Approximations to the Lifetime Distribution of k-Out-of-n Systems with Cold Standby

We consider several approximations to the lifetime distribution of general k-out-of-n systems with cold standby, when n becomes large. The approximations are derived from limiting results for N(t), the number of failures in [0, t], when t → ∞. The approximations can be easily evaluated even though the derivation of the limiting result is rather technical, due to the discrete character of N(t). Numerical work shows excellent agreement with the theoretical error structure of the approximations.