The substitution model for CFR

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Let us consider the special case of the general substitution model where T_i is an exponential random variable with constant failure rate λ. Let also D_i be an exponential random variable with constant repair rate μ. Since the reparable system has a constant failure rate (CFR), we know that aging and the impact of corrective maintenance are irrelevant on reliability performance. For this system it can be shown that the limit availability is:

Table 4.7 Equation
$A=\frac{\mu }{\lambda +\mu }$

Let us analyze, for example, a repairable system, subject to a replacement policy, with failure and repair times distributed according to negative exponential distribution. MTTF=1000 hours and MTTR=10 hours.

Let’s calculate the limit availability of the system. The formulation of the limit availability in this system is given by Table 4.7 , so we have:

$A=\frac{\mu }{\lambda +\mu }=\frac{\frac{1}{10}}{\frac{1}{1000}+\frac{1}{10}}=\frac{0,1}{0.101}=0.990$

This means that the system is available for 99% of the time.

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The substitution model for CFR