i. It is the inverse of the failure rate, l, i.e. 1=1/Ti. If the component is not an object of maintenance its reliability and unreliability coincide, i.e., qi(t)=ui(t).

For the component subjected to maintenance, the unavailability of the component is given by: ut (t) = 1 - exp[1 - A, (t - ndi )] (t > 0) (F-11)

Where, 0i is the time between inspections, and n is integer parts of the quotient t/ 0i.

An average unavailability can be obtained by integrating Eq.F-11 over the time interval between two inspections is given by:

Due to li 0i < 1, the exponential function of the Eq.F-12 may be approximated by the first three term of its Taylor Series. This procedure leads to the well-known results:

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