this is a markov model. n and k are maintenance treshold values as integers. lambda and mu are transition probabilities. first of all i want to solve it in closed form to get a A-Lambda[in] plot and there for to obtain optimal Lambda[in] which max. availability. if i couldn't solve in i try to give some numeric values and i don't know if it's become too complicated for maple? thanks and a small mistake: Availability should be: Availability (A) = P(0,0)*(k + (a * ((1-a^(n-k))/(1-a)) ))