# Through-Life Maintenance Cost of Digital Avionics
## 5 Post-Warranty Maintenance Models of Avionics Systems
We determine EMCPW for the second option as follows:  
\[EC_{PW,2}=q\Big{[}(C_{TR}+C_{PF})P_{PF}+LC\Big{(}t_{M}^{O-level}+t_{TE}^{I-level }\Big{)}\Big{]}ER(T_{PW})+\]  
\[C_{TE}^{I-level}/\Big{(}N_{PW}\times F_{TE}^{I-level}\Big{)}\ +C_{LRU}(PS+US)/N_{PW} \tag{34}\]  
For the second PWM option the average LRU repair time \(E(T_{repair})\) is calculated by Equation (24). In the third maintenance option of the two-level system, the I-level uses a ground ATE to recheck the dismounted LRU and detect the failure location with depth to the faulty SRU. As is well-known [35], conventional ATE is not capable of detecting intermittent faults. Therefore, dismounted LRU with intermittent faults and units removed due to in-flight false-positives of BITE after rechecking by ATE will be delivered to the warehouse of spare LRU. Repair of LRU with permanent failures is carried out by replacing the faulty SRU. After identifying the defective SRU, they are delivered to the outsourcing company or manufacturer for repair. Therefore, EMCPW includes the following constituent elements: the cost of O-level maintenance during time \(T_{W}\), the cost of checking the dismounted LRU using ATE and detection of the faulty SRU, the cost of shipping the faulty SRU to the outsourcing company or manufacturer, as well as the repaired SRU back to the airline, the cost of repairing faulty SRU at the outsourcing company or manufacturer, and the cost of ATE and spare LRU and SRU recalculated per one aircraft. We determine EMCPW for the third option as follows:  
\[EC_{PW,3}=q\Big{[}LC\Big{(}t_{M}^{O-level}+t_{ATE}^{I-level}\Big{)}+\Big{(}C_{ PF,R}+LC\times t_{PF,D}^{I-level}\Big{)}P_{PF}+C_{TR,SRU}\Big{]}ER(T_{PW})+\]  
\[C_{ATE}^{I-level}/\Big{(}N_{PW}\times F_{ATE}^{I-level}\Big{)}+[C_{LRU}(PS+US)+ \sum\limits_{j=1}^{n}C_{j}SRU_{j}\Big{]}/N_{PW} \tag{35}\]  
where \(t_{ATE}^{I-level}\) is the mean time of checking the LRU with help of ATE at the I-level, \(C_{PF,R}\) is the mean cost of SRU repair with permanent failure at the outsourcing company or manufacturer, \(t_{PF,D}^{I-level}\) is the mean time to detect the place of a permanent failure in the failed LRU with depth to SRU using ATE, \(C_{TR,SRU}\) is the mean cost of delivering the faulty SRU to the outsourcing company or manufacturer and back to the airline's warehouse,\(C_{ATE}^{I-level}\) is the cost of ATE that serves the I-level, \(F_{ATE}^{I-level}\) is the quantity of LRU types that ATE can check, \(C_{j}\) is the \(j\)-th type SRU cost \(\left(j=\overline{1,n}\right)\), \(SRU_{j}\) is the quantity of spare \(j\)-th type SRU, and \(n\) is the quantity of SRU types in the examined LRU. For the third PWM option the average LRU repair time we calculate as follows:  
\[E\left(T_{repair}\right)=t_{ATE}^{I-level}+t_{PF,D}^{I-level}P_{PF}. \tag{36}\]  
The number of spare SRU we can calculate from the condition of guaranteed provision of all LRU (onboard and spare) with spare SRU at a high probability (0.95-0.99) [36]. In the case when the flow of failures is the homogeneous Poisson point process, we determine the optimum quantity of spare SRU of the \(j\)-th type by the Poisson formula as the minimal number \(SRU_{j}\) satisfying the next condition [36]:  
\[1-P\left(\mathrm{H}_{j}\right)>\frac{\left(\mathrm{H}_{j}\lambda_{j}t_{RS,j} \right)^{\left(SRU_{j}+1\right)}}{\left(SRU_{j}+1\right)!}\exp\left(-\mathrm{ H}_{j}\lambda_{j}t_{RS,j}\right), \tag{37}\]  
where \(\mathrm{H}_{j}=mN_{PW}+PS_{j}+US_{j}\) is the aggregated quantity of the \(j\)-th type SRU that installed in all aircraft' LRU of the airline fleet and spare LRU located in the warehouse, \(P(\mathrm{H}_{j})\) is the probability that the total number of LRU will be provided with SRU type \(j\), \(\lambda_{j}\) is the rate of permanent failures of \(j\)-th type SRU, and \(t_{RS,j}\) is the average repair time of the \(j\)-th type SRU at the manufacturer.