# Through-Life Maintenance Cost of Digital Avionics
## 7 Results and Discussion
### Warranty Maintenance
Figure 4b illustrates the dependency of the optimal quantity of spare LRU on the quantity of aircraft for the WM option number one when \(\theta=1\times 10^{-4}\) h\({}^{-1}\) (red circles),  
\(\theta=1\times 10^{-3}\) h\({}^{-1}\) (black squares) and \(P_{flight}^{FP}=1\times 10^{-4}\). As we can see in Figure 4b, a rise in the rate of intermittent faults results in a significant rise in the quantity of spare LRU. Moreover, the influence of intermittent faults is even more considerable than in-flight false-positives. Figure 5a,b show the dependency of the expected unplanned quantity of spare LRU (_US_) on the planned quantity of spare LRU (_PS_) for the first WM option. As seen, the _US_ decreases rapidly as _PS_ increases. Besides, the _US_ highly depends on the intermittent fault rate (\(\theta\)), in-flight conditional probability of a false-positive (\(P_{flight}^{FP}\)), and expedited delivery time (\(T_{ED}\)). With an increase of \(\theta\) and \(P_{flight}^{FP}\) and a decrease of \(T_{ED}\), _US_ decreases as well. Let's analyze the dependences of the posterior probabilities of dismantling the LRU on the conditional probability of in-flight false-positive, rate of intermittent faults and permanent failures. We calculated the plots in Figures 6-8 by using Equations (A2)-(A4). Figure 6 shows the dependences of the posterior probabilities of dismantling the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the conditional probability of in-flight false-positive when \(T=5000\) h, \(\tau=2.5\) h, and \(\lambda=10^{-4}\) h\({}^{-1}\). Figure 6a corresponds to the case when \(\theta=1\times 10^{-3}\) h\({}^{-1}\) and Figure 6b--\(\theta=1\times 10^{-4}\) h\({}^{-1}\). As we can see in Figure 6a,b, the probabilities \(P_{PF}\) (blue curve) and \(P_{IF}\) (black curve) decrease, and the probability \(P_{FP}\) (red curve) increases with the rise in the conditional probability of in-flight false-positive. Moreover, the impact of in-flight false-positives increases at a lower intermittent fault rate. Figure 7 shows the dependences of the posterior probabilities of dismantling the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the intermittent fault rate. The initial data are the same as in Figure 6.  
We can see in Figure 7 that the posterior probabilities \(P_{FP}\) (red curve) and \(P_{PF}\) (blue curve) decrease, and the probability \(P_{IF}\) (black curve) increases with the rise in the rate of intermittent faults. We should note that the conditional probability \(P_{flight}^{FP}\) does note have big impact on the probability \(P_{IF}\) but it has strong influence on the probabilities \(P_{FP}\) and \(P_{PF}\). Figure 8 shows the dependences of the posterior probabilities of dismounting the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the rate of permanent failures. The initial data are the same as in Figure 6. As we can see in Figure 8, the posterior probabilities \(P_{FP}\) (red curve) and \(P_{IF}\) (black curve) decrease, and the probability (blue curve) increases with the rise in the rate of permanent failures. Figure 6: Dependences of the posterior probabilities of dismounting the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the conditional probability of in-flight false-positive when \(\lambda=10^{-4}\) h\({}^{-1}\); (a) \(\theta=1\times 10^{-3}\) h\({}^{-1}\); (b) \(\theta=1\times 10^{-4}\) h\({}^{-1}\). Figure 7: Dependences of the posterior probabilities of dismounting the LRU due to the in-flight false-positive (red curve), intermittent fault (black curve), and permanent failure (blue curve) on the intermittent fault rate when \(\lambda=10^{-4}\) h\({}^{-1}\); (a) \(P_{flight}^{FP}=1\times 10^{-3}\); (b) \(P_{flight}^{FP}=1\times 10^{-4}\).