Aircraft maintainability verification evaluation based on fuzzy analytic hierarchy process

This paper uses the fuzzy analytic hierarchy process to establish the mathematical model of aircraft maintainability verification in the flight test stage. The maintainability evaluation index system is constructed from the factors that affect the aircraft maintainability level, such as equipment layout and accessibility, cover design, marking and error prevention, standardization and interchangeability, and human factor engineering. Through case analysis, the application of this method in the maintainability verification of the military aircraft flight test phase is introduced.


Introduction
Maintainability refers to the ability of the product to maintain or restore to the specified state when it is repaired according to the specified procedures and methods under the specified conditions and within the specified time [1][2][3] .
The evaluation of the maintainability level of military aircraft in the flight test stage is generally a quantitative evaluation of the average repair time or the maximum repair time index of the aircraft, which can reflect the maintainability level to a certain extent.At the same time, in the early and middle stages of the flight test, to find out the maintainability design defects as soon as possible, the flight test unit will organize the aircraft maintainability verification and put forward the aircraft maintainability problems and improvement suggestions through the verification, for the aircraft development unit to refer to and implement the changes.
At present, researchers only put forward dozens or even hundreds of maintainability problems and corresponding change suggestions according to the verification situation.Still, the maintainability of this type of aircraft is not described in general, and there is no intuitive manifestation of the overall maintainability level of the aircraft [4][5] .
In this paper, the fuzzy analytic hierarchy process is used to quantitatively and qualitatively evaluate the overall maintainability level of the aircraft through the maintainability verification in the flight test stage.

Analytic hierarchy process
Analytic hierarchy process (AHP) is a method to quantify the human thinking process and solve multiobjective, multi-level, and multi-criteria decision-making problems [6][7][8] .The basic principle is to first hierarchically decompose the complex decision-making problem into various components, and group these factors according to their mutual membership relationship to form an orderly hierarchical model; Then the relative importance of each factor in the hierarchy is determined by pairwise comparison; Finally, the synthesis is carried out to determine the overall order of the relative importance of each factor.
The analytic hierarchy process generally has the following four steps: establishing a hierarchical structure model, constructing a judgment matrix, hierarchical single sorting and consistency test, and hierarchical total sorting.
(1) Establish hierarchical structure model When applying the AHP method, it is first determined which factors it involves and the interrelationships between these factors, and then these factors are hierarchically categorised according to their relationships.After classification, the first layer is the target layer, that is, to achieve the overall goal; the second layer is the criterion layer, which is the benchmark that affects the realization of the goal; the third layer is the measure layer, which is the measures and ways to achieve the goal.The hierarchical structure model usually uses a structural model diagram to illustrate the affiliation between various factors.The structural model diagram is shown in Figure 1.(2) Construct judgment matrix After establishing the hierarchical structure model, the relative importance of each factor in each level is compared by pairwise comparison, and the judgment matrix is obtained.The judgment matrix reflects the relative importance of each factor at the same level.Before constructing the judgment matrix, each factor should be compared and scored.The number 1-9 scale is generally used, as shown in Table 1.

Scale value Define 1
Indicator j and indicator i are equally important 3 Indicator j is slightly more important than indicator i. 5 Index j is more important than index i.

7
Index j is much more important than index i.9 Index j is more important than index i.

2, 4, 6, 8
The scale value corresponds to the intermediate state between the above judgments.

Reciprocal
If the index j is not as important as the index i, the corresponding reciprocal value is taken.
The general form of the judgment matrix is as follows: (3) Hierarchical single sorting and consistency test The hierarchical single ranking refers to the ranking of all factors at this level according to the importance of the factors at the previous level.By solving the characteristic roots and feature vectors of the judgment matrix and normalizing the feature vectors, it is the weight ranking of the relative importance of the corresponding factors at the same level to a certain factor at the previous level.The feature vector of the judgment matrix is obtained by the square root method.
(i=1, 2, 3…n).The vector and the consistency ratio CR= RI CI are calculated.Among them, RI is the average random consistency index, which can be retrieved in Table 2 according to the order n of the matrix.When CR < 0.1, it is considered that the judgment matrix meets the consistency ratio requirements, otherwise the judgment matrix should be adjusted until the requirements are met.The hierarchical total ranking is to use the results of a single ranking of all levels in the same level to calculate the weight of the importance of all factors in the previous level.The calculation of the hierarchical total ranking is carried out from top to bottom layer by layer, and finally, the weight value of the relative importance of each factor to the total goal is calculated.

Fuzzy comprehensive judgment
The fuzzy comprehensive evaluation method is based on fuzzy mathematics, the application of the principle of fuzzy relation synthesis, according to several factors on the evaluation of the object under the level of a comprehensive evaluation method.
The application process of the fuzzy comprehensive method is: (1) Determine the evaluation factor set U and the comment set V We determine the evaluation factor set U= ) represents the specific evaluation factor index and the IOP Publishing doi:10.1088/1742-6596/2764/1/012057 represents the evaluator's evaluation of the evaluation object.The collection of all possible evaluation results is generally ) evaluated by 'excellent', 'good', 'medium', 'general', and 'poor'.
(2) Determine the weight of each index in the evaluation factor set.Each factor in the evaluation factor set has an impact on the evaluation results, but the degree of impact is different, so it is necessary to give a certain weight to each index.W is a set of weight coefficients of each index, which can usually be obtained by an analytic hierarchy process.
(3) List the fuzzy relation matrix The m * n-order matrix composed of the membership degree of each comment level of each index is a fuzzy relation matrix, which is as follows: The evaluation results are obtained by the weighted average method.According to the principle of maximum membership degree, the maximum value is the evaluation conclusion.

Formatting the text
The level of aircraft maintainability will directly affect the daily maintenance and use of aircraft, so it is very necessary to carry out maintainability verification in the flight test stage.According to the situation of maintainability verification, the changes are implemented to achieve aircraft maintainability growth [9] .The evaluation index system is constructed by combining the factors affecting the aircraft maintainability level with the daily maintenance work, including five first-level indicators: equipment layout and accessibility, mouth cover design, marking and error prevention, standardization and interchangeability, and human factor engineering.There are 32 second-level indicators such as visual accessibility of important equipment and parts, standardization of screws, warning signs, size and shape of the mouth cover, and maintenance posture [10][11][12][13] .Specific indicators are shown in Table 3.

Criterion layer Indicator layer
Aircraft maintenance verification index system (A) Equipment layout and accessibility (B1) Visual accessibility of important equipment and parts (C1) Equipment maintenance operation space (C2) Frequent preventive maintenance equipment layout (C3) Equipment external test point layout (C4) Arrangement of pipelines and lines (C5) Cover design (B2) The size and shape of the mouth cover (C6) Design position of frequently used cover (C7) Mouth cover rainproof, windproof sand ability (C8) The anti-fit fault ability of the mouth cover (C9) Aircraft maintenance verification index system (A) Maintain posture (C18) Maintenance Safety (C19) About the indicators in the above table, the focus of verification and areas requiring special attention are explained as follows: 1. C1 mainly checks the parts of important stress components such as engine lifting joints, whether they provide the mouth cover and window needed for visual inspection or use of detection instruments.
2. C2 mainly checks whether the equipment has enough maintenance operation space.
3. C3 mainly checks whether the equipment with a high failure rate and frequent preventive maintenance is arranged in an easy-to-contact position.
4. C4 mainly checks whether the operation point, switch, and test point of the equipment are set in the direction of the outer side of the equipment to the cover.
5. C5 mainly checks whether the aircraft pipeline and line laying are separated by a certain distance.The line should be placed above the pipeline, where it is not easy to approach and check, and generally should not be laid.
6. C7 mainly checks whether the frequently used mouth cover can be opened by hand and whether it is designed in a relatively easy-to-contact position such as the side and lower part of the aircraft.
7. C8 mainly verifies whether the maintenance channel cover and hatch cover of each electronic and electromechanical equipment cabin take rain-proof and sand-proof measures.
8. C10 mainly verifies whether the maintenance parts that may endanger the safety of personnel or be harmful to the health of personnel have eye-catching warning marks.9. C11 mainly checks whether the connection parts such as cable plugs and connectors have adopted error prevention measures such as "different sizes" and "different pinhole positions" that cannot be installed in dislocation.
10. C12 mainly checks whether the cable is distinguished by text, color, and character.11.C14 mainly checks whether the equipment on the machine is equipped with a nameplate, whether the position of the nameplate is reasonable and meets the requirements of the standard.12. C15 mainly checks whether the same type of screw is used in the same cover, and whether the screws used in the whole cover are universal.
13. C16 and C17 mainly check whether the same model, the same functional parts, and the symmetrical installation parts on the aircraft are interchangeable.
14. C18 mainly checks whether the equipment and system are maintained in a more comfortable position.
15. C19 mainly checks whether the shell of each piece of equipment has been rounded and the sharp edge removed and will not cause scratches to personnel during maintenance.

Application example
Taking the maintenance verification of a certain type of aircraft as an example, this paper introduces the application of the fuzzy analytic hierarchy process in the evaluation of maintenance verification in the flight test stage.
The first step is to carry out maintenance verification.The maintenance verification of this type of aircraft lasted two and a half days and was carried out on two aircraft.The maintainability of the aircraft was comprehensively verified from 19 aspects of the above 5 major items in 4 groups, including machinery, ad hoc, avionics, and ordnance.A total of 71 maintainability problems were proposed, including 18 equipment layout and accessibility, 6 cover design, 23 marking and error prevention, 12 standardization and interchangeability, and 12 human factor engineering.
Step 2: We uses the form of a questionnaire to let the inspectors score the aircraft one by one with 'excellent', 'good', 'medium', 'general', and 'poor' in 19 aspects.The fuzzy relation matrix of the maintainability level of the machine is listed by the method in Section 2.2 (3), as follows: The third step: By asking 12 senior maintenance personnel and maintenance experts to compare the relative importance of the five criteria layer indicators by using the method in the analytic hierarchy process in Section 2.1, and to compare the relative importance of the corresponding index layer indicators in each criterion layer.The judgment matrix is formed, and the weight value of each index relative to the importance of aircraft maintainability is calculated, that is the index weight matrix.Through calculation and consistency tests, the weight of each index is as follows: Equipment layout and accessibility: 1 B = (0.30, 0.14, 0.22, 0.18, 0.16).

Figure 1 .
Figure 1.Hierarchical analysis structure model diagram.(2)Construct judgment matrix After establishing the hierarchical structure model, the relative importance of each factor in each level is compared by pairwise comparison, and the judgment matrix is obtained.The judgment matrix reflects the relative importance of each factor at the same level.Before constructing the judgment matrix, each factor should be compared and scored.The number 1-9 scale is generally used, as shown in Table1.Table1.Relative importance table.
, K A represents the Kth factor in the target layer A level, 1 B , 2 B ,… n B represents the factor in the next level B related to the K A factors, and ij b represents the comparison value of the relative importance of factor i and factor j.

4 )
indicates the degree of membership of the evaluator in the j-level evaluation of the i-th factor in the evaluation factor set; ij u indicates the number of experts who make the jth level comment on the ith factor in the evaluation factor set.  of experts who make all comments on the evaluation factors, that is, the total number of experts participating in the evaluation K, According to the principle of fuzzy transformation to evaluate the comprehensive evaluation A fuzzy comprehensive evaluation problem is to transform a fuzzy set W on the domain of the evaluation index set U into a fuzzy set B on the domain of the comment set V through a fuzzy relationship R, and a fuzzy comprehensive mathematical model can be obtained.

Table 2 .
Random consistency index RI value.