Probability of failure (PF) of fatigue-prone aircraft (AC) and failure rate (FR) of airline (AL) for speci c inspection program can be calculated using Markov Chains (MC) and Semi-Markov process (SMP) theory if parameters of corresponding models are known. Exponential approximation of fatigue crack size growth function, a(t) = a0 exp(Qt), where a0, Q are random variables , is used. Estimation of the parameters of distribution function of these variables and the choice of nal inspection program under condition of limitation of PF and FR can be made using results of observation of some random fatigue crack in full-scale fatigue test of the airframe. For processing of acceptance type test, when redesign of new aircraft should be made if some reliability requirements are not met, the minimax decision is used.The process of operation of AC is considered as absorbing MC with (n + 4) states. The states E1;E2; :::;En+1 correspond to AC operation in time intervals [t0; t1); [t1; t2); :::; [tn; tSL), where n is an inspection number, tSLis speci ed life (SL), i. e. AC retirement time. States En+2, En+3, and En+4 are absorbing states: AC is descarded from ser- vice when the SL is reached or fatigue failure (FF) or fatigue crack detection (CD) take place. In corresponding matrix for operation process of AL the states En+2, En+3 and En+4 are not absorbing but correspond to return of MC to state E1(AL operation returns to rst interval). In matrix of tran- sition probabilities of AC ,PAC , there are three units in three last lines in diagonal, but for corresponding lines in matrix for AL, PAL, the units are in rst column, corresponding to state E1. Using PAC we can get the probabil- ity of FF of AC and cumulative distribution function, mean and variance of AC life. Using PAL we can get the stationary probabilities of AL operation f1; :::; n+1; n+2; :::; n+4g. Here n+3de nes the part of MC steps, when FF takes place and MC appears in state En+3. The failire rate (intensity of FF), F , and economic characteristics of AL are calculated using the theory of SMP with reword. The gain of this process is de ned by equation g = Pn+4 i=1 igi;where gi = ai ui + b qi + c vi; i = 1; :::n + 1; d; i = n + 2; :::; n + 4 ; ui; qi; vi, i = 1; :::; n + 1, are probabilities of successful transitions from one to the following interval, to En+3 and En+4states; ai = at(ti ti1)is the reward, related with successful transi- tions from interval [ti1; ti) to the following one [ti; ti+1) (it is supposed that all intervals are equal, atde nes reword of succesful operation in one time unit, b and c are the rewards (negative) related with transitions from any state E1,. . . ,En+1 to state En+3 (FF takes place) and En+4 (CD takes place) cor- respondingly; - d is the cost of acquisition of new AC after SL, FF or CD and transition to E1 takes place (d is negative value). For b = c = a(n),at = 1and d = 0 valuegide nes the mean time in Ei if time transition to state E1 is equal to zero. Then Qj = jgj=g de nes the part of time which SMP spends in stateEj ; j = 1; :::; n + 1; Lj = g=j de nes the mean return time for stateEj ; speci cally, L1 is a mean time of renewal of AL operation in rst interal, Ln+3 is a mean time between FF; the intensity of fatigue failure F = 1=Ln+3. The problem of inspection planning is the choice of the sequance ft1; t2; :::; tn; tSLg corresponding to maximum of gain under limitation of AC intensity of fatigue failure. In numerical example the minimax decision, based on observation of some fatigue crack during acceptance full-scale fatigue test of airframe, is con- sidered.