“…The standby redundancy technique is especially important, for computer and communication systems used in life critical or mission critical applications, such as flight control and space missions where replacing or Acronyms: pdf, probability density function; cdf, cumulative distribution function; pmf, probability mass function Notations: N, number of elements in multi-state standby system; J + 1, number of states for the element; s k (i,j), transition rate from state i to state j for element k in standby mode; o k (i,j), transition rate from state i to state j for element k in operation mode; s * k i; j ð Þ, transition rate from state i to state j for element k in standby mode after aggregation; o * k i; j ð Þ, transition rate from state i to state j for element k in operation mode after aggregation; p k (j,t), probability that element k is in state j at time t when it is in standby mode; w k,h (j,t), probability that element k is in state j after operating for time t given it was in state h when being activated; T n , random time when the last element from the sequence 1,2, …,n fails; x n (t), pdf of T n ; X n (t), pmf of T n ; Z, mission time; R, reliability of the multi-state standby system repairing a failed element through online or onboard manual intervention is difficult or even impossible. 3,4 In power systems, repairs of failed elements can take long time, and a fast replacement by standby element is essential to meet a demand.…”