The existing material classification is proposed to improve the inventory management. However, different materials have the different quality-related attributes, especially in the aircraft industry. In order to reduce the cost without sacrificing the quality, we propose a quality-oriented material classification system considering the material quality character, Quality cost, and Quality influence. Analytic Hierarchy Process helps to make feature selection and classification decision. We use the improved Kraljic Portfolio Matrix to establish the three-dimensional classification model. The aircraft materials can be divided into eight types, including general type, key type, risk type, and leveraged type. Aiming to improve the classification accuracy of various materials, the algorithm of Support Vector Machine is introduced. Finally, we compare the SVM and BP neural network in the application. The results prove that the SVM algorithm is more efficient and accurate and the quality-oriented material classification is valuable.
There is no doubt that aircraft industry should pay more attention to quality. For the purpose of ensuring the quality of aircraft, aircraft factories have made a lot of study and most of them have established quality management system. However, there are so many parts in one airplane, and even if one screw has quality problems, it may cause catastrophic damage. As a result, the aircraft factories are facing greater challenges in the quality control and management. The quality of aircraft materials determines the quality of the aircraft directly. Therefore, the quality of aircraft material should be guaranteed. However, it is almost impossible to do continuous quality inspection of each aircraft material for there are large numbers of component parts of an aircraft, more than millions [
For material classification, ABC analysis originated by Dickie [
In the application of the algorithm for classification, some scholars are interested in the artificial intelligence and machine learning such as genetic algorithm (GA) [
Of course, aircraft companies take the material management seriously. For example, Boeing has invested nearly 2 billion to realize the management of production resources. In Airbus Fasteners’ Supply Chain Optimization Plan, they simplify the logistics by determining the material qualitatively and quantitatively. China also makes a lot of effort to material management during the project of ARJ21 [
A general aircraft contains more than millions of parts. The aircraft materials also cover a very wide range including raw materials purchased by businesses, homemade semifinished products, outsourcing semifinished products, finished products, office supplies, tools and even drawings, and documents. The role of quality played in the classification is ignored, so the traditional unified classification system exposes the following shortcomings.
Through the above analysis, it is necessary to further propose another classification system according to several indicators of quality. The classification considering quality characters will improve the quality and the reliability in the aircraft industry.
AHP (Analytic Hierarchy Process) developed by Saaty is a three-layer framework of decision: objectives, criteria, and alternative solutions. It is actually a hierarchical weighted decision analysis method that is proposed by using the multiobjective comprehensive evaluation method. AHP is a widely used multicriteria decision-making tool due to its simplicity, ease of use, and great flexibility. It is particularly useful to the decision problem that the system is lacking quantitative data or is difficult to complete with quantitative analysis. It is one of the most frequently discussed multiobjective decision methods in the manufacturing industry.
The basic steps of AHP method are as follows.
Apply AHP method in aircraft material according to the above steps. Firstly, we construct the hierarchy for aircraft material. The objective layer is aircraft material classification. The quality-oriented aircraft materials evaluation system considers all the quality factors involved in airplane manufacturing process. Therefore, after considering all properties of the material in the quality management, we select “Quality basic-value,” “Quality influence value,” and “Quality cost” and these three properties are defined as criteria layer. We increase the subcriterion properties to quantitatively describe the detailed indicators in the quality evaluation system. Finally, we get the set for aircraft material evaluation system. The set of Quality basic-value: The set of Quality influence value: The set of Quality cost:
The AHP model diagram is shown in Figure
The AHP model diagram of aircraft material evaluation system.
The illustration of each property is as follows.
In this study, three criteria have the same effect proportion on the material evaluation. So, we apply hierarchy analysis, respectively, to three criteria. We get the pairwise comparison matrix
In the same way, we can also construct the pairwise comparison matrix such that
According to the following formula,
In order to check the consistency, we use the random consistency index (RI) and the consistency index (CI) to calculate the consistency ratio (CR). The results are
Based on AHP method, we have established the material evaluation system and obtained the weights of each subcriteria impact on material evaluation.
Kraljic Portfolio Matrix proposed by Peter Kraljic appeared firstly in his paper “Purchasing must become supply management.” Kraljic portfolio model aims at developing differentiated purchasing and supplier strategies through classifying commodities on the basis of two dimensions: supply risk and profit impact (“low” and “high”) [
Kraljic Portfolio Matrix.
Quality-oriented classification system applies the thought of Kraljic Portfolio Matrix. Considering that each property on criteria layer belongs to high or low, namely, evaluation sets
Three-dimensional model diagram of material classification.
As in Table
Quality-oriented material classification list.
Types | Quality eigenvalue | Quality influence value | Quality cost | Attention | |
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Quality |
General material | High | Low | Low | Unnecessary |
Key material | High | Low | High | ** | |
Lever-type material | High | High | Low | ** | |
Core material | High | High | High | **** | |
Adjustable material | Low | Low | Low | ** | |
Risk material | Low | Low | High | **** | |
Bottleneck-type material | Low | High | Low | *** | |
Strategic material | Low | High | High | ***** |
More “∗” represent that we need to pay more attention to this type. For example, we should pay enough attention to strategic material with five “∗” during material management, whereas we can pay less attention to key material which just has two “∗”.
Support Vector Machine [
SVM method is evolved from optimal hyperplane of linearly separable case. In this case, the general form of hyperplane equation is
However, most classification problems belong to nonlinear separable situation which need to increase the penalty parameter
Introducing Lagrange formula into the above equation, then the problem can be expressed as
Its dual problem is
When converting to a linear problem in the high-dimensional space by a nonlinear exchange, the kernel function is used so that the problem can correspond to the inner product of a transform space according to relevant functional principle. At last, the corresponding classification function becomes as follows:
BP neural network was put forward by the group of Rumelhart and McCelland and so forth, in 1986. As one of the widely adopted neural networks nowadays, it is a type of multilayer feed-forward network trained by an algorithm that backward propagates the errors [
Assuming the weight between input layer and hide layer is The output of hide layer is
The output of output layer is
Error formula of the output layer is
In network training, the output error of output layer propagates to the hidden layer and input layer and the weight between each layer has been amended. Finally the mean square error (
In this section, we will take one of the aircraft factory’s material systems (named as Samc) as an example to illustrate our theory. The classification steps are shown in Figure
The classification process of civil aircraft materials.
The material quantization table.
Criteria layer |
Subcriteria layer |
Quantitative values | ||
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1 | 3 | 5 | ||
Quality basic-value | Qualification rate | Below 90% | 90%~95% | 95%~100% |
Quality failure rate | Over 10% | 3%~10% | Below 3% | |
Quality stability | Less stable | General | Stable | |
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Quality influence value | Mean time to repair | Short processing time | Medium processing time | Long processing time |
Impact depth | Weak | General | Severe | |
Influence range | Weak | General | Severe | |
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Quality cost | Quality management cost | Low | Medium | High |
Detection complexity | Simple | General | Complex | |
Quality traceability | Complete | Medium | Nonretroactivity |
From Table
The original data set.
Criteria |
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Subcriteria |
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3 | 3 | 5 | 1 | 5 | 3 | 5 | 1 | 3 |
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1 | 1 | 3 | 3 | 3 | 3 | 3 | 5 | 5 |
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5 | 3 | 3 | 3 | 1 | 5 | 1 | 3 | 5 |
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3 | 1 | 3 | 3 | 1 | 5 | 3 | 1 | 5 |
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1 | 5 | 1 | 3 | 5 | 3 | 5 | 5 | 1 |
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3 | 3 | 3 | 1 | 5 | 5 | 1 | 1 | 5 |
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5 | 1 | 1 | 5 | 3 | 5 | 3 | 1 | 1 |
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5 | 3 | 3 | 5 | 1 | 3 | 1 | 1 | 5 |
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3 | 3 | 5 | 1 | 1 | 5 | 5 | 3 | 1 |
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1 | 3 | 1 | 5 | 1 | 1 | 5 | 1 | 1 |
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3 | 3 | 1 | 3 | 1 | 1 | 3 | 5 | 3 |
After calculating the original data with the appointed weights, we obtained the processed data, as shown in Table
The processed data.
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The types of material | |
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3.5949 | 3.4 | 3.8288 | 4 |
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1.5947 | 3 | 3.8462 | 8 |
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4.0783 | 3 | 2.318 | 3 |
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2.6727 | 3 | 3.1354 | 8 |
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1.6553 | 3.8 | 4.0602 | 8 |
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3.0003 | 4.2 | 1.9626 | 3 |
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3.1561 | 4.2 | 2.1766 | 3 |
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4.0783 | 2.6 | 1.9626 | 1 |
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3.5949 | 2.6 | 3.7048 | 2 |
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1.3277 | 1.8 | 3.3494 | 6 |
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2.4057 | 1.4 | 3.3668 | 6 |
During the experiment of BP neural network, its training step is 1000, error goal is 0.01, the maximum convergence time is 1000, and training and learning rate is 0.1.
Without loss of generality, randomly select 130 samples as training samples from the 160 proceeded data. The remaining 30 samples are set as test samples. Because the training set and test set are randomly generated, the running results will be different each time. We randomly conducted a simulation test, the accuracy rate of training samples by SVM was 100%, and the accuracy rate of test samples was 96.6667%. However, prediction result of BP neural network is not very desirable. Its prediction accuracy is pretty low. Additionally, the results belong to two types sometimes, leading to the fact that we need to judge forecast situation by ourselves. The results of the simulation test are shown in Figures
Prediction result of test samples by SVM.
Prediction result of test samples by BP neural network.
It is obvious that the classification accuracy of SVM classifier is better than BP neural network classifier. In other words, the learning rate and efficiency of the former is much better than the latter. We also found that, in the experimental process, the accurate rate of SVM classifier was above 95% through many experiments. And multiple learning can also enhance the accuracy of BP neural network. When BP neural network classifier was stable, take 10 times cyclic forecast of sample set. The predicted results showed that the average accuracy rate was only 84.333%. What is worse, the tenth prediction accuracy was less than 60%. Compared with BP neural network, higher classification accuracy can be obtained by SVM without a lot of training. Similarly, randomly take 10 times forecast. The average accuracy rate was 96%, far better than BP neural network, and extreme minimum condition did not appear. That is, the classification result of SVM is ideal which can be used to classify aircraft materials.
From Table
Comparison of the prediction results of BP neural network and SVM.
Sequence number | Accuracy | |
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BP neural network | SVM | |
1 | 73.333% | 100.0% |
2 | 86.667% | 96.667% |
3 | 83.333% | 100.0% |
4 | 86.667% | 100.0% |
5 | 86.667% | 90.0% |
6 | 93.333% | 86.667% |
7 | 96.667% | 100.0% |
8 | 93.333% | 100.0% |
9 | 86.667% | 96.667% |
10 | 56.667% | 90.0% |
Average |
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We propose a quality-oriented material classification considering the quality character, Quality influence, and Quality cost. The quality-oriented material evaluation system is established to quantify each property by AHP method. Through improving conventional Kraljic Portfolio Matrix, we establish a three-dimensional material classification model, which divides the aircraft materials into eight categories: General material, Key material, and so on. Compared with the BP neural network, the study verifies that SVM algorithm has a good advantage in the classification of multiple small samples in the aircraft industry. The contribution of this paper lies in two aspects: in general, the material classification is oriented to inventory management based on ABC inventory control and so on. However, different materials have different quality-related attributes, especially in the aircraft industry. After fully evaluating the quality-related attributes in the aircraft industry, we apply AHP and improve conventional Kraljic Portfolio Matrix to establish a three-dimensional material classification model. Therefore, we could take different strategies for the different materials to improve the quality and reduce the cost in the quality management of the aircraft industry. On the other hand, this study not only provides a new idea for manufacturing material classification to improve the quality management, but also proves it is feasible to apply SVM in civil aviation material classification. We all know that SVM shows many unique advantages in solving small sample, nonlinear, and high-dimensional pattern recognition. Although the SVM is applied extensively as the best way for small sample classification and regression problems, it has not been used in the aircraft material classification. There are a large number of component parts of an aircraft, more than millions. However, each part is few. The case study shows the SVM is effective to solve the classification when the categories are extensive and the sample is very small. However, we should do further research. For example, taking into account the practicability, we now only consider the level of low and high in the evaluating indicator. If possible, we should try to supplement level of “medium,” and the classified management for the quality may be more considerate. Although we have verified this classification model in an aircraft company, it is not enough. We should try to improve this model in this company and the other aircraft companies, and even the other industries. We should further propose the specific management strategies to the different category of material and evaluate the effectiveness, so that we could know the value of this research indeed.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by Shanghai Science and Technology Committee under Grants nos. 12dz1124300 and 13521103604. It is also supported by Shanghai Key Laboratory of Intelligent Manufacturing and Robotics. The authors are grateful for the financial support and also would like to thank the anonymous reviewers and the editor for their comments and suggestions.