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By Seidenberg A.

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0). 54) 1amt = input('Enter lambdat in l/year ... '); lamc = input('Enter lambdacdash in l/year ... '); fix (clock) disp('Other parameter values assumed ... 25 mu1 1095 mu2 = 1095 mut = 46 disp('Now calculating Q and alpha ... '); c1 lam1 + lam2 + lamc + lamt; c2 = lam2 + lamc + mul + lamt; c3 = lam1 + lamc + mu2 + lamt; c4 = mul + mu2 + lamt; U = [ 0 laml/c1 lam2/c1 lamc/c1 mu1/c2 0 0 (lam2 + lamc)/c2 mu2/c3 0 0 (laml + lamc)/c3 o mu2/c4 mu1/c4 0 1 0 0 0 lamt/cl lamt/c2 lamt/c3 lamt/c4 o 1; unit = eye(5); e1 unit ( : ,1) ; e2 uni t ( : , 2 ) ; e3 = unit (: ,3) ; e4 = uni t ( : , 4) ; e5 = unit(:,5); % P IS A SQUARE MATRIX OF SIZE 25.

This certainly holds for irreducible chains. 1 implies the following corollary. 3. Let Z be an irreducible Markov chain on S = Al U A2. 1), the probability mass function of the joint distribution ofNAJ,I, ... , NA),rn is given for nl, ... , nrn;::: 1 by Pr{ NAJ,I =nl, ... , NA),rn =nrn } = vT QAjAj 01- 1 QAjA2 rn n {(I - QA2A2rl QA2A) QA\A) oj-I QA\A2} 1. 3. 1 to the Markov chain on Al U A2 U {w} which is identical to Z on Al U A2 and all transition probabilities of which to Ware equal to zero.

This is because those two parameters are primarily associated with the duration of a repair but not with its nature (minor/major). 5. l2, the sojourns in the states '2' and '3' will tend to be 48 longer. These repair periods are critical in the sense that whenever the only remaining power line fails, system failure ensues. For this reason, as a secondary effect, we observe a slight stochastic increase in the distribution of RIO. 469xlO-5 9. 696xlO-2 9. 15 has not been used in the present MATLAB implementation, it should be useful for larger problems where computing time is at a premium.