# Through-Life Maintenance Cost of Digital Avionics
## 7 Results and Discussion
### Numerical Example  
Let's consider an example of minimizing the expected cost of warranty maintenance for the A380 airborne inertial reference system (ADIRS). In 2012, the airline Eminrates (UAE) received eight aircraft A380 [39]. Each aircraft had three air data inertial reference units (ADIRU) of HG2030 BE (Honeywell) type that form the redundant ADIRS system. The reliability characteristics of the HG2030 BE ADIRU are as follows: MTBF is 40,000 h, and MTBUR is 23,500 h [40]. ADIRS gives aerial information (airspeed, angle of attack, and altitude) and inertial control information (location and altitude) to pilot display and other aircraft systems such as engines, autopilot, and aircraft chassis. ADIRS comprises three fault-tolerant ADIRU located in the electronic rack of the aircraft. The third ADIRU is a standby unit that may be selected to provide data to the first or second pilot's displays in the case of a partial or total failure of ADIRU 1 or N* 2. ADIRS does not have crossover redundancy between ADIRU 1 and ADIRU 12, since ADIRU 13 is the only alternative source of air and inertial data. Failure of air data stream from ADIRU 1 or ADIRU 2 will result in a loss of airspeed and altitude information on the corresponding display. In any case, the information can only be restored by selecting ADIRU 3. According to the data given in [40], the approximate price of ADIRU is $31,000. According to [41], the average flight time (\(\tau\)) of the A380 is 8 h, and the average flying hours per year for a single A380 is approximately 5000 h. Data on testing and setting up ADIRU in the laboratory are given in [42]. The rest of the initial data are taken from various instructions, technical descriptions and are as follows: \(T_{W}=5000\) h, \(t_{M}^{O-level}=1\) h, \(LC=15\) $, \(C_{LRU}=531,000\), \(T_{RS}=15\) days, \(T_{ED}=1\) day, \(t_{TE}^{I-level}=2\) h, \(F_{TE}^{I-level}=1\), and \(C_{TE}^{I-level}=\$20,000\).  
Since \(MTBF=40,000\) h, then \(\lambda=2.5\times 10^{-5}\) h\({}^{-1}\). As far as MTBUR is less than MTBF, this decrease is associated with false-positives and intermittent faults. Let's assume that false-positives and intermittent faults have the same impact on MTBUR. In this case, from Equation (A1) on infinite horizon we numerically find that \(P_{flight}^{FP}=1.25\times 10^{-5}\) and \(\theta=1.25\times 10^{-5}\) h\({}^{-1}\).  
As we can see in Table 1, the expected maintenance costs per aircraft for the first WM option is less than for the second option. Therefore, the first WM option is preferable for the given data.  
Let's consider an example of minimizing the expected cost of post-warranty maintenance for the ADIRS of the aircraft Airbus A380. By September 2017, the Eminrates (UAE) airline received 97 A380 aircraft for operation [43]. We determine the average cost per one ADIRS of the A380 for various PWM options by using Equations (33)-(42). According to [44; 45], each ADIRU includes the following SRU: an air data computer (ADC), a multi-mode receiver (MMR), three digital ring laser gyros, three quartz accelerometers, and a power supply module. As indicated in [46], the cost of three digital ring laser gyroscopes is about $15,000. In the calculation of the expected maintenance cost per aircraft for various options of PWM, we used the following data: \(T_{PW}=50,000\) h, \(N_{PW}=97\), \(C_{TR}=$3000\), \(C_{IF}=C_{FP}=$53000\), \(C_{PF}=$5000\), \(C_{PF}=$6000\), \(C_{PF,R}=$600\), \(C_{IF,R}=$1500\), \(C_{TR,SRU}=$5100\), \(C_{ATE}^{l-level}=$52,000\), \(000\), \(U_{ATE}^{l-level}=3\) h, \(F_{ATE}^{l-level}=120\), \(C_{I}=$58000\) (\(j=1,2,3\)), \(C_{j}=$52670\) (\(j=\overline{4,9}\)), \(t_{ATE}^{l-Level}=1\) h, \(C_{IFD}=$5100,000\), \(F_{IFD}^{l-Level}=120\), \(t_{PF,D}^{l-Level}=0.25\) h, \(t_{PF,D}^{p-Level}=2\) h, \(t_{LFD}^{p-Level}=3\) h, \(t_{LFD}^{p-Level}=3\) h, \(C_{PF,R}^{p-Level}=$200\), \(C_{IF,R}^{p-Level}=$200\), \(C_{DRT}^{p-Level}=$2000\), \(C_{DRT}^{D-Level}=$500\), and \(\sum_{j=1}^{9}\sum_{z=1}^{SRU,y}C_{y,z}X_{yz}=$40,000\).