# Commonality Benefit Analysis for Maintenance Technical Publications of Civil Aircraft Based on Learning Effect

Authors: Yongjie ZHANG; Yongqi ZENG; Kang CAO; Yuefan JIANG; Ke LIANG
Journal: International Journal of Aerospace Engineering
 (2022)

---

## Abstract

The maintenance technical publications of civil aircraft are important engineering information for maintaining the continued airworthiness of aircraft, strictly guiding the maintenance of aircraft, and seriously affecting the efficiency of aircraft maintenance. The commonality between maintenance technical publications corresponding to different aircraft types brings primitive experience to aircraft operators for the maintenance of newly introduced types, which can accelerate the adaptation of maintenance personnel and reduce the maintenance time of aircraft. To quantify the commonality of maintenance technical publications, we constructed a commonality evaluation system for maintenance technical publications by combining the Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation Method. Then, a commonality benefit evaluation model of maintenance technical publications is established by analyzing the impact of commonality on the learning effect, which can analyze and calculate the monthly maintenance time savings of newly introduced models after the effects of commonality. The commonality benefit analysis for maintenance technical publications in this paper is mainly for aircraft operators, which can provide the reference for their decision to introduce new aircraft types.


---

## Body

## 1. Introduction

Civil aircraft technical publications have been found as vital engineering information offered by aircraft manufacturers, which can maintain the continuous airworthiness of aircraft and primarily aim to help operators more effectively use and maintain aircraft through manuals. Civil aircraft technical publications should comply with international technical publication specifications (e.g., S1000D and ATA2200) [1, 2] to achieve standardization and structurization of documents. Aircraft maintenance is an essential basis for ensuring the continued safe operation of aircraft. During aircraft maintenance, aircraft maintenance engineers should develop and implement maintenance plans by strictly complying with the maintenance technical publications to accurately identify possible problems and successfully implement maintenance.The more familiar maintenance engineers are with civil aircraft maintenance technical publications, the faster they can plan maintenance, thus shortening maintenance time, reducing aircraft downtime, and improving aircraft utilization, enabling airlines to generate higher benefits. Because of the similarities in the structure, shape, and systems of various civil aircraft and the need to comply with common international norms when preparing maintenance technical publications, there are commonalities among civil aircraft maintenance technical publications. Especially when airlines operate new aircraft types, the commonality of maintenance technical publications will give engineers primitive experience and faster familiarization with the manuals, leading to more rapid adaptation of the new aircraft and improving the efficiency of aircraft maintenance. Therefore, it is important to research how to quantitatively evaluate the commonality among maintenance technical publications and explore commonality benefits in maintenance technical publications for aircraft maintenance.The understanding of commonality varies in different fields and under different focus perspectives. But there is no uniform definition of commonality. From a product perspective, some scholars define commonality as a common characteristic that products have, or a manifestation that different products use the same components [3–5]; from an inventory perspective, others define commonality as a method that can simplify inventory management and control [6–8]. Although the cognitive perspectives and degrees are different, they all reflect the similarity in the research process of commonality. Therefore, based on their research, we combine our understanding to define commonality as the reuse and sharing of a series of assets developed according to generalized similarity. The study of commonality in maintenance technical publications reflects the experience-sharing effect of commonality that leads to increased maintenance efficiency.To evaluate commonality, Thevenot and Simpson [9] summarized six commonality indices (including DCI, TCCI, CI, %C, PCI, and CI(C)) and proposed a novel commonality index called as Comprehensive Metric for Commonality (CMC) through comparative analysis [10]. Table 1 summarizes these seven commonality indices. However, these commonality indices are specific to products consisting of parts or components and cannot be used for products such as apparel or knowledge. Maintenance technical publications are knowledge-based products that exist in different forms, either in paper form or electronic form. To evaluate the commonality of maintenance technical publications, indicators for judging similarity can be extracted according to product characteristics as commonality indicators, which generally have fuzzy properties. For the measurement of such fuzzy indicators, expert systems can be fully utilized to obtain analytical data by designing questionnaires [11–14].Table 1
Commonality indexes [6, 9].
NameCommonality measure forNo commonalityComplete commonalityDICDegree of commonality indexThe whole family1β=∑j=i+1i+dϕjTCCITotal constant commonality indexThe whole family01CIProduct line commonality indexThe whole family0100%CPercent commonality indexIndividual product0100PCIPercent commonality indexThe whole family01CI(C)Component part commonalityThe whole family1α=∑j=1d∑i=1i+dϕijCMCComprehensive metric for commonalityThe whole family01There has been much research into the benefits of commonality in the aviation field. Boeing was the first to propose the concept of “commonality,” whose primary purpose was to reduce the cost of manufacturers and improve the quality of their products, and customers could also benefit from it. Boeing has used the philosophy of commonality of design for the B757 and B767 [15, 16], developing both aircraft in parallel, significantly reducing the development cycle, and saving costs. Damien et al. studied cockpit commonality and found that commonality in the cockpit simplified the pilot training process for airlines, particularly decreasing the time required for pilot transfer training [17]. Nuffort, one of the first researchers to investigate the full life cycle of aircraft to determine the appropriate level of commonality in aircraft series, suggested that the proper use of commonality could lower the cost of ownership by reducing procurement costs and operating and support costs [18]. Zhang et al. developed a model of the impact of commonality on aircraft lifecycle costs for civil aircraft. The model calculated the break-even point for target aircraft with and without commonality, verifying that commonality has a positive impact [19].Based on the current situation of commonality in the aviation field, we found that the research on commonality in civil aircraft mainly focuses on the aircraft itself but rarely extends to the aircraft operation and support system. Specifically, we must establish a commonality evaluation system for maintenance technology publications. The combined method of the Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation Method has the characteristics of requiring fewer data and being able to analyze systematically. At the same time, it is also widely used in engineering evaluation with fuzzy properties. Therefore, this method is very suitable for evaluating the commonality of maintenance technical publications. Then, a model of commonality benefits was established by analyzing the effect of commonality on learning effects. The model can calculate the maintenance time saving for aircraft operators introducing new types by the effect of maintenance technology publications.The remainder of this paper is organized as follows: in Section2, a system is constructed to evaluate the commonality of maintenance technical publications. The commonality benefit of maintenance technical publications is analyzed in the context of learning curves in Section 3. On this basis, the methods and models in the previous paper are demonstrated with examples in Section 4. Finally, conclusions are drawn in Section 5.


## 2. Commonality Evaluation System for Maintenance Technical Publications

### 2.1. Maintenance Technical Publications

Technical publications, an indispensable product provided to the customer by the main manufacturer of the aircraft, can effectively protect the aircraft during the entire operation of the aircraft [20]. In practice, aircraft technical publications are presented as manuals, which are large in number and highly customizable. Based on the usage scenarios of the manuals, they can fall into two types, including aircraft operation manuals and aircraft maintenance manuals. The aircraft maintenance manuals, a significant subcategory of technical publications for aircraft, provide text, diagrams, and processes to describe the technical characteristics, composition, inspection and monitoring, maintenance realization, and maintenance constraints of the aircraft. It offers instructions for using and maintaining the product and guarantees that the aircraft is operated safely within the permitted operational parameters.Since a large number and rich content characterize aircraft maintenance technical publications (manuals), it will be a considerable workload and challenging to evaluate each manual. Accordingly, when conducting the commonality evaluation, we select representative manuals from the main maintenance technical publications in maintenance engineering listed in Table2 as the evaluation objects and build the evaluation system. A survey of the aircraft maintenance personnel is carried out through questionnaires. They are required to select five technical publications that are applied more frequently in their work or have a more significant effect on maintenance work in accordance with the actual work situation. Based on the feedback from the questionnaire, Aircraft Maintenance Manual (AMM), Illustrated Parts Catalog (IPC), Structural Repair Manual (SRM), Fault Isolation Manual (FIM), and Component Repair Manual (CMM) are selected from the aircraft maintenance technical publications listed in Table 2 as the representative manuals for the commonality evaluation of maintenance manuals, as illustrated in Figure 1. These five manuals have a significant impact on the aircraft maintenance process, with the AMM and IPC manuals being used by all maintenance personnel.Table 2
Main aircraft maintenance technical publications.
Aircraft maintenance manual (AMM)Structural repair manual (SRM)Nondestructive testing manual (NTM)Fault isolation manual (FIM)Fault reporting manual (FRM)Consumed product manual (CPM)Ground equipment manual (GEM)Aircraft rescue manual (ARM)Power plant buildup manual (PPBM)Component maintenance manual (CMM)Engine manual (EM)Electrical standard practices manual (ESPM)Electrical wiring interconnection system manual (EWISM)Aircraft wiring manual (AWM)System schematic manual (SSM)Illustrated parts catalog (IPC)Illustrated tools and equipment manual (ITEM)Maintenance review board report (MRBR)Maintenance planning document (MPD)Schedule maintenance request (SMR)Airworthiness limited section (ALS)Figure 1
Commonly used manuals for aircraft maintenance.


### 2.2. Commonality Evaluation Indicators for Maintenance Technical Publications

Maintenance manuals involve necessary information for maintenance work and can guide the smooth progress of maintenance work. It is indicated that the commonality assessment is the broad similarity of two products based on the definition of commonality in the first section. It should include the similarity of other influencing factors for the products. By comparing the five manuals of different aircraft, we extracted the main features of the manuals, including manual structure, manual layout, text, pictures, and tables, and six indicators with fuzzy attributes were picked as manual content commonality indicators including manual overall structure, manual organization structure, style habits, textual content description, picture content description, and form and content of tables. By investigating the process of manual use by maintenance engineers, it was found that the manual in the format of existence, use method, use scenario, and update process affects maintenance work, so they were selected as the manual use commonality indicators. Therefore, the evaluation system of manual commonality is established, as shown in Figure2, by evaluating the manual content and manual use. In the following, the specific indicators of content commonality and use commonality for manual commonality evaluation are described in detail.Figure 2
Generic evaluation indicators system of manual commonality.


#### 2.2.1. Content Commonality Indicators

(1) Manual Overall Structure. The structure of the manual in accordance with the distribution of functional parts or chapters. For instance, the overall structure of the AMM manual is distributed based on the ATA100 chapter number, and the overall structure of the Flight Crew Operations Manual (FCOM) is distributed in line with the three functional parts (system description, operating procedures, and operating data).(2) Manual Organization Structure. The organization structure within the functional parts and chapters in the manual (e.g., chapter cover - effective page-sub-chapter and other subdivision structures).(3) Manual Style Habits. The style habits of the manual content (e.g., font size, line spacing, indentation methods, and the form of tips and warnings information).(4) Textual Content Description. The description of the content of the text part of the manual, primarily referring to some process content description and description of the introductory content description.(5) Picture Content Description. The existence of the dimension of the picture in the manual (2D diagram or 3D diagram) and the general content of the corresponding picture expressed.(6) Form and Content of Tables. The format of the tables in the manual and the description of the content in the tables.


#### 2.2.2. Use Commonality Indicators

(1) Presence Medium. The use of the manual in the form of paper, PDF, or interactive electronic technical publication (IETP) alone, or a combination of the above two or three.(2) Query Mode. The query and use mode of the manual.(3) Usage Scenario. The situation in which the manual is employed. For instance, the AMM manual has been commonly applied in airline maintenance.(4) Manual Update. The relevant process of receiving the novel manual and the display of the updated content of the manual after manual updating.


### 2.3. Introduction of Commonality Evaluation Methods for Maintenance Technical Publications

#### 2.3.1. Analytic Hierarchy Process (AHP)

Analytic Hierarchy Process has been commonly applied in systems engineering to decompose a complex problem into its component factors [21], group the above factors into an orderly hierarchy in accordance with the dominant relationship, determine the relative importance of the factors in the hierarchy by comparing them with each other, and then integrate human judgment to decide the order of relative importance of the factors in the decision. The major steps are elucidated below.(1) A Hierarchical Structure Is Established. The manual commonality evaluation index system was built in the previous section, forming the progressive hierarchy in the hierarchical analysis method.(2) Pairwise Judgment Matrix Is Constructed. When comparing the maintenance manual’s commonality between two different aircraft types, the two manuals are compared in terms of the importance of the impact of the indicators on maintenance work in the actual use of the manuals. Besides, the quantitative scoring is conducted according to Table 3. Lastly, a judgment matrix, the forward reciprocal matrix, is built. For instance, the text content of the AMM is strongly more important than the overall structure of the manual for the maintenance work, so the two have a comparison score of 7. The IPC primarily consists of pictures, and the importance of picture content of the IPC manual is extremely more important than that of the text content, so the comparison score of the two is 9.Table 3
Meaning of the scalar method (1-9).
Take valueMeaning1Two elements have the same importance compared with each other3One element is slightly more important than the other as compared with the other element5One element is significantly more important than the other as compared with the two elements7One element is strongly more important than the other as compared with two elements9One element is extremely more important than the other as compared with the other elementOthers2, 4, 6, and 8 are the median values of the above adjacent judgments(3) Calculation of the Relative Weights of Indicators Under a Single Criterion. In the above step, the ranking weights of 6 individual indicators and 4 individual indicators are calculated according to the manual content commonality and manual use commonality. The consistency test is performed to verify whether the requested weights meet the requirements. The calculation of indicator weights can be solved precisely by the eigenvalue method. But when the order of the judgment matrix is too large, the eigenvalue method is not easy to solve. Thus, approximate methods such as the summation method and the square root method can be used to calculate the ranking weights.During the construction of the pairwise judgment matrix, the judgment matrix is not required to have consistency, which is determined by the complexity of objective things and the diversity of human perception, whereas it is recommended to require general consistency of the judgment. Thus, a consistency test is required in the calculation process, and the steps are presented below.(a)
Calculate Consistency Index C.I..(1)C.I.=λmax−nn−1,where n denotes the order of the pairwise judgment matrix; λmax represents the maximum eigenvalue of matrix A(b)
Find the Average Random Consistency Index R.I.. The average random consistency index is obtained by taking the arithmetic average after the eigenvalue of the random judgment matrix is calculated several times (more than 500 times). Its introduction can make up for the drawback that the consistency judgment index increases significantly with the increase inn. Table 4 lists the average random consistency index obtained by calculating the reciprocal matrix of order 1-15 for 1000 times(c)
Calculation of Consistency Ratio C.R..(2)C.R.=C.I.R.I..Table 4
Average random consistency index.
Order12345678R.I.000.520.891.121.261.361.41Order9101112131415R.I.1.461.491.521.541.561.581.59WhenC.R.<0.1, the consistency of the two-comparison judgment matrix is generally considered acceptable, and the calculated indicator weights are based on the requirementsAfter experts compare the scores of manual content commonality indicators and manual use commonality indicators, a judgment matrix is built. A consistency test can determine the indicator weights of manual content commonality indicators and manual use commonality indicators.


#### 2.3.2. Fuzzy Comprehensive Evaluation Method

Fuzzy Comprehensive Evaluation Method is to provide some evaluation methods for some practical comprehensive evaluation problems based on several concepts of fuzzy mathematics. To be specific, a fuzzy comprehensive evaluation is based on fuzzy mathematics, which follows the principle of fuzzy relationship synthesis and quantifies some elements with unclear boundaries and is not easy to quantify; it can comprehensively evaluate the evaluated thing’s affiliation status from multiple factors [22, 23].The main steps of the Fuzzy Comprehensive Evaluation Method for the commonality of maintenance technical publications are elucidated below.(a)
Determining the Set of FactorsFand the Set of RubricsE. Factor set F refers to the set of evaluation items or indicators, i.e., manual content commonality indicators and manual use commonality indicators; F=fi=manualcontentcommonalityindicators or {manual use commonality indicators}.The set of rubricsE refers to the set of evaluation levels; the set of commonality rubrics is E=e1,e2,e3,e4,e5=extremecommonality,highcommonality,averagecommonality,lowcommonality,andminimalcommonality(b)
The Single-Factor Evaluation Affiliation Vector is Statistically Determined, and the Affiliation MatrixRIs Formed. The degree of affiliation is the most basic and important concept in the Fuzzy Comprehensive Evaluation Method. The so-called affiliation degree represents the size (degree) of the possibility of multiple evaluation subjects to evaluate ej of the evaluation object according to fi. The affiliation vector Ri=ri1,ri2,⋯,rim,i=1,2,⋯,n,∑j=1mrij=1, the affiliation matrix is written as
(3)R=R1,R2,⋯,RnT=r11r12⋯r1mr21r22⋯r2m⋮⋮⋱⋮rn1rn2⋯rnm(c)
Determine the Weight VectorWF. WF denotes the weight of the indicator, which can be determined by AHP. Moreover, the numerical results (standard satisfaction vector) WE of the set of rubrics can be available. Based on the statistical description of the occurrence of small probability events, the numerical results of extremely common and minimal common are obtained as 0.95 and 0.05, thus determining WE=0.95,0.7,0.5,0.3,0.05.(d)
Calculate the Commonality ValueC. The commonality values are generally calculated through matrix operations S=WFR, C=WESTThe above steps can be adopted to obtain the content commonality and use commonality values of the same manual for two different models.


### 2.4. Commonality Evaluation System for Technical Publications

The technical publication commonality evaluation system, as shown in Figure3, was built by synthesizing the previous paper. Five manuals, AMM, IPC, RSM, FIM, and CMM, were extracted as the representative manuals for the commonality evaluation of maintenance technical publications, and the weights in the commonality evaluation system of maintenance technical publications were determined by AHP according to the frequency of use of the five manuals in maintenance work. Subsequently, according to the manual commonality evaluation system, the indicator weights are determined by AHP, and the content commonality value and the use commonality value of each manual are calculated by combining the Fuzzy Comprehensive Evaluation Method [24]. Moreover, the commonality value of the same manual of two different models can be obtained by weighting the commonality value of the manual content and the commonality value of the manual use. Lastly, the final commonality value of maintenance publications between two different models is calculated by weighting the weights of the manuals. The final commonality values obtained lay a basis for analyzing the commonality benefits of the maintenance technical publications.Figure 3
The overall evaluation system of technical publication commonality.


## 2.1. Maintenance Technical Publications

Technical publications, an indispensable product provided to the customer by the main manufacturer of the aircraft, can effectively protect the aircraft during the entire operation of the aircraft [20]. In practice, aircraft technical publications are presented as manuals, which are large in number and highly customizable. Based on the usage scenarios of the manuals, they can fall into two types, including aircraft operation manuals and aircraft maintenance manuals. The aircraft maintenance manuals, a significant subcategory of technical publications for aircraft, provide text, diagrams, and processes to describe the technical characteristics, composition, inspection and monitoring, maintenance realization, and maintenance constraints of the aircraft. It offers instructions for using and maintaining the product and guarantees that the aircraft is operated safely within the permitted operational parameters.Since a large number and rich content characterize aircraft maintenance technical publications (manuals), it will be a considerable workload and challenging to evaluate each manual. Accordingly, when conducting the commonality evaluation, we select representative manuals from the main maintenance technical publications in maintenance engineering listed in Table2 as the evaluation objects and build the evaluation system. A survey of the aircraft maintenance personnel is carried out through questionnaires. They are required to select five technical publications that are applied more frequently in their work or have a more significant effect on maintenance work in accordance with the actual work situation. Based on the feedback from the questionnaire, Aircraft Maintenance Manual (AMM), Illustrated Parts Catalog (IPC), Structural Repair Manual (SRM), Fault Isolation Manual (FIM), and Component Repair Manual (CMM) are selected from the aircraft maintenance technical publications listed in Table 2 as the representative manuals for the commonality evaluation of maintenance manuals, as illustrated in Figure 1. These five manuals have a significant impact on the aircraft maintenance process, with the AMM and IPC manuals being used by all maintenance personnel.Table 2
Main aircraft maintenance technical publications.
Aircraft maintenance manual (AMM)Structural repair manual (SRM)Nondestructive testing manual (NTM)Fault isolation manual (FIM)Fault reporting manual (FRM)Consumed product manual (CPM)Ground equipment manual (GEM)Aircraft rescue manual (ARM)Power plant buildup manual (PPBM)Component maintenance manual (CMM)Engine manual (EM)Electrical standard practices manual (ESPM)Electrical wiring interconnection system manual (EWISM)Aircraft wiring manual (AWM)System schematic manual (SSM)Illustrated parts catalog (IPC)Illustrated tools and equipment manual (ITEM)Maintenance review board report (MRBR)Maintenance planning document (MPD)Schedule maintenance request (SMR)Airworthiness limited section (ALS)Figure 1
Commonly used manuals for aircraft maintenance.


## 2.2. Commonality Evaluation Indicators for Maintenance Technical Publications

Maintenance manuals involve necessary information for maintenance work and can guide the smooth progress of maintenance work. It is indicated that the commonality assessment is the broad similarity of two products based on the definition of commonality in the first section. It should include the similarity of other influencing factors for the products. By comparing the five manuals of different aircraft, we extracted the main features of the manuals, including manual structure, manual layout, text, pictures, and tables, and six indicators with fuzzy attributes were picked as manual content commonality indicators including manual overall structure, manual organization structure, style habits, textual content description, picture content description, and form and content of tables. By investigating the process of manual use by maintenance engineers, it was found that the manual in the format of existence, use method, use scenario, and update process affects maintenance work, so they were selected as the manual use commonality indicators. Therefore, the evaluation system of manual commonality is established, as shown in Figure2, by evaluating the manual content and manual use. In the following, the specific indicators of content commonality and use commonality for manual commonality evaluation are described in detail.Figure 2
Generic evaluation indicators system of manual commonality.


### 2.2.1. Content Commonality Indicators

(1) Manual Overall Structure. The structure of the manual in accordance with the distribution of functional parts or chapters. For instance, the overall structure of the AMM manual is distributed based on the ATA100 chapter number, and the overall structure of the Flight Crew Operations Manual (FCOM) is distributed in line with the three functional parts (system description, operating procedures, and operating data).(2) Manual Organization Structure. The organization structure within the functional parts and chapters in the manual (e.g., chapter cover - effective page-sub-chapter and other subdivision structures).(3) Manual Style Habits. The style habits of the manual content (e.g., font size, line spacing, indentation methods, and the form of tips and warnings information).(4) Textual Content Description. The description of the content of the text part of the manual, primarily referring to some process content description and description of the introductory content description.(5) Picture Content Description. The existence of the dimension of the picture in the manual (2D diagram or 3D diagram) and the general content of the corresponding picture expressed.(6) Form and Content of Tables. The format of the tables in the manual and the description of the content in the tables.


### 2.2.2. Use Commonality Indicators

(1) Presence Medium. The use of the manual in the form of paper, PDF, or interactive electronic technical publication (IETP) alone, or a combination of the above two or three.(2) Query Mode. The query and use mode of the manual.(3) Usage Scenario. The situation in which the manual is employed. For instance, the AMM manual has been commonly applied in airline maintenance.(4) Manual Update. The relevant process of receiving the novel manual and the display of the updated content of the manual after manual updating.


## 2.2.1. Content Commonality Indicators

(1) Manual Overall Structure. The structure of the manual in accordance with the distribution of functional parts or chapters. For instance, the overall structure of the AMM manual is distributed based on the ATA100 chapter number, and the overall structure of the Flight Crew Operations Manual (FCOM) is distributed in line with the three functional parts (system description, operating procedures, and operating data).(2) Manual Organization Structure. The organization structure within the functional parts and chapters in the manual (e.g., chapter cover - effective page-sub-chapter and other subdivision structures).(3) Manual Style Habits. The style habits of the manual content (e.g., font size, line spacing, indentation methods, and the form of tips and warnings information).(4) Textual Content Description. The description of the content of the text part of the manual, primarily referring to some process content description and description of the introductory content description.(5) Picture Content Description. The existence of the dimension of the picture in the manual (2D diagram or 3D diagram) and the general content of the corresponding picture expressed.(6) Form and Content of Tables. The format of the tables in the manual and the description of the content in the tables.


## 2.2.2. Use Commonality Indicators

(1) Presence Medium. The use of the manual in the form of paper, PDF, or interactive electronic technical publication (IETP) alone, or a combination of the above two or three.(2) Query Mode. The query and use mode of the manual.(3) Usage Scenario. The situation in which the manual is employed. For instance, the AMM manual has been commonly applied in airline maintenance.(4) Manual Update. The relevant process of receiving the novel manual and the display of the updated content of the manual after manual updating.


## 2.3. Introduction of Commonality Evaluation Methods for Maintenance Technical Publications

### 2.3.1. Analytic Hierarchy Process (AHP)

Analytic Hierarchy Process has been commonly applied in systems engineering to decompose a complex problem into its component factors [21], group the above factors into an orderly hierarchy in accordance with the dominant relationship, determine the relative importance of the factors in the hierarchy by comparing them with each other, and then integrate human judgment to decide the order of relative importance of the factors in the decision. The major steps are elucidated below.(1) A Hierarchical Structure Is Established. The manual commonality evaluation index system was built in the previous section, forming the progressive hierarchy in the hierarchical analysis method.(2) Pairwise Judgment Matrix Is Constructed. When comparing the maintenance manual’s commonality between two different aircraft types, the two manuals are compared in terms of the importance of the impact of the indicators on maintenance work in the actual use of the manuals. Besides, the quantitative scoring is conducted according to Table 3. Lastly, a judgment matrix, the forward reciprocal matrix, is built. For instance, the text content of the AMM is strongly more important than the overall structure of the manual for the maintenance work, so the two have a comparison score of 7. The IPC primarily consists of pictures, and the importance of picture content of the IPC manual is extremely more important than that of the text content, so the comparison score of the two is 9.Table 3
Meaning of the scalar method (1-9).
Take valueMeaning1Two elements have the same importance compared with each other3One element is slightly more important than the other as compared with the other element5One element is significantly more important than the other as compared with the two elements7One element is strongly more important than the other as compared with two elements9One element is extremely more important than the other as compared with the other elementOthers2, 4, 6, and 8 are the median values of the above adjacent judgments(3) Calculation of the Relative Weights of Indicators Under a Single Criterion. In the above step, the ranking weights of 6 individual indicators and 4 individual indicators are calculated according to the manual content commonality and manual use commonality. The consistency test is performed to verify whether the requested weights meet the requirements. The calculation of indicator weights can be solved precisely by the eigenvalue method. But when the order of the judgment matrix is too large, the eigenvalue method is not easy to solve. Thus, approximate methods such as the summation method and the square root method can be used to calculate the ranking weights.During the construction of the pairwise judgment matrix, the judgment matrix is not required to have consistency, which is determined by the complexity of objective things and the diversity of human perception, whereas it is recommended to require general consistency of the judgment. Thus, a consistency test is required in the calculation process, and the steps are presented below.(a)
Calculate Consistency Index C.I..(1)C.I.=λmax−nn−1,where n denotes the order of the pairwise judgment matrix; λmax represents the maximum eigenvalue of matrix A(b)
Find the Average Random Consistency Index R.I.. The average random consistency index is obtained by taking the arithmetic average after the eigenvalue of the random judgment matrix is calculated several times (more than 500 times). Its introduction can make up for the drawback that the consistency judgment index increases significantly with the increase inn. Table 4 lists the average random consistency index obtained by calculating the reciprocal matrix of order 1-15 for 1000 times(c)
Calculation of Consistency Ratio C.R..(2)C.R.=C.I.R.I..Table 4
Average random consistency index.
Order12345678R.I.000.520.891.121.261.361.41Order9101112131415R.I.1.461.491.521.541.561.581.59WhenC.R.<0.1, the consistency of the two-comparison judgment matrix is generally considered acceptable, and the calculated indicator weights are based on the requirementsAfter experts compare the scores of manual content commonality indicators and manual use commonality indicators, a judgment matrix is built. A consistency test can determine the indicator weights of manual content commonality indicators and manual use commonality indicators.


### 2.3.2. Fuzzy Comprehensive Evaluation Method

Fuzzy Comprehensive Evaluation Method is to provide some evaluation methods for some practical comprehensive evaluation problems based on several concepts of fuzzy mathematics. To be specific, a fuzzy comprehensive evaluation is based on fuzzy mathematics, which follows the principle of fuzzy relationship synthesis and quantifies some elements with unclear boundaries and is not easy to quantify; it can comprehensively evaluate the evaluated thing’s affiliation status from multiple factors [22, 23].The main steps of the Fuzzy Comprehensive Evaluation Method for the commonality of maintenance technical publications are elucidated below.(a)
Determining the Set of FactorsFand the Set of RubricsE. Factor set F refers to the set of evaluation items or indicators, i.e., manual content commonality indicators and manual use commonality indicators; F=fi=manualcontentcommonalityindicators or {manual use commonality indicators}.The set of rubricsE refers to the set of evaluation levels; the set of commonality rubrics is E=e1,e2,e3,e4,e5=extremecommonality,highcommonality,averagecommonality,lowcommonality,andminimalcommonality(b)
The Single-Factor Evaluation Affiliation Vector is Statistically Determined, and the Affiliation MatrixRIs Formed. The degree of affiliation is the most basic and important concept in the Fuzzy Comprehensive Evaluation Method. The so-called affiliation degree represents the size (degree) of the possibility of multiple evaluation subjects to evaluate ej of the evaluation object according to fi. The affiliation vector Ri=ri1,ri2,⋯,rim,i=1,2,⋯,n,∑j=1mrij=1, the affiliation matrix is written as
(3)R=R1,R2,⋯,RnT=r11r12⋯r1mr21r22⋯r2m⋮⋮⋱⋮rn1rn2⋯rnm(c)
Determine the Weight VectorWF. WF denotes the weight of the indicator, which can be determined by AHP. Moreover, the numerical results (standard satisfaction vector) WE of the set of rubrics can be available. Based on the statistical description of the occurrence of small probability events, the numerical results of extremely common and minimal common are obtained as 0.95 and 0.05, thus determining WE=0.95,0.7,0.5,0.3,0.05.(d)
Calculate the Commonality ValueC. The commonality values are generally calculated through matrix operations S=WFR, C=WESTThe above steps can be adopted to obtain the content commonality and use commonality values of the same manual for two different models.


## 2.3.1. Analytic Hierarchy Process (AHP)

Analytic Hierarchy Process has been commonly applied in systems engineering to decompose a complex problem into its component factors [21], group the above factors into an orderly hierarchy in accordance with the dominant relationship, determine the relative importance of the factors in the hierarchy by comparing them with each other, and then integrate human judgment to decide the order of relative importance of the factors in the decision. The major steps are elucidated below.(1) A Hierarchical Structure Is Established. The manual commonality evaluation index system was built in the previous section, forming the progressive hierarchy in the hierarchical analysis method.(2) Pairwise Judgment Matrix Is Constructed. When comparing the maintenance manual’s commonality between two different aircraft types, the two manuals are compared in terms of the importance of the impact of the indicators on maintenance work in the actual use of the manuals. Besides, the quantitative scoring is conducted according to Table 3. Lastly, a judgment matrix, the forward reciprocal matrix, is built. For instance, the text content of the AMM is strongly more important than the overall structure of the manual for the maintenance work, so the two have a comparison score of 7. The IPC primarily consists of pictures, and the importance of picture content of the IPC manual is extremely more important than that of the text content, so the comparison score of the two is 9.Table 3
Meaning of the scalar method (1-9).
Take valueMeaning1Two elements have the same importance compared with each other3One element is slightly more important than the other as compared with the other element5One element is significantly more important than the other as compared with the two elements7One element is strongly more important than the other as compared with two elements9One element is extremely more important than the other as compared with the other elementOthers2, 4, 6, and 8 are the median values of the above adjacent judgments(3) Calculation of the Relative Weights of Indicators Under a Single Criterion. In the above step, the ranking weights of 6 individual indicators and 4 individual indicators are calculated according to the manual content commonality and manual use commonality. The consistency test is performed to verify whether the requested weights meet the requirements. The calculation of indicator weights can be solved precisely by the eigenvalue method. But when the order of the judgment matrix is too large, the eigenvalue method is not easy to solve. Thus, approximate methods such as the summation method and the square root method can be used to calculate the ranking weights.During the construction of the pairwise judgment matrix, the judgment matrix is not required to have consistency, which is determined by the complexity of objective things and the diversity of human perception, whereas it is recommended to require general consistency of the judgment. Thus, a consistency test is required in the calculation process, and the steps are presented below.(a)
Calculate Consistency Index C.I..(1)C.I.=λmax−nn−1,where n denotes the order of the pairwise judgment matrix; λmax represents the maximum eigenvalue of matrix A(b)
Find the Average Random Consistency Index R.I.. The average random consistency index is obtained by taking the arithmetic average after the eigenvalue of the random judgment matrix is calculated several times (more than 500 times). Its introduction can make up for the drawback that the consistency judgment index increases significantly with the increase inn. Table 4 lists the average random consistency index obtained by calculating the reciprocal matrix of order 1-15 for 1000 times(c)
Calculation of Consistency Ratio C.R..(2)C.R.=C.I.R.I..Table 4
Average random consistency index.
Order12345678R.I.000.520.891.121.261.361.41Order9101112131415R.I.1.461.491.521.541.561.581.59WhenC.R.<0.1, the consistency of the two-comparison judgment matrix is generally considered acceptable, and the calculated indicator weights are based on the requirementsAfter experts compare the scores of manual content commonality indicators and manual use commonality indicators, a judgment matrix is built. A consistency test can determine the indicator weights of manual content commonality indicators and manual use commonality indicators.


## 2.3.2. Fuzzy Comprehensive Evaluation Method

Fuzzy Comprehensive Evaluation Method is to provide some evaluation methods for some practical comprehensive evaluation problems based on several concepts of fuzzy mathematics. To be specific, a fuzzy comprehensive evaluation is based on fuzzy mathematics, which follows the principle of fuzzy relationship synthesis and quantifies some elements with unclear boundaries and is not easy to quantify; it can comprehensively evaluate the evaluated thing’s affiliation status from multiple factors [22, 23].The main steps of the Fuzzy Comprehensive Evaluation Method for the commonality of maintenance technical publications are elucidated below.(a)
Determining the Set of FactorsFand the Set of RubricsE. Factor set F refers to the set of evaluation items or indicators, i.e., manual content commonality indicators and manual use commonality indicators; F=fi=manualcontentcommonalityindicators or {manual use commonality indicators}.The set of rubricsE refers to the set of evaluation levels; the set of commonality rubrics is E=e1,e2,e3,e4,e5=extremecommonality,highcommonality,averagecommonality,lowcommonality,andminimalcommonality(b)
The Single-Factor Evaluation Affiliation Vector is Statistically Determined, and the Affiliation MatrixRIs Formed. The degree of affiliation is the most basic and important concept in the Fuzzy Comprehensive Evaluation Method. The so-called affiliation degree represents the size (degree) of the possibility of multiple evaluation subjects to evaluate ej of the evaluation object according to fi. The affiliation vector Ri=ri1,ri2,⋯,rim,i=1,2,⋯,n,∑j=1mrij=1, the affiliation matrix is written as
(3)R=R1,R2,⋯,RnT=r11r12⋯r1mr21r22⋯r2m⋮⋮⋱⋮rn1rn2⋯rnm(c)
Determine the Weight VectorWF. WF denotes the weight of the indicator, which can be determined by AHP. Moreover, the numerical results (standard satisfaction vector) WE of the set of rubrics can be available. Based on the statistical description of the occurrence of small probability events, the numerical results of extremely common and minimal common are obtained as 0.95 and 0.05, thus determining WE=0.95,0.7,0.5,0.3,0.05.(d)
Calculate the Commonality ValueC. The commonality values are generally calculated through matrix operations S=WFR, C=WESTThe above steps can be adopted to obtain the content commonality and use commonality values of the same manual for two different models.


## 2.4. Commonality Evaluation System for Technical Publications

The technical publication commonality evaluation system, as shown in Figure3, was built by synthesizing the previous paper. Five manuals, AMM, IPC, RSM, FIM, and CMM, were extracted as the representative manuals for the commonality evaluation of maintenance technical publications, and the weights in the commonality evaluation system of maintenance technical publications were determined by AHP according to the frequency of use of the five manuals in maintenance work. Subsequently, according to the manual commonality evaluation system, the indicator weights are determined by AHP, and the content commonality value and the use commonality value of each manual are calculated by combining the Fuzzy Comprehensive Evaluation Method [24]. Moreover, the commonality value of the same manual of two different models can be obtained by weighting the commonality value of the manual content and the commonality value of the manual use. Lastly, the final commonality value of maintenance publications between two different models is calculated by weighting the weights of the manuals. The final commonality values obtained lay a basis for analyzing the commonality benefits of the maintenance technical publications.Figure 3
The overall evaluation system of technical publication commonality.


## 3. Analysis of the Commonality Benefits of Maintenance Technical Publications

### 3.1. Learning Curve and Learning Effect

By observing and analyzing numerous relevant data and cases, Dr. TP. Wright et al. proposed the Learning Curve in their research about aircraft manufacturing at Cornell University in 1936 [25]. They reported that the direct labor time required to produce each aircraft regularly decreased with the increase in the cumulative number of aircraft. As indicated by a survey of the major aircraft manufacturers, regardless of the time taken to produce the first aircraft, the time required for the 8th is only 80% of that for the 4th, and the time required for the 12th is 80% of that for the 6th. In other words, what happens, in any case, is that when production doubles, the required production time is shortened by 20%. The above result is plotted as a series of curves that is the learning curve. This efficiency factor and the related decreasing cost is termed the “learning effect” and expressed in terms of the “learning rate” as the ratio of the time required per unit of output when a given output is doubled to the time required per unit of output before the change.As shown in Figure4, the learning curve [26–28] consists of two stages. One is the learning stage, in which the production time of unit products tends to be shortened with the increase in the number of products. The second refers to the standard stage; when the learning effect can be ignored, enterprises can apply the standard time for production. Notably, the learning curve can be individual or organizational, or a combination of the two learning effects. The personal learning effect is that when a person repeatedly produces a product, the direct labor time needed to produce a product will decrease with the increase in the accumulation of labor products due to the gradual proficiency of the movement or the gradual exploration of some more effective operation methods. Organizational learning effect implies the learning effect in management, thus revealing that an enterprise keeps accumulating experience in product design, process design, organizational structure, institutional arrangement, capital investment, and other aspects and improving management methods as an attempt to continuously increase the production and operation efficiency of the organization. The following are common mathematical expressions of learning effects.Figure 4
Learning curve.The mathematical expression equation for the learning effect is based on two basic conditions.First, the direct labor time required to produce then+1st product is constantly less than the nth.Second, with the increase in the cumulative quantity produced, the direct labor time required is shortened at a decreasing rate.In accordance with the above conditions, the learning curve can be written as the following log-linear model:(4)Yca=ax−s,(5)s=−lnrln2,where a denotes the direct labor time (cost) to produce the first product; Yca represents the cumulative average direct labor time (cost) to produce the xth product; x is the cumulative production quantity; s expresses the index of the learning curve, 0<s<1, as n increases, Yca decreases, and the size of s reveals the strength of the learning effect; r denotes the learning rate or the decreasing rate of man-hours. If the output doubles, the time required per output unit is shortened to 80%, then r=80%, which is also termed 80% learning curve; at this time, s=0.322. A small learning rate implies that with the increase in the cumulative output, the man-hours (cost) decreases rapidly; a high learning rate is an opposite.


### 3.2. Analysis of Maintenance Benefits Based on Learning Effects and Commonality

Considering the individual learning effect and organizational learning effect, with the accumulation of experience, the time of aircraft maintenance work will be shortened and stabilize with the increase in maintenance times, which is similar to a learning curve for each maintenance task. Due to the complexity of aircraft maintenance tasks, the workload and working time of each maintenance task are different, and the time of a particular maintenance task is unlikely to discuss individually. Thus, the monthly maintenance time of a sortie is adopted as the unit of measurement in this study, i.e., the total maintenance time of an aircraft in the maintenance state during a month of operation time as the object of discussion.Assuming that an airline puts into service a previously unoperated aircraft type A, based on the above description and the mathematical expression equation for the learning effect (Equations (4) and (5)), the following maintenance benefit analysis model is built:
(6)TnA=T0⋅nA−sA,sA=−lnrln2,T0=α×∑i=1mTimi=1,2⋯m,where nA denotes the nth month of an A model operation; sA is the learning curve index; r represents the learning rate. The aircraft maintenance task is not repetitive work, which will encounter numerous emergencies and has a strong complexity. Thus, r is generally taken as 0.95 in the maintenance task; TnA expresses the nth month of an A model maintenance time; T0 is the average monthly maintenance time of an A model aircraft in the first months (M) of maintenance; m is generally taken 12; α represents the correction coefficient. As the aircraft operation after a certain period is to be fixed, fixed inspection is longer than the route maintenance time. For instance, the aircraft for a C inspection takes one to two weeks at a time, and a D inspection takes one to two months at a time, so the correction factor is basically taken 1.1.Maintenance technical publications provide a vital reference for maintenance work during aircraft maintenance. The maintenance personnel can use maintenance technical publications to carry out maintenance work and the entire airline maintenance department. Maintenance technical publications cover the preparation of maintenance work cards, the deployment of aviation materials, as well as the completion of maintenance tasks in the entire process. Accordingly, if there is a commonality between the maintenance technical publications of two types of aircraft, the maintenance efficiency of one type of aircraft can be effectively improved based on another type of aircraft, thus reducing maintenance costs and effectively increasing the utilization rate of aircraft.The commonality values of maintenance technical publications of two different aircraft types can be determined using the commonality evaluation system of maintenance technical publications built in the previous section. Assuming that an airline has already owned a model A and has been operating for months (M), a model B is introduced, and the commonality value of the maintenance technology publications of A and B can be evaluated using the maintenance technology publication commonality evaluation system asC0<C<1. The existence of commonality will significantly increase the maintenance efficiency and shorten the maintenance time of the B model; the larger the learning curve index, the higher the learning effect will be. With the commonality in the maintenance class technical publications, the learning effect of the airline will increase, thus having an effect on the learning rate (r) and lowering its value. Thus, the commonality in the maintenance technical publications is introduced in the learning curve index (as expressed by R=r1−1−rC2) to decrease the value of r. Equation (1)−r represents the yield due to the learning effect, C2 denotes the square of the value of the commonality in the maintenance class technical publications, and the use of square is adopted to reduce the effect of the commonality of the technical publications in the maintenance category. Since the commonality is negatively correlated with the learning rate, r×1−fC is adopted. Besides, since the learning curve is highly sensitive to the change of learning rate, (1−r) is adopted to decrease the effect of C2 and reduce the sensitivity of the learning curve due to the change of C.Thus, a maintenance benefit analysis model for model B due to the effect of commonality of maintenance class technical publications is developed based on the maintenance benefit analysis model for model A, which is expressed as:(7)TnB=TM⋅nB−sB,sB=−lnRln2,R=r1−1−rC2,TM=∑x=1MT0x−sAM,where nB denotes the nth month of operation of model B; sB represents the learning curve index; r denotes the learning rate, and r is taken 0.95 in the same class of maintenance tasks; C expresses the commonality value of maintenance technical publications between the two models A and B; R is the learning rate due to the effect of commonality; TnB represents the maintenance time of model B in the nth month; TM denotes the average monthly maintenance time of model A aircraft in the months (M) after the effect of learning, and takes it as the starting time for the maintenance benefit analysis of model B.Since the main parameter variables in this model are the learning rater and the commonality value C, the following sensitivity analysis is conducted on the above two variables:By deriving the learning rater, it yields
(8)dTnBdr=TM⋅lnnB⋅nB−sB⋅1ln2⋅1−C2+2rC2r1−1−rC2>0.SincedTnB/dr is lower than 0, TnB is smaller with the decrease in the learning rate r, the learning rate is generally determined for the operating state and personnel replacement of the company. If the airline has a good operating state and stable personnel, the learning rate is lower than the value in the ordinary operating state, and the airline exhibits a good learning effect and higher efficiency.By deriving the commonality valueC, it yields
(9)dTnBdC=TM⋅lnnB⋅nB−sB⋅1ln2⋅−21−rCr1−1−rC2<0.SincedTnB/dC is greater than 0, TnB it becomes smaller as the commonality C increases. The commonality is a comparison of two products. For airlines, with the increase in the value of commonality of maintenance-type technical publications of two types of aircraft introduced, the company can adapt to the situation faster and reduce the maintenance time more significantly.


## 3.1. Learning Curve and Learning Effect

By observing and analyzing numerous relevant data and cases, Dr. TP. Wright et al. proposed the Learning Curve in their research about aircraft manufacturing at Cornell University in 1936 [25]. They reported that the direct labor time required to produce each aircraft regularly decreased with the increase in the cumulative number of aircraft. As indicated by a survey of the major aircraft manufacturers, regardless of the time taken to produce the first aircraft, the time required for the 8th is only 80% of that for the 4th, and the time required for the 12th is 80% of that for the 6th. In other words, what happens, in any case, is that when production doubles, the required production time is shortened by 20%. The above result is plotted as a series of curves that is the learning curve. This efficiency factor and the related decreasing cost is termed the “learning effect” and expressed in terms of the “learning rate” as the ratio of the time required per unit of output when a given output is doubled to the time required per unit of output before the change.As shown in Figure4, the learning curve [26–28] consists of two stages. One is the learning stage, in which the production time of unit products tends to be shortened with the increase in the number of products. The second refers to the standard stage; when the learning effect can be ignored, enterprises can apply the standard time for production. Notably, the learning curve can be individual or organizational, or a combination of the two learning effects. The personal learning effect is that when a person repeatedly produces a product, the direct labor time needed to produce a product will decrease with the increase in the accumulation of labor products due to the gradual proficiency of the movement or the gradual exploration of some more effective operation methods. Organizational learning effect implies the learning effect in management, thus revealing that an enterprise keeps accumulating experience in product design, process design, organizational structure, institutional arrangement, capital investment, and other aspects and improving management methods as an attempt to continuously increase the production and operation efficiency of the organization. The following are common mathematical expressions of learning effects.Figure 4
Learning curve.The mathematical expression equation for the learning effect is based on two basic conditions.First, the direct labor time required to produce then+1st product is constantly less than the nth.Second, with the increase in the cumulative quantity produced, the direct labor time required is shortened at a decreasing rate.In accordance with the above conditions, the learning curve can be written as the following log-linear model:(4)Yca=ax−s,(5)s=−lnrln2,where a denotes the direct labor time (cost) to produce the first product; Yca represents the cumulative average direct labor time (cost) to produce the xth product; x is the cumulative production quantity; s expresses the index of the learning curve, 0<s<1, as n increases, Yca decreases, and the size of s reveals the strength of the learning effect; r denotes the learning rate or the decreasing rate of man-hours. If the output doubles, the time required per output unit is shortened to 80%, then r=80%, which is also termed 80% learning curve; at this time, s=0.322. A small learning rate implies that with the increase in the cumulative output, the man-hours (cost) decreases rapidly; a high learning rate is an opposite.


## 3.2. Analysis of Maintenance Benefits Based on Learning Effects and Commonality

Considering the individual learning effect and organizational learning effect, with the accumulation of experience, the time of aircraft maintenance work will be shortened and stabilize with the increase in maintenance times, which is similar to a learning curve for each maintenance task. Due to the complexity of aircraft maintenance tasks, the workload and working time of each maintenance task are different, and the time of a particular maintenance task is unlikely to discuss individually. Thus, the monthly maintenance time of a sortie is adopted as the unit of measurement in this study, i.e., the total maintenance time of an aircraft in the maintenance state during a month of operation time as the object of discussion.Assuming that an airline puts into service a previously unoperated aircraft type A, based on the above description and the mathematical expression equation for the learning effect (Equations (4) and (5)), the following maintenance benefit analysis model is built:
(6)TnA=T0⋅nA−sA,sA=−lnrln2,T0=α×∑i=1mTimi=1,2⋯m,where nA denotes the nth month of an A model operation; sA is the learning curve index; r represents the learning rate. The aircraft maintenance task is not repetitive work, which will encounter numerous emergencies and has a strong complexity. Thus, r is generally taken as 0.95 in the maintenance task; TnA expresses the nth month of an A model maintenance time; T0 is the average monthly maintenance time of an A model aircraft in the first months (M) of maintenance; m is generally taken 12; α represents the correction coefficient. As the aircraft operation after a certain period is to be fixed, fixed inspection is longer than the route maintenance time. For instance, the aircraft for a C inspection takes one to two weeks at a time, and a D inspection takes one to two months at a time, so the correction factor is basically taken 1.1.Maintenance technical publications provide a vital reference for maintenance work during aircraft maintenance. The maintenance personnel can use maintenance technical publications to carry out maintenance work and the entire airline maintenance department. Maintenance technical publications cover the preparation of maintenance work cards, the deployment of aviation materials, as well as the completion of maintenance tasks in the entire process. Accordingly, if there is a commonality between the maintenance technical publications of two types of aircraft, the maintenance efficiency of one type of aircraft can be effectively improved based on another type of aircraft, thus reducing maintenance costs and effectively increasing the utilization rate of aircraft.The commonality values of maintenance technical publications of two different aircraft types can be determined using the commonality evaluation system of maintenance technical publications built in the previous section. Assuming that an airline has already owned a model A and has been operating for months (M), a model B is introduced, and the commonality value of the maintenance technology publications of A and B can be evaluated using the maintenance technology publication commonality evaluation system asC0<C<1. The existence of commonality will significantly increase the maintenance efficiency and shorten the maintenance time of the B model; the larger the learning curve index, the higher the learning effect will be. With the commonality in the maintenance class technical publications, the learning effect of the airline will increase, thus having an effect on the learning rate (r) and lowering its value. Thus, the commonality in the maintenance technical publications is introduced in the learning curve index (as expressed by R=r1−1−rC2) to decrease the value of r. Equation (1)−r represents the yield due to the learning effect, C2 denotes the square of the value of the commonality in the maintenance class technical publications, and the use of square is adopted to reduce the effect of the commonality of the technical publications in the maintenance category. Since the commonality is negatively correlated with the learning rate, r×1−fC is adopted. Besides, since the learning curve is highly sensitive to the change of learning rate, (1−r) is adopted to decrease the effect of C2 and reduce the sensitivity of the learning curve due to the change of C.Thus, a maintenance benefit analysis model for model B due to the effect of commonality of maintenance class technical publications is developed based on the maintenance benefit analysis model for model A, which is expressed as:(7)TnB=TM⋅nB−sB,sB=−lnRln2,R=r1−1−rC2,TM=∑x=1MT0x−sAM,where nB denotes the nth month of operation of model B; sB represents the learning curve index; r denotes the learning rate, and r is taken 0.95 in the same class of maintenance tasks; C expresses the commonality value of maintenance technical publications between the two models A and B; R is the learning rate due to the effect of commonality; TnB represents the maintenance time of model B in the nth month; TM denotes the average monthly maintenance time of model A aircraft in the months (M) after the effect of learning, and takes it as the starting time for the maintenance benefit analysis of model B.Since the main parameter variables in this model are the learning rater and the commonality value C, the following sensitivity analysis is conducted on the above two variables:By deriving the learning rater, it yields
(8)dTnBdr=TM⋅lnnB⋅nB−sB⋅1ln2⋅1−C2+2rC2r1−1−rC2>0.SincedTnB/dr is lower than 0, TnB is smaller with the decrease in the learning rate r, the learning rate is generally determined for the operating state and personnel replacement of the company. If the airline has a good operating state and stable personnel, the learning rate is lower than the value in the ordinary operating state, and the airline exhibits a good learning effect and higher efficiency.By deriving the commonality valueC, it yields
(9)dTnBdC=TM⋅lnnB⋅nB−sB⋅1ln2⋅−21−rCr1−1−rC2<0.SincedTnB/dC is greater than 0, TnB it becomes smaller as the commonality C increases. The commonality is a comparison of two products. For airlines, with the increase in the value of commonality of maintenance-type technical publications of two types of aircraft introduced, the company can adapt to the situation faster and reduce the maintenance time more significantly.


## 4. Example Applications

### 4.1. Calculation of Commonality of Maintenance Technical Publications

After a questionnaire is designed and distributed to the maintenance staff of domestic airlines and maintenance bases, 113 common feedback questionnaires are collected for maintenance technical publications. The questionnaires are analyzed and processed, and 89 valid and qualified questionnaires are extracted. Through the data analysis of the qualified questionnaires (transforming the data collected from the questionnaires into the importance scale values of the AHP and building the affiliation matrix of the Fuzzy Comprehensive Evaluation Method through statistics), the weight values of the commonality evaluation indicators (graphs2) of the five manuals can be determined. Subsequently, the commonality values of the maintenance technical publications among the above three comparative aircraft types can be calculated using the affiliation matrix of the Fuzzy Comprehensive Evaluation Method.With the AMM manual as an example, the judgment matrix of content (Mc) commonality indicators and the judgment matrix of use (Mu) commonality indicators can be built by analyzing the questionnaire data below.(10)Mc=1241/2461/2131/2351/41/311/4132241461/41/311/4131/61/51/31/61/31,Mu=13351/31221/31/2121/51/21/21.Through the consistency test, matricesMc and Mu can be obtained as C.I.c=0.032, R.I.c=0.026<0.1; C.I.u=0.022, R.I.u=0.024<0.1, thus passing the test. On that basis, the weight values obtained from the calculation satisfy the requirements. Through the program operation, we can get the weight table of AMM manual commonality assessment secondary indicators shown in Table 5. Since the primary indicator of manual content and manual use is the inherent characteristics of the manual existence, the degree of effect on the operation of the aircraft is equally important, so the equal weight value is adopted.Table 5
Weighting table of commonality indicators relating to AMM manual.
Level indicatorsWeightsSecondary indicatorsWeightsContent commonality indicators0.5Manual organization structure0.270Textual content description0.189Form and content of tables0.081Manual overall structure0.340Picture content description0.081Manual style habits0.038Use commonality indicators0.5Query mode0.524Manual update0.222Presence medium0.158Usage scenario0.096Likewise, the fuzzy judgment affiliation values of the commonality evaluation indicators between A320 and A330/A320 and B737NG can be determined using the questionnaire statistics, and the following four affiliation matrices are built, respectively, whereA−A represents A320 and A330, A−B represents A320 and 737BNG, c represents content commonality indicators, and u represents use commonality indicators. For instance, MA−Ac represents the affiliation matrix of the content commonality between A320 and A330.
(11)MA‐Ac=0.540.430.030.000.000.220.700.080.000.000.560.300.130.010.000.190.660.140.010.000.170.670.150.010.000.160.650.180.010.00,MA‐Au=0.640.300.060.000.000.630.300.060.010.000.600.360.040.000.000.580.380.030.010.00,MA‐Bc=0.110.580.220.070.020.070.300.530.080.020.010.090.320.280.300.000.190.370.420.020.010.130.400.430.030.000.110.430.420.04,MA‐Bu=0.090.580.170.120.040.040.150.270.470.070.040.490.350.090.030.010.270.350.310.06.The Fuzzy Comprehensive Evaluation Method can calculate the content commonality value of AMM manual as 0.79 between A320 and A330, with a use commonality value of 0.86, while calculating the content commonality value of AMM manual as 0.51 between A320 and B737NG, with a use commonality value of 0.57.Likewise, the commonality values of the rest four manuals can also be calculated, as listed in Table6. Moreover, the frequency of use of the five manuals by professional aviation maintenance personnel is determined through questionnaires to rank the five manuals, and the weights of the five manuals can be calculated (2nd column of Table 6). Lastly, as show in Table 7, the commonality values of maintenance technical publications between A320 and A330/A320 and B737NG are determined by weighted summation to achieve the effect of commonality quantification.Table 6
Five manual weights and commonality values for level indicators.
ManualsManual weightingContent commonality valueUse commonality valueA320-A330A320-B737NGA320-A330A320-B737NGAMM0.4980.790.510.860.57IPC0.2610.790.510.840.56FIM0.0640.730.500.680.54SRM0.1110.800.520.850.56CMM0.0660.790.540.840.55Table 7
Commonality values for maintenance technical publications between A320 and A330/between A320 and B737NG.
A320-A330A320-B737NGCommonality values for maintenance technical publications0.810.54


### 4.2. Benefit Model Application

It is assumed that a new airline introduced an A320 and has been operating for 2 years. As the company’s growth strategy has been modified, the airline plans to introduce an A330 to meet the demand for routes with a longer range and a higher passenger volume. Based on the above assumption, a learning effect-based maintenance benefit analysis model can be adopted to calculate the maintenance time savings due to the commonality of maintenance technical publications. For the coefficients in the model, the coefficients recommended by the formula are adopted, and the total maintenance time of a novel model in its first year of operation is statistically about 3000 h. Thus, the model formula for specific calculations is expressed as(12)T0=1.1×300012=275,TnA=T0×nA−ln0.95/ln2,TM=∑x=1MT0x−ln0.95/ln2M,TnB=TM×nA−ln0.951−0.05×C2/ln2.It is calculated that without the consideration of the commonality, the maintenance time of A330 of this airline in the 12th month (M=12) is 217.25 h due to the learning effect. Based on the consideration of the commonality, the maintenance time of A330 of this airline in the 12th month (M=12) is 171.8 h due to the effect of the commonality on the learning effect and the commonality (C=0.81) obtained from the above calculation, which is a relative saving of 45.45 h.In the same case, if the airline introduces a B737-800 at this time, it is calculated that the maintenance time of the airline’s A330 in the 12th month is also 217.25 h without considering the commonality due to the learning effect. Based on the consideration of the commonality, the maintenance time of B737-800 of this airline in the 12th month (M=12) is 183.7 h due to the effect of the commonality on the learning effect and the commonality (C=0.54) determined according to the above calculation, which is a relative saving of 57.35 h.As revealed by the above calculation, due to the learning effect, when airlines operate a novel type of aircraft, the time that the aircraft is in maintenance status will decrease continuously over time and with the accumulation of experience. The time in the 12th month of operation can be compared with the first month of maintenance time savings of 21%. On that basis, if a novel model is introduced, this model can have a relative maintenance time saving of 15% in the first month. Besides, due to the effect of commonality between maintenance technical publications of different models, the maintenance time will be significantly shortened with the increase in the commonality value.


## 4.1. Calculation of Commonality of Maintenance Technical Publications

After a questionnaire is designed and distributed to the maintenance staff of domestic airlines and maintenance bases, 113 common feedback questionnaires are collected for maintenance technical publications. The questionnaires are analyzed and processed, and 89 valid and qualified questionnaires are extracted. Through the data analysis of the qualified questionnaires (transforming the data collected from the questionnaires into the importance scale values of the AHP and building the affiliation matrix of the Fuzzy Comprehensive Evaluation Method through statistics), the weight values of the commonality evaluation indicators (graphs2) of the five manuals can be determined. Subsequently, the commonality values of the maintenance technical publications among the above three comparative aircraft types can be calculated using the affiliation matrix of the Fuzzy Comprehensive Evaluation Method.With the AMM manual as an example, the judgment matrix of content (Mc) commonality indicators and the judgment matrix of use (Mu) commonality indicators can be built by analyzing the questionnaire data below.(10)Mc=1241/2461/2131/2351/41/311/4132241461/41/311/4131/61/51/31/61/31,Mu=13351/31221/31/2121/51/21/21.Through the consistency test, matricesMc and Mu can be obtained as C.I.c=0.032, R.I.c=0.026<0.1; C.I.u=0.022, R.I.u=0.024<0.1, thus passing the test. On that basis, the weight values obtained from the calculation satisfy the requirements. Through the program operation, we can get the weight table of AMM manual commonality assessment secondary indicators shown in Table 5. Since the primary indicator of manual content and manual use is the inherent characteristics of the manual existence, the degree of effect on the operation of the aircraft is equally important, so the equal weight value is adopted.Table 5
Weighting table of commonality indicators relating to AMM manual.
Level indicatorsWeightsSecondary indicatorsWeightsContent commonality indicators0.5Manual organization structure0.270Textual content description0.189Form and content of tables0.081Manual overall structure0.340Picture content description0.081Manual style habits0.038Use commonality indicators0.5Query mode0.524Manual update0.222Presence medium0.158Usage scenario0.096Likewise, the fuzzy judgment affiliation values of the commonality evaluation indicators between A320 and A330/A320 and B737NG can be determined using the questionnaire statistics, and the following four affiliation matrices are built, respectively, whereA−A represents A320 and A330, A−B represents A320 and 737BNG, c represents content commonality indicators, and u represents use commonality indicators. For instance, MA−Ac represents the affiliation matrix of the content commonality between A320 and A330.
(11)MA‐Ac=0.540.430.030.000.000.220.700.080.000.000.560.300.130.010.000.190.660.140.010.000.170.670.150.010.000.160.650.180.010.00,MA‐Au=0.640.300.060.000.000.630.300.060.010.000.600.360.040.000.000.580.380.030.010.00,MA‐Bc=0.110.580.220.070.020.070.300.530.080.020.010.090.320.280.300.000.190.370.420.020.010.130.400.430.030.000.110.430.420.04,MA‐Bu=0.090.580.170.120.040.040.150.270.470.070.040.490.350.090.030.010.270.350.310.06.The Fuzzy Comprehensive Evaluation Method can calculate the content commonality value of AMM manual as 0.79 between A320 and A330, with a use commonality value of 0.86, while calculating the content commonality value of AMM manual as 0.51 between A320 and B737NG, with a use commonality value of 0.57.Likewise, the commonality values of the rest four manuals can also be calculated, as listed in Table6. Moreover, the frequency of use of the five manuals by professional aviation maintenance personnel is determined through questionnaires to rank the five manuals, and the weights of the five manuals can be calculated (2nd column of Table 6). Lastly, as show in Table 7, the commonality values of maintenance technical publications between A320 and A330/A320 and B737NG are determined by weighted summation to achieve the effect of commonality quantification.Table 6
Five manual weights and commonality values for level indicators.
ManualsManual weightingContent commonality valueUse commonality valueA320-A330A320-B737NGA320-A330A320-B737NGAMM0.4980.790.510.860.57IPC0.2610.790.510.840.56FIM0.0640.730.500.680.54SRM0.1110.800.520.850.56CMM0.0660.790.540.840.55Table 7
Commonality values for maintenance technical publications between A320 and A330/between A320 and B737NG.
A320-A330A320-B737NGCommonality values for maintenance technical publications0.810.54


## 4.2. Benefit Model Application

It is assumed that a new airline introduced an A320 and has been operating for 2 years. As the company’s growth strategy has been modified, the airline plans to introduce an A330 to meet the demand for routes with a longer range and a higher passenger volume. Based on the above assumption, a learning effect-based maintenance benefit analysis model can be adopted to calculate the maintenance time savings due to the commonality of maintenance technical publications. For the coefficients in the model, the coefficients recommended by the formula are adopted, and the total maintenance time of a novel model in its first year of operation is statistically about 3000 h. Thus, the model formula for specific calculations is expressed as(12)T0=1.1×300012=275,TnA=T0×nA−ln0.95/ln2,TM=∑x=1MT0x−ln0.95/ln2M,TnB=TM×nA−ln0.951−0.05×C2/ln2.It is calculated that without the consideration of the commonality, the maintenance time of A330 of this airline in the 12th month (M=12) is 217.25 h due to the learning effect. Based on the consideration of the commonality, the maintenance time of A330 of this airline in the 12th month (M=12) is 171.8 h due to the effect of the commonality on the learning effect and the commonality (C=0.81) obtained from the above calculation, which is a relative saving of 45.45 h.In the same case, if the airline introduces a B737-800 at this time, it is calculated that the maintenance time of the airline’s A330 in the 12th month is also 217.25 h without considering the commonality due to the learning effect. Based on the consideration of the commonality, the maintenance time of B737-800 of this airline in the 12th month (M=12) is 183.7 h due to the effect of the commonality on the learning effect and the commonality (C=0.54) determined according to the above calculation, which is a relative saving of 57.35 h.As revealed by the above calculation, due to the learning effect, when airlines operate a novel type of aircraft, the time that the aircraft is in maintenance status will decrease continuously over time and with the accumulation of experience. The time in the 12th month of operation can be compared with the first month of maintenance time savings of 21%. On that basis, if a novel model is introduced, this model can have a relative maintenance time saving of 15% in the first month. Besides, due to the effect of commonality between maintenance technical publications of different models, the maintenance time will be significantly shortened with the increase in the commonality value.


## 5. Conclusion

The commonality benefit of maintenance technical publications on aircraft maintenance is studied in this research. By analyzing the characteristics of the manuals, the commonality indicator system of maintenance technical publications is established, which consists of content commonality indicators and use commonality indicators. The Hierarchical Analysis Process and Fuzzy Comprehensive Evaluation Method are used to quantify commonality, providing a commonality evaluation idea for products with fuzzy attributions. Aircraft maintenance time will gradually decrease as experience accumulates, which can meet the basic conditions of the learning curve model. The commonality benefits model of maintenance technical publications is then established through an analysis of the impact of commonality on learning effects. Assuming that an aircraft operator initially has experience operating a specific aircraft type and needs to introduce a new one, they can use the model to calculate the monthly aircraft maintenance time saving of the new one with the impact of commonality. The model can be used as one of the references for the operator to introduce a new aircraft type, weighing all the influencing factors and then making a decision.The commonality evaluation in this research has some engineering applicability, and the benefit model can analyze the time benefits from commonality. There are some future research directions based on the existing studies. Firstly, for the commonality evaluation of technical publications, the natural language processing approach can be used to compare the similarities between technical publications to quantify the commonality and make the commonality evaluation more accurate. Secondly, the benefit of commonality in aircraft maintenance is also influenced by the commonality of maintenance tools and aviation materials, which can be incorporated into the commonality benefit model to make the model more reference value. Finally, in the civil aircraft operation system, commonality affects the operation of the enterprise in both management and engineering aspects. It can bring hidden benefits to the enterprise, which deserves further study.



---

*Source: 5880391-2022-09-15.xml*