By Al-Dahoud Ali

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1999). 112-119, ISBN 0-7695-0371-3, Hong Kong, December 1999. Duque O. & Morinigo D. (2004). 3, pp. 841-844, ISBN 0-7803-8271-4, Dubrovnik, May 2004. Endrenyi J. (1978). Reliability Modeling in Electric Power Systems, J. Wiley & Sons, Chichester, 1978. J. & Leite da Silva A. M. (1998). Probabilistic Evaluation of the Effect of Maintenance on Reliability - An Application. IEEE Transactions on Power Systems, vol. 13, no. 2 (May 1998), pp. 575-583. L. & Asgarpoor S. (2007). 541-546, ISBN 9-7814-2441-7254, Las Cruces, NM, USA, September/October 2007.

5 work well. Even if the initial value of X1r computed this way does not meet (6) for particular value of then (7) can be re-applied with increased, although it should be noted that each such correction requires solving a new M1 model and in effect this is the extra computational cost almost equal to that of the whole iteration. 3 Comparison of the methods We shall now discuss effectiveness of the above three approximation methods using a sample Markov model tuned for four different repair frequencies.

D1 Initial 10 P D2 Minor deterioration P20 I1 11 P M11 12 P P M12 P30 I2 21 M21 D3 Major deterioration 22 I3 P32 31 P P M22 F Failure M31 M33 D1 D2 D2 D1 D3 Choice possibilities (decisions) D1 D3 D2 F Outcome possibilities D2 F Waiting periods Fig. 2. Model of the ageing process for equipment undergoing inspections and maintenance activities. Decision probabilities after inspection states are placed by respective transitions. K = 3, R = 2. Mathematically, the model in Fig. 2 can be represented by a Markov process, and solved by well-known procedures.