**5. Cost comparison between two maintenance processes**

In this chapter, the lifecycle cost of an airplane is considered to be the sum of manufacturing cost, fuel cost incurred during lifecycle, and maintenance cost. Other costs that remain constant for two different approaches are not considered. Cost comparison of two maintenance approaches is discussed in two aspects: cost increase and cost decrease. **Table 1** summarizes the parameters that are used for cost calculation for the two maintenance processes based on Boeing 737-300 Structural Repair Manual and estimated the cost in the maintenance field.

Based on the Structure Repair Manual of a Boeing 737-300, the fuselage skin in the pressurized area is not a regular cylinder. However, it was assumed to be a cylinder to simplify calculation, by using the average diameter *D* ¼ 148in. In addition, the length of the cylinder can be calculated as *L* ¼ 977in. As already stated, the thickness of the fuselage skin varies from station to station; however, the most common thickness of *t* ¼ 0*:*063in is used herein. In addition, the density of fuselage skin, which is made of aluminum alloy 2024-T3, is about *<sup>ρ</sup>* <sup>¼</sup> <sup>0</sup>*:*1lb*=*in3. Therefore, the total weight of fuselage skin in the pressurized area is *W* ¼ *πDLtρ* ¼ 2957lb.

#### **5.1 Cost increased**

**4. Parameters assumed for scheduled and condition-based maintenance**

repair *agvi*

**Figure 4.**

**34**

*scheduled maintenance at every 2800 flight cycles.*

old for requesting maintenance ð Þ *ath* .

*Reliability and Maintenance - An Overview of Cases*

percentile of critical crack size distribution.

Cracks that are missed or intentionally left unattended during maintenance and grow to critical size before the next maintenance interval affect the safety of the aircraft structure. In the case of scheduled maintenance, the thickness of the fuselage skin ð Þ*t* , the interval of scheduled maintenance ð Þ *Nman* , and the threshold for

affect the aircraft's safety, which is influenced by the thickness of the

fuselage skin ð Þ*t* , the frequency of maintenance assessment ð Þ *Nshm* , and the thresh-

This section deals with quantifying the range of parameters for scheduled and condition-based maintenance. As such, each damage instance is modeled as a through-the-thickness center crack in an infinite plate subject to Mode-I fatigue loading, as shown in Appendix A. The uncertainty in the loading condition and material parameters are summarized in **Table 4**. A crack grows due to pressure differential between the cabin and atmosphere, which is modeled by the Paris-Erdogan model, as shown in Appendix A. From fracture mechanics, the critical crack size (Eq. (3)) to cause failure of a fuselage skin depends on the pressure load and, hence, may also be modeled as a probability distribution. This chapter considers a fuselage skin to be failed if the crack grows undetected beyond the 10�<sup>7</sup>

In the scheduled maintenance of a B737-300/400/500, the C check is carried out at about every 2800 flight cycles ð Þ *Nman* ¼ 2*;* 800 [4] for an airplane life of 50,000 flights. The threshold for repair is equal to the detection capability of GVI, *agvi* ¼ 0*:*5 in (12.7 mm). The fraction of cracks which cause failure of fuselage skins due to excessive crack propagation until the end of life is computed by Monte Carlo

*Variation of lifetime (50,000 flight cycles) probability of failure as a function of fuselage skin thickness for*

(1) Manufacturing cost.

Manufacturing cost with SHM system: \$600/lb. Manufacturing cost without SHM system: \$500/lb.


**Table 1.** *Parameters for maintenance cost calculation.* Cost increased : ð Þ� <sup>600</sup> � <sup>500</sup> <sup>2</sup>*;* <sup>957</sup> <sup>¼</sup> <sup>3</sup> � <sup>10</sup><sup>5</sup> ð Þ\$

The downtime for C checks of B737 CL varies from several days to 2 months as the age of the aircraft increases. This chapter regards 30 days as a typical downtime for a C check. Usually, the inspection procedure takes up about 1/3–1/4 of the whole downtime in scheduled maintenance. In condition-based maintenance, however, it is assumed that the assessment process can be completed in 1 day using the SHM

*Advantages of Condition-Based Maintenance over Scheduled Maintenance Using Structural…*

Downtime is shortened not only because of the efficient assessment process in condition-based maintenance but also due to the time spent on removing/installing the surrounding structures for GVI in scheduled maintenance. In the latter case, the general visual inspection can only be carried out when surrounding structures are removed. For example, if general visual inspection is performed on fuselage skins in the cargo area, all floor panels, sidewalls, insulation blankets, etc. have to be removed. Downtime of CBM can be reduced by about 5 days by skipping this

From the analysis above, the downtime can be shortened by 12 days for each maintenance trip in condition-based maintenance. Therefore, the downtime for condition-based maintenance is assumed as 18 days for each maintenance trip:

Cost saved : <sup>27</sup>*;* <sup>428</sup> � <sup>ð</sup><sup>18</sup> � <sup>30</sup> � <sup>7</sup>*:*<sup>8</sup> � <sup>18</sup>Þ ¼ <sup>1</sup>*:*<sup>1</sup> � <sup>10</sup><sup>7</sup>

As stated above, the time shortened on inspection by using SHM system is 7 days. Assume that 100 h of labor is needed on inspection per day at \$60/h:

Cost saved : <sup>7</sup> � <sup>100</sup> � <sup>60</sup> � <sup>18</sup> <sup>¼</sup> <sup>7</sup>*:*<sup>56</sup> � <sup>10</sup><sup>5</sup>

The time spent on removing/installing surrounding structures for easy access of

Cost saved : <sup>5</sup> � <sup>300</sup> � <sup>60</sup> � <sup>18</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>62</sup> � <sup>10</sup><sup>6</sup>ð Þ\$

As calculated above, the number of cracks that need to be repaired is 10 in scheduled maintenance and 5.8 in condition-based maintenance for each maintenance trip. Fuselage skin with cracks detected is repaired by different methods depending on the size of the crack [10]. In the case of fuselage skin, the doubler repair is the most common method. Although different repair methods are adopted according to the size of the crack, in this chapter, it is assumed that the typical

For a doubler of 10 � 10 in, 60 h of labor is needed. The cost for this doubler

Cost saved : <sup>360</sup> � <sup>ð</sup><sup>18</sup> � <sup>10</sup> � <sup>7</sup>*:*<sup>6</sup> � <sup>5</sup>*:*8Þ ¼ <sup>4</sup>*:*<sup>9</sup> � <sup>10</sup><sup>4</sup>ð Þ\$

which is about 10% of the lifecycle cost, by using SHM system on condition-based maintenance over scheduled maintenance. The main factor leading to this cost savings is the reduced net revenue lost due to shortened downtime. The effect of cost saved on inspection and removing/installing the surrounding structures is

**Table 3** summarizes cost increase and decrease for the two maintenance strategies. It can be concluded from the table that total cost saved is about \$1.18 � <sup>10</sup><sup>7</sup>

(3) Cost for removing/installing surrounding structures.

GVI is about 5 days with 300 h of labor per day:

repair is about \$360 with \$60 labor cost per hour:

ð Þ\$

,

ð Þ\$

system. Therefore, about 7 days can be saved on inspection.

*DOI: http://dx.doi.org/10.5772/intechopen.83614*

procedure.

(2) Inspection cost.

(4) Crack repair cost.

doubler repair be implemented.

**37**

(2) Cost on replacing SHM equipment.

A finite life of 12,000 flight cycles for SHM equipment is assumed so that the system will need to be replaced four times during 50,000 flight cycles. The lifetime cost for replacing the SHM system after manufacturing is as follows:

Cost increased : <sup>3</sup> � <sup>10</sup><sup>5</sup> � <sup>4</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>2</sup> � <sup>10</sup>6ð Þ\$

(3) Fuel cost.

Weight penalty: lifetime fuel consumption cost per aircraft weight. Kaufmann et al. [29] used \$1000 per pound as the lifetime fuel cost for 1 pound of gross weight of aircraft. About 5% extra weight is considered for fuselage skin with SHM equipment. Therefore, the cost increase due to SHM equipment weight increased is as follows:

> Cost increased : <sup>2957</sup> � 5% � <sup>1000</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>5</sup> � <sup>10</sup><sup>5</sup> ð Þ\$

### **5.2 Cost decreased**

As damage assessment intervals in condition-based maintenance are much smaller than that of the scheduled maintenance, the threshold ath for requesting condition-based maintenance to be much larger than agvi in scheduled maintenance. This high damage tolerance reduces the number of maintenance trips. In addition, because the threshold for repair *arep*�*shm* is larger than agvi, the number of cracks that are repaired is reduced in condition-based maintenance. It is assumed that these are two factors that would cause savings in aircraft lifecycle maintenance costs.

Monte Carlo simulation (MCS) is performed to compute the number of maintenance trips and the number of cracks repaired on fuselage skins for scheduled and condition-based maintenance. It is assumed that 500 initial cracks on a B733 are distributed on fuselage skins, showing a typical thickness of 0.063 in (1.6 mm).

The damage detection process is governed by the Palmberg expression (Appendix B) with different parameters for scheduled and condition-based maintenance. The parameters computed are listed in **Table 2**. Values in parentheses are MCS standard deviations based on 20,000 airplanes. It is considered that SHM equipment is replaced every 12,000 flight cycles.

It is noted that for the same fuselage skin thickness, condition-based maintenance leads to better reliability and lower number of maintenance trips and cracks repaired. The reason is that scheduled maintenance repairs all the cracks that might grow to threaten safety until the next maintenance, while the condition-based maintenance repairs only those that actually grow to threaten safety.

Based on the results computed above, the cost saved can be calculated as follows: (1) Net revenue saved due to shortened downtime.


**Table 2.**

*Comparison between scheduled and condition-based maintenance.*

*Advantages of Condition-Based Maintenance over Scheduled Maintenance Using Structural… DOI: http://dx.doi.org/10.5772/intechopen.83614*

The downtime for C checks of B737 CL varies from several days to 2 months as the age of the aircraft increases. This chapter regards 30 days as a typical downtime for a C check. Usually, the inspection procedure takes up about 1/3–1/4 of the whole downtime in scheduled maintenance. In condition-based maintenance, however, it is assumed that the assessment process can be completed in 1 day using the SHM system. Therefore, about 7 days can be saved on inspection.

Downtime is shortened not only because of the efficient assessment process in condition-based maintenance but also due to the time spent on removing/installing the surrounding structures for GVI in scheduled maintenance. In the latter case, the general visual inspection can only be carried out when surrounding structures are removed. For example, if general visual inspection is performed on fuselage skins in the cargo area, all floor panels, sidewalls, insulation blankets, etc. have to be removed. Downtime of CBM can be reduced by about 5 days by skipping this procedure.

From the analysis above, the downtime can be shortened by 12 days for each maintenance trip in condition-based maintenance. Therefore, the downtime for condition-based maintenance is assumed as 18 days for each maintenance trip:

> Cost saved : <sup>27</sup>*;* <sup>428</sup> � <sup>ð</sup><sup>18</sup> � <sup>30</sup> � <sup>7</sup>*:*<sup>8</sup> � <sup>18</sup>Þ ¼ <sup>1</sup>*:*<sup>1</sup> � <sup>10</sup><sup>7</sup> ð Þ\$

(2) Inspection cost.

Cost increased : ð Þ� <sup>600</sup> � <sup>500</sup> <sup>2</sup>*;* <sup>957</sup> <sup>¼</sup> <sup>3</sup> � <sup>10</sup><sup>5</sup>

A finite life of 12,000 flight cycles for SHM equipment is assumed so that the system will need to be replaced four times during 50,000 flight cycles. The lifetime

Cost increased : <sup>3</sup> � <sup>10</sup><sup>5</sup> � <sup>4</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>2</sup> � <sup>10</sup>6ð Þ\$

Weight penalty: lifetime fuel consumption cost per aircraft weight. Kaufmann et al. [29] used \$1000 per pound as the lifetime fuel cost for 1 pound of gross weight of aircraft. About 5% extra weight is considered for fuselage skin with SHM equipment. Therefore, the cost increase due to SHM equipment weight increased is as

Cost increased : <sup>2957</sup> � 5% � <sup>1000</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>5</sup> � <sup>10</sup><sup>5</sup>

As damage assessment intervals in condition-based maintenance are much smaller than that of the scheduled maintenance, the threshold ath for requesting condition-based maintenance to be much larger than agvi in scheduled maintenance. This high damage tolerance reduces the number of maintenance trips. In addition, because the threshold for repair *arep*�*shm* is larger than agvi, the number of cracks that are repaired is reduced in condition-based maintenance. It is assumed that these are

two factors that would cause savings in aircraft lifecycle maintenance costs.

Monte Carlo simulation (MCS) is performed to compute the number of maintenance trips and the number of cracks repaired on fuselage skins for scheduled and condition-based maintenance. It is assumed that 500 initial cracks on a B733 are distributed on fuselage skins, showing a typical thickness of 0.063 in (1.6 mm). The damage detection process is governed by the Palmberg expression (Appendix B) with different parameters for scheduled and condition-based maintenance. The parameters computed are listed in **Table 2**. Values in parentheses are MCS standard deviations based on 20,000 airplanes. It is considered that SHM equip-

It is noted that for the same fuselage skin thickness, condition-based maintenance leads to better reliability and lower number of maintenance trips and cracks repaired. The reason is that scheduled maintenance repairs all the cracks that might grow to threaten safety until the next maintenance, while the condition-based

Based on the results computed above, the cost saved can be calculated as follows:

**Avg. no. of maintenance trips per airplane**

maintenance repairs only those that actually grow to threaten safety.

Scheduled 1E-8 18 10 (0.6) Condition-based 1E-13 7.6 (0.3) 5.8 (0.2)

(1) Net revenue saved due to shortened downtime.

**Probability of failure**

*Comparison between scheduled and condition-based maintenance.*

cost for replacing the SHM system after manufacturing is as follows:

(2) Cost on replacing SHM equipment.

*Reliability and Maintenance - An Overview of Cases*

ment is replaced every 12,000 flight cycles.

(3) Fuel cost.

**5.2 Cost decreased**

**Types of maintenance**

**Table 2.**

**36**

follows:

ð Þ\$

ð Þ\$

**Avg. no. of cracks repaired/airplane**

As stated above, the time shortened on inspection by using SHM system is 7 days. Assume that 100 h of labor is needed on inspection per day at \$60/h:

> Cost saved : <sup>7</sup> � <sup>100</sup> � <sup>60</sup> � <sup>18</sup> <sup>¼</sup> <sup>7</sup>*:*<sup>56</sup> � <sup>10</sup><sup>5</sup> ð Þ\$

(3) Cost for removing/installing surrounding structures.

The time spent on removing/installing surrounding structures for easy access of GVI is about 5 days with 300 h of labor per day:

Cost saved : <sup>5</sup> � <sup>300</sup> � <sup>60</sup> � <sup>18</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>62</sup> � <sup>10</sup><sup>6</sup>ð Þ\$

(4) Crack repair cost.

As calculated above, the number of cracks that need to be repaired is 10 in scheduled maintenance and 5.8 in condition-based maintenance for each maintenance trip. Fuselage skin with cracks detected is repaired by different methods depending on the size of the crack [10]. In the case of fuselage skin, the doubler repair is the most common method. Although different repair methods are adopted according to the size of the crack, in this chapter, it is assumed that the typical doubler repair be implemented.

For a doubler of 10 � 10 in, 60 h of labor is needed. The cost for this doubler repair is about \$360 with \$60 labor cost per hour:

$$\text{Cost saved}: \textbf{360} \times (\textbf{18} \times \textbf{10} - 7.6 \times \textbf{5.8}) = \textbf{4.9} \times \textbf{10}^4(\textbf{s})$$

**Table 3** summarizes cost increase and decrease for the two maintenance strategies. It can be concluded from the table that total cost saved is about \$1.18 � <sup>10</sup><sup>7</sup> , which is about 10% of the lifecycle cost, by using SHM system on condition-based maintenance over scheduled maintenance. The main factor leading to this cost savings is the reduced net revenue lost due to shortened downtime. The effect of cost saved on inspection and removing/installing the surrounding structures is


desired level of safety. Recently, with the development of SHM techniques, condition-based maintenance uses onboard SHM sensors and actuators to detect damage on fuselage skins, which, in turn, may be performed as frequently as needed. Hence, maintenance is requested only when a particular condition is met. The improved reliability and cost savings of condition-based maintenance over scheduled one are discussed. As the usage of onboard SHM system, downtime for each maintenance trip is shortened significantly in condition-based maintenance, leading to considerable cost saving of net revenue. This SHM system also avoids removing/installing the surrounding structures. All these factors may lead to significant cost savings in CBM. In addition, some potential advantages of conditionbased maintenance are discussed in this chapter, which includes reducing the possibility of human error during the maintenance process, preparing maintenance equipment in advance, and using the same sensors to detect other types of damages.

*Advantages of Condition-Based Maintenance over Scheduled Maintenance Using Structural…*

This research was partly supported by NASA Langley Research Center (Contract

No. NNX08AC33A). The authors gratefully acknowledge this support.

**A. Fatigue damage growth due to fuselage pressurization**

Fatigue crack growth can be modeled in a number of ways. Beden et al. [30] provided an extensive review of crack growth models. Mohanty et al. [31] used an exponential model to model fatigue crack growth. Scarf [32] advocated the use of simple models, when the objective was to demonstrate the predictability of crack growth. In this chapter, a simple Paris-Erdogan model [33] is considered to describe the crack growth behavior. However, other advanced models can also be used.

Damage in the fuselage skin of an airplane is modeled as a through-the-thickness center crack in an infinite plate. The life of an airplane can be viewed as consisting of damage growth cycles, interspersed with inspection and repair. The cycles of pressure difference between the interior and the exterior of the cabin during each flight is instrumental in fatigue damage growth. The crack growth behavior is modeled using the Paris-Erdogan model, which gives the rate of damage size

**Acknowledgements**

**List of abbreviations**

CBM condition-based maintenance CVM comparative vacuum monitoring

*DOI: http://dx.doi.org/10.5772/intechopen.83614*

MRO maintenance, repair, and overhaul

PDF probability density function PWAS piezoelectric wafer active sensor SHM structural health monitoring

DVI detailed visual inspection FBG fiber Bragg grating GVI general visual inspection MCS Monte Carlo simulation

NDT nondestructive test

**Appendices**

**39**

#### **Table 3.**

*Summary of cost increased and decreased for two maintenance approaches.*

relatively small (20% of the total cost saved). It is also noted that cost saved by the reduced number of cracks repaired is negligible.
