CN112036586B - Statistical distribution inspection method for aviation equipment maintenance equipment requirements - Google Patents
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Abstract
The invention relates to a statistical distribution inspection method for the demand of aviation equipment maintenance equipment, which comprises the following steps: collecting historical fault data of various typical equipment requirements, and manufacturing a historical fault data sample set according to the historical fault data; drawing a histogram of each typical equipment requirement according to the historical fault data sample set; obtaining statistical distribution of each typical equipment requirement according to histogram fitting of each typical equipment requirement; the statistical distribution of the requirements of each typical equipment is checked by adopting a chi-square checking method; adopting a K-S test method to test the statistical distribution of the requirements of each typical equipment; and judging the statistical distribution of the requirements of each typical equipment according to the test result of the chi-square test method and the test result of the K-S test method. The invention adopts two inspection methods of chi-square inspection and K-S inspection to inspect the equipment demand distribution so as to avoid false discarding or false taking errors as much as possible, ensure the inspection correctness and improve the accuracy and reliability of inspection results.
Description
Technical Field
The invention belongs to the technical field of aviation maintenance and guarantee, and particularly relates to a statistical distribution inspection method for requirements of aviation equipment maintenance equipment.
Background
At present, the application research of the requirement distribution of aviation equipment maintenance equipment at home and abroad is more, the contradiction condition that different documents adopt different statistical distributions for the same equipment exists, and the research of A.A. Syntetos is equal to 2012, and the statistical distribution inspection research of Poisson distribution, normal distribution, gamma distribution and the like is carried out on the requirements of U.S. military equipment spare parts, british and European military equipment spare parts by adopting a chi-square distribution inspection method. They set the observation period to 1 month, with the sample observation time being 84 months at maximum and 48 months at minimum. However, in practice, the observation period should not be too short, which would result in a large change in the difference-to-average ratio, which may have a large influence on the analysis result. However, they do not provide sample data and a verification process. Lengu D was equal to 2014, and various composite Poisson distributions were studied for goodness of fit and classification methods based on the distributions were proposed, but the statistical distributions obeyed by various equipment were not clarified. The existing literature only assumes statistical distributions of different classes of equipment without evidence, nor does it verify and explain whether other distributions are suitable for the proposed equipment class.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a statistical distribution inspection method for the requirements of aviation equipment maintenance equipment, which can improve the accuracy and reliability of inspection results.
In order to achieve the above-mentioned purpose, the present invention provides a statistical distribution inspection method for demand of maintenance equipment of aviation equipment, which comprises the following steps:
collecting historical fault data of various typical equipment requirements, and manufacturing a historical fault data sample set according to the historical fault data;
drawing a histogram of each typical equipment requirement according to the historical fault data sample set;
obtaining statistical distribution of each typical equipment requirement according to histogram fitting of each typical equipment requirement;
the statistical distribution of the requirements of each typical equipment is checked by adopting a chi-square checking method;
adopting a K-S test method to test the statistical distribution of the requirements of each typical equipment;
and judging the statistical distribution of the requirements of each typical equipment according to the test result of the chi-square test method and the test result of the K-S test method.
Preferably, when judging the statistical distribution of each typical equipment, if the test result of the chi-square test method is consistent with the test result of the K-S test method, determining that the statistical distribution of the requirements of the typical equipment is compliant with the statistical distribution obtained according to the histogram; if the test result of the chi-square test method is inconsistent with the test result of the K-S test method, determining that the statistical distribution of the typical equipment requirements does not follow the statistical distribution obtained according to the histogram.
Preferably, the step of performing the test by using the chi-square test method comprises the steps of:
assume that:
H 0 : the distribution function of X is F 0 (x)(1)
Wherein X is a historical failure data sample set of typical equipment requirements, F 0 (x) A statistical distribution function of typical equipment requirements obtained for the histogram, wherein X is a sample in a historical fault data sample set X;
test statistic χ 2 The method comprises the following steps:
where n is the total number of samples x, n i To observe value equal to x i Is the actual measurement frequency of x i For the ith sample, p i As theoretical probability, np i For theoretical frequency, k is the number of packets;
H 0 the receiving domain is:
χ 2 ≤χ 2 1-α (k-1) (3)
in χ 2 1-α (k-1) is the test statistic χ 2 α is the significance level;
and judging whether the actual statistical distribution of the typical equipment demands is subjected to the statistical distribution of the typical equipment demands obtained by the histogram according to the formula (3).
Preferably, when the actual statistical distribution of the typical equipment requirement is determined according to the formula (3), if the formula (3) is satisfied, the actual statistical distribution of the typical equipment requirement is determined to be compliant with the statistical distribution of the typical equipment requirement obtained by the histogram, and if the formula (3) is not satisfied, the actual statistical distribution of the typical equipment requirement is determined to be not compliant with the statistical distribution of the typical equipment requirement obtained by the histogram.
Preferably, the step of performing the test using the K-S test method is:
assume that:
H 0 ：F(x)＝F 0 (x) (4)
wherein F (x) is the actual statistical distribution of typical equipment requirements;
the test statistic D is:
in the method, in the process of the invention,for the actual cumulative frequency, m i For observations less than or equal to x i A total number of n samples x;
H 0 the receiving domain is:
D≤D α (6)
wherein D is α For the distribution threshold of test statistic D, α is the significance level;
and judging whether the actual statistical distribution of the typical equipment requirements is subjected to the statistical distribution of the typical equipment requirements obtained by the histogram according to the formula (6).
Preferably, when the actual statistical distribution of the typical equipment requirement is determined according to the formula (6), if the formula (6) is satisfied, the actual statistical distribution of the typical equipment requirement is determined to be compliant with the statistical distribution of the typical equipment requirement obtained by the histogram, and if the formula (6) is not satisfied, the actual statistical distribution of the typical equipment requirement is determined to be not compliant with the statistical distribution of the typical equipment requirement obtained by the histogram.
Preferably, when the statistical distribution of each typical deviceIf the two or more statistical distributions are consistent with the test result of the chi-square test method and the test result of the K-S test method, the statistical distribution with the largest P value is selected as the final statistical distribution of the typical equipment, wherein the P value is represented by test statistic χ 2 Or test statistic D.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention comprehensively uses two inspection methods of chi-square inspection and K-S inspection to inspect the equipment demand distribution so as to avoid false discarding or false taking errors as much as possible, ensure the inspection correctness and improve the accuracy and reliability of inspection results. The method lays a scientific theoretical foundation for developing the research of demand prediction, planning of the supply standard, inventory optimization and the like of the aviation equipment by using a probability statistical method, and has higher scientificity and popularization and application values.
(2) The invention performs demonstration inspection on whether the requirements of various typical equipment obey the same distribution or not and whether the requirements of the same equipment obey various distributions or not. According to the inspection results, the requirements of most of typical equipment are subject to poisson distribution, and meanwhile, the requirements of the same typical equipment can be subject to multiple distributions, so that the problems that the requirement distribution assumptions of the equipment described in the existing literature are contradictory to each other, and the equipment lacks example verification and is difficult to serve as scientific basis are solved.
Drawings
FIG. 1 is a schematic diagram of a type accumulator histogram of an aircraft repair kit according to an embodiment of the present invention;
FIG. 2 is a diagram of a centrifugal pump of an aircraft maintenance device of type A according to an embodiment of the invention;
FIG. 3 is a histogram of a sensor of aircraft repair kit type A according to an embodiment of the invention;
FIG. 4 is a histogram of a station of aircraft repair equipment type A according to an embodiment of the invention;
FIG. 5 is a chart of an altimeter histogram of an aircraft repair kit of embodiment A of the invention;
FIG. 6 is a top histogram of an aircraft repair kit of embodiment A of the present invention;
FIG. 7 is a histogram of a servo valve of a type B aircraft repair kit according to an embodiment of the invention;
FIG. 8 is a histogram of a processor of an aircraft repair kit of type B according to an embodiment of the invention;
FIG. 9 is a top histogram of a type B aircraft repair kit according to an embodiment of the invention;
FIG. 10 is a histogram of a regulator of aircraft repair kit type C according to an embodiment of the invention;
FIG. 11 is a diagram of a receiver histogram of an aircraft repair kit of type C in accordance with an embodiment of the invention;
FIG. 12 is a histogram of an electromagnetic valve of a type D aircraft repair kit according to an embodiment of the invention;
FIG. 13 is a histogram of a fuel pump of a type D aircraft repair kit according to an embodiment of the invention;
FIG. 14 is a histogram of a centrifugal pump of a type E aircraft repair kit according to an embodiment of the invention;
FIG. 15 is a histogram of a control box of an exemplary embodiment of an E-type aircraft repair kit;
FIG. 16 is a histogram of a compass of an embodiment E of the present invention;
FIG. 17 is a diagram illustrating a transceiver histogram of an exemplary E-type aircraft repair kit;
FIG. 18 is a histogram of a sensor of an embodiment of the invention;
FIG. 19 is a histogram of a meter of an exemplary embodiment of an E-type aircraft repair kit;
FIG. 20 is a histogram of a starter of an embodiment of the present invention;
FIG. 21 is a graph showing a fit between a normal distribution, a Weibull distribution and an exponential distribution in accordance with an embodiment of the present invention;
fig. 22 is a plot of poisson distribution versus negative binomial distribution fit for an embodiment of the present invention.
Detailed Description
The present invention will be specifically described below by way of exemplary embodiments. It is to be understood that elements, structures, and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.
The invention provides a statistical distribution inspection method for the demand of aviation equipment maintenance equipment, which comprises the following steps:
s1, collecting historical fault data of various typical equipment requirements, and manufacturing a historical fault data sample set according to the historical fault data.
And S2, drawing a histogram of each typical equipment requirement according to the historical fault data sample set.
S3, fitting according to the histogram of each typical equipment requirement to obtain the statistical distribution of each typical equipment requirement.
S4, checking the statistical distribution of the requirements of each typical equipment by adopting a chi-square checking method. The method comprises the following specific steps:
assume that:
H 0 : the distribution function of X is F 0 (x) (1)
Wherein X is a historical failure data sample set of typical equipment requirements, F 0 (x) A statistical distribution function of typical equipment requirements obtained for the histogram, wherein X is a sample in a historical fault data sample set X;
test statistic χ 2 The method comprises the following steps:
where n is the total number of samples x, n i To observe value equal to x i Is the actual measurement frequency of x i For the ith sample, p i As theoretical probability, np i For theoretical frequency, k is the number of packets;
H 0 the receiving domain is:
χ 2 ≤χ 2 1-α (k-1) (3)
in χ 2 1-α (k-1) is the test statistic χ 2 α is the significance level;
and judging whether the actual statistical distribution of the typical equipment demands is subjected to the statistical distribution of the typical equipment demands obtained by the histogram according to the formula (3).
Specifically, when the actual statistical distribution of the typical equipment needs is determined according to the formula (3), if the formula (3) is satisfied, the actual statistical distribution of the typical equipment needs is determined to follow the statistical distribution of the typical equipment needs obtained by the histogram, and if the formula (3) is not satisfied, the actual statistical distribution of the typical equipment needs is determined to not follow the statistical distribution of the typical equipment needs obtained by the histogram.
Generally, the larger the theoretical frequency, the closer the distribution is to the chi-square distribution, and when the theoretical frequency is 5 or more, the better the chi-square distribution is satisfied. Therefore, when the expected theoretical frequency is small, it is generally necessary to merge adjacent groups so that the theoretical frequency of each group is not less than 5 as much as possible. In this example, the significance level α=0.05.
S5, adopting a K-S test method to test the statistical distribution of the requirements of each typical equipment. The method comprises the following specific steps:
assume that:
H 0 ：F(x)＝F 0 (x) (4)
wherein F (x) is the actual statistical distribution of typical equipment requirements;
the test statistic D is:
in the method, in the process of the invention,for the actual cumulative frequency, m i For observations less than or equal to x i A total number of n samples x;
H 0 the receiving domain is:
D≤D α (6)
wherein D is α For the distribution threshold of test statistic D, α is the significance level;
and judging whether the actual statistical distribution of the typical equipment requirements is subjected to the statistical distribution of the typical equipment requirements obtained by the histogram according to the formula (6).
Specifically, when the actual statistical distribution of the typical equipment needs is determined according to the formula (6), if the formula (6) is satisfied, the actual statistical distribution of the typical equipment needs is determined to follow the statistical distribution of the typical equipment needs obtained by the histogram, and if the formula (6) is not satisfied, the actual statistical distribution of the typical equipment needs is determined to not follow the statistical distribution of the typical equipment needs obtained by the histogram.
S6, judging the statistical distribution of the requirements of each typical equipment according to the test result of the chi-square test method and the test result of the K-S test method.
Specifically, when the statistical distribution of each typical equipment is judged, if the result of the chi-square test is consistent with the result of the K-S test, determining that the statistical distribution of the requirements of the typical equipment is compliant with the statistical distribution obtained according to the histogram; if the result of the chi-square test and the result of the K-S test are inconsistent, it is determined that the statistical distribution of the typical equipment requirements does not follow the statistical distribution obtained from the histogram.
When the statistical distribution of each typical device is two or more, if the test result of the chi-square test method and the test result of the K-S test method of each statistical distribution are identical, the statistical distribution with the largest P value is selected as the final statistical distribution of the typical device, wherein the P value is represented by the test statistic χ 2 Or test statistic D. Specifically, if P is the value of P when determining the statistical distribution<And alpha, the equipment of the type does not obey the statistical distribution obtained according to the histogram, and if P is more than or equal to alpha, the equipment of the type obeys the statistical distribution obtained according to the histogram.
The application range of chi-square test is wider. However, when the expected frequency is small, the chi-square test needs to be calculated after merging the adjacent groups, which can lead to the sample losing some information. The K-S check does not require a packet and therefore retains more information. In fact, whatever the method of inspection, it is possible to obtain the opposite result from the previous if the confidence level or the number of samples is changed, and the chi-square inspection is also affected by the grouping. In order to ensure the correctness of the test, the method adopts two methods of chi-square test and K-S test to carry out non-parameter hypothesis test on various statistical distributions, thereby reducing the incidence rate of false rejection or false taking errors.
The above-described method of the present invention will be described in detail with reference to specific embodiments.
Example 1: taking an A-type aircraft maintenance device as an example
The aircraft equipment strength and the flight mission quantity are not greatly changed, the statistical years of fault data samples are 2003-2017, and the sample capacity according to the statistics of half a year is 30, so that the inspection requirement is met.
(1) Certain type accumulator
The machine is a mechanical machine, and a fault data sample is shown in table 1.
TABLE 1
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 1 | 6 | 3 | 2 | 1 | 6 | 4 | 0 | 4 | 1 | 2 | 4 | 2 | 7 | 1 | 2 | 4 | 0 | 5 | 1 | 0 | 2 | 0 | 2 | 2 | 0 | 1 | 5 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in figure 1.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 2.3333. The results of the chi-square test are shown in table 2.
TABLE 2
Statistics χ of chi-square test 2 ＝3.7503，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(2) Centrifugal pump of some kind
The device is an electromechanical device, and a fault data sample thereof is shown in table 3.
TABLE 3 Table 3
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 1 | 0 | 0 | 3 | 4 | 1 | 5 | 6 | 0 | 2 | 6 | 9 | 4 | 1 | 8 | 3 | 5 | 6 | 7 | 2 | 6 | 11 | 1 | 2 | 5 | 8 | 8 | 0 | 6 | 7 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in figure 2.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 4.2333. The results of the chi-square test are shown in table 4.
TABLE 4 Table 4
Statistics χ of chi-square test 2 ＝3.4757，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(3) Certain type of sensor
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 5.
TABLE 5
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 1 | 1 | 1 | 6 | 2 | 14 | 14 | 11 | 8 | 10 | 8 | 14 | 9 | 9 | 4 | 6 | 5 | 8 | 1 | 7 | 4 | 5 | 5 | 7 | 12 | 17 | 6 | 21 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in figure 3.
The samples were divided into 4 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 7.2667. The results of the chi-square test are shown in table 6.
TABLE 6
Statistics χ of chi-square test 2 ＝4.9993，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (3) = 7.8147. Obviously, χ 2 <χ 2 0.95 (3) The equipment requirements are subject to poisson distribution.
(4) Certain radio station
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 7.
TABLE 7
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 1 | 6 | 6 | 4 | 6 | 7 | 4 | 11 | 5 | 11 | 9 | 5 | 8 | 10 | 5 | 14 | 2 | 10 | 8 | 8 | 5 | 8 | 10 | 14 | 15 | 7 | 9 | 9 | 5 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 4.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 7.4. The results of the chi-square test are shown in table 8.
TABLE 8
Statistics χ of chi-square test 2 ＝2.2177，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(5) Certain altimeter
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 9.
TABLE 9
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 1 | 3 | 6 | 5 | 11 | 8 | 11 | 9 | 2 | 1 | 4 | 11 | 9 | 9 | 6 | 2 | 6 | 0 | 4 | 10 | 7 | 12 | 7 | 5 | 17 | 6 | 8 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 5.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 6.1333. The results of the chi-square test are shown in table 10.
Table 10
Statistics χ of chi-square test 2 ＝4.4212，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(6) Certain type top
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 11.
TABLE 11
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 2 | 6 | 1 | 3 | 4 | 2 | 6 | 6 | 9 | 11 | 7 | 10 | 8 | 8 | 9 | 6 | 4 | 5 | 5 | 7 | 8 | 8 | 10 | 9 | 8 | 5 | 8 | 10 | 0 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 6.
The samples were divided into 4 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 6.1667. The results of the chi-square test are shown in table 12.
Table 12
Statistics χ of chi-square test 2 ＝1.3821，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (3) = 7.8147. Obviously, χ 2 <χ 2 0.95 (3) The equipment requirements are subject to poisson distribution.
Example 2: taking B-type aircraft maintenance equipment as an example
The aircraft equipment strength and the flight mission quantity are not greatly changed, the statistical years of fault data samples are 2005-2017, and the sample capacity according to the statistics of half year is 26, so that the inspection requirement is basically met.
(1) Certain type servo valve
The device is an electromechanical device, and a fault data sample thereof is shown in table 13.
TABLE 13
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 6 | 2 | 6 | 5 | 5 | 3 | 8 | 8 | 16 | 5 | 12 | 9 | 9 | 0 | 7 | 4 | 1 | 1 | 0 | 4 | 2 | 2 | 4 | 5 | 9 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 7.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 5.1923. The results of the chi-square test are shown in table 14.
TABLE 14
Statistics χ of chi-square test 2 ＝1.078，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(2) Certain processor
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 15.
TABLE 15
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 0 | 0 | 1 | 0 | 1 | 1 | 8 | 3 | 6 | 4 | 8 | 7 | 2 | 5 | 12 | 5 | 7 | 3 | 3 | 3 | 3 | 3 | 2 | 2 | 3 | 4 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 8.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 3.6923. The results of the chi-square test are shown in table 16.
Table 16
Statistics χ of chi-square test 2 ＝0.0829，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(3) Certain type top
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 17.
TABLE 17
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 0 | 1 | 1 | 4 | 0 | 3 | 4 | 3 | 5 | 3 | 7 | 7 | 5 | 6 | 4 | 2 | 2 | 4 | 4 | 6 | 5 | 7 | 7 | 3 | 2 | 3 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 9.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 3.7692. The results of the chi-square test are shown in table 18.
TABLE 18
Statistics χ of chi-square test 2 ＝0.0491，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
Example 3: use C-type aircraft maintenance equipment case
The aircraft equipment strength and the flight mission quantity are not greatly changed, the statistical years of fault data samples are 2005-2017, and the sample capacity according to the statistics of half year is 26, so that the inspection requirement is basically met.
(1) Certain regulator
The device is an electromechanical device, and a fault data sample thereof is shown in table 19.
TABLE 19
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 1 | 1 | 2 | 0 | 0 | 2 | 9 | 4 | 2 | 2 | 4 | 0 | 0 | 3 | 2 | 2 | 1 | 0 | 6 | 2 | 4 | 4 | 9 | 2 | 2 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 10.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 2.5385. The results of the chi-square test are shown in table 20.
Table 20
Statistics χ of chi-square test 2 ＝0.2306，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(2) Certain type of receiver
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 21.
Table 21
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 0 | 2 | 0 | 0 | 0 | 2 | 0 | 1 | 3 | 2 | 1 | 1 | 0 | 4 | 4 | 0 | 2 | 4 | 4 | 6 | 13 | 4 | 11 | 8 | 9 | 4 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 11.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 3.2692. The results of the chi-square test are shown in table 22.
Table 22
Statistics χ of chi-square test 2 ＝1.8388，χ 2 Critical of distributionValue χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
Example 4: taking a D-type aircraft maintenance device as an example
The aircraft equipment strength and the flight mission quantity are not greatly changed, the statistical years of fault data samples are 2005-2017, and the sample capacity according to the statistics of half year is 26, so that the inspection requirement is basically met.
(1) Certain electromagnetic valve
The device is an electromechanical device, and a fault data sample thereof is shown in table 23.
Table 23
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 1 | 0 | 6 | 3 | 2 | 2 | 1 | 0 | 6 | 4 | 3 | 4 | 5 | 3 | 5 | 6 | 2 | 1 | 4 | 3 | 3 | 2 | 2 | 2 | 3 | 1 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 12.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 2.8462. The results of the chi-square test are shown in table 24.
Table 24
Statistics of chi-square testMeasuring χ 2 ＝0.0734，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(2) Certain type fuel pump
The device is an electromechanical device, and a fault data sample thereof is shown in table 25.
Table 25
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| X i | 1 | 2 | 2 | 1 | 1 | 5 | 6 | 5 | 11 | 4 | 4 | 1 | 4 | 7 | 2 | 2 | 9 | 4 | 2 | 7 | 4 | 3 | 3 | 7 | 4 | 3 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 13.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 4. The results of the chi-square test are shown in table 26.
Table 26
Statistics χ of chi-square test 2 ＝2.992，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
Example 5: taking E-type aircraft maintenance equipment as an example
The aircraft equipment strength and the flight mission quantity are not greatly changed, the statistical years of fault data samples are 2005-2018, the sample capacity is 27 when the fault data samples are counted in half years, and the statistical distribution test is carried out on specific equipment of the aircraft.
(1) Centrifugal pump of some kind
The device is an electromechanical device, and a fault data sample thereof is shown in table 27.
Table 27
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 3 | 1 | 5 | 6 | 0 | 2 | 6 | 9 | 4 | 1 | 8 | 3 | 4 | 6 | 5 | 2 | 6 | 10 | 1 | 2 | 4 | 8 | 8 | 0 | 6 | 8 | 5 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 14.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 4.5556. The results of the chi-square test are shown in table 28.
Table 28
Statistics χ of chi-square test 2 ＝2.4388，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(2) Certain control box
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 29.
Table 29
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 0 | 0 | 2 | 5 | 4 | 5 | 4 | 6 | 3 | 5 | 1 | 2 | 6 | 4 | 5 | 4 | 8 | 12 | 4 | 7 | 5 | 11 | 3 | 14 | 12 | 8 | 3 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 15.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 5.2963. The results of the chi-square test are shown in table 30.
Table 30
Statistics χ of chi-square test 2 ＝0.767，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(3) Certain compass
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 31.
Table 31
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 4 | 4 | 4 | 5 | 8 | 2 | 3 | 8 | 8 | 4 | 0 | 1 | 4 | 5 | 4 | 0 | 1 | 1 | 3 | 2 | 4 | 2 | 8 | 4 | 1 | 3 | 0 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 16.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 3.4444. The results of the chi-square test are shown in table 32.
Table 32
Statistics χ of chi-square test 2 ＝0.3046，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(4) Certain transceiver
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 33.
Table 33
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 3 | 6 | 6 | 3 | 5 | 8 | 5 | 3 | 3 | 6 | 3 | 2 | 1 | 3 | 1 | 1 | 2 | 1 | 5 | 2 | 7 | 5 | 4 | 5 | 4 | 5 | 5 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in figure 17.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 3.8519. The results of the chi-square test are shown in table 34.
Watch 34
Statistics χ of chi-square test 2 ＝1.5154，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(5) Certain type of sensor
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 35.
Table 35
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 6 | 2 | 15 | 14 | 14 | 9 | 10 | 8 | 14 | 8 | 9 | 3 | 6 | 5 | 7 | 1 | 7 | 4 | 5 | 5 | 7 | 12 | 18 | 6 | 7 | 4 | 2 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in fig. 18.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The desired mean value is 7.7037. The results of the chi-square test are shown in table 36.
Table 36
Statistics χ of chi-square test 2 ＝2.391，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
(6) Certain instrument
The fixture is an ad hoc fixture, and a fault data sample thereof is shown in table 37.
Table 37
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| X i | 8 | 11 | 12 | 13 | 10 | 8 | 17 | 11 | 8 | 8 | 11 | 14 | 13 | 12 | 6 | 7 | 4 | 5 | 6 | 6 | 3 | 13 | 10 | 8 | 8 | 17 | 8 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, and obtaining the statistical distribution of the equipment requirements as poisson distribution as shown in figure 19.
Samples were divided into 3 groups under the condition that the theoretical frequency of each group was not less than 5. The expected mean is 9.5185 and the chi-square test results are shown in table 38.
Table 38
Statistics χ of chi-square test 2 ＝0.3215，χ 2 Distribution critical value χ 2 0.95 (k-1)＝χ 2 0.95 (2) = 5.9915. Obviously, χ 2 <χ 2 0.95 (2) The equipment requirements are subject to poisson distribution.
To further verify the results of the chi-square test, K-S tests were performed on typical equipment of the five aircraft in the 5 examples described above using the statistical analysis software SPSS Statistics, the results of which are shown in Table 39.
It can be seen from this table that the P-value of all the devices is greater than 0.05, and that the requirements of these devices obey the poisson distribution, further validating the results of the chi-square distribution.
Table 39
Example 6: taking a certain starter as an example, adopting statistical analysis software easy to carry out non-parameter hypothesis test on several statistical distributions which are commonly used.
The starter is an electromechanical device, and a fault data sample of the starter is shown in a table 40.
Table 40
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| X i | 0 | 0 | 3 | 3 | 5 | 2 | 4 | 4 | 9 | 4 | 6 | 8 | 7 | 8 | 6 | 11 | 8 | 8 | 17 | 14 | 9 | 11 | 9 | 13 | 12 | 12 | 9 | 8 | 4 | 3 |
And drawing a histogram according to the actual measurement frequency of the equipment faults, wherein the obtained demand statistical distribution of the equipment can be continuous distribution such as normal distribution, weibull distribution, exponential distribution and the like and discrete distribution such as poisson distribution, negative binomial distribution and the like as shown in fig. 20.
1) Continuously distributed
(1) Normal distribution
Assuming that the starter demand is subject to normal distribution, the results of the K-S test and the chi-square test are shown in table 41.
As can be seen from the table, the P values are greater than the significance levels 0.01, 0.02, 0.05, 0.1, 0.2, whether it is the K-S test or the chi-square test, which means that the device is subject to normal distribution regardless of the significance level conditions.
Table 41
(2) Weibull distribution
Assuming that the starter demand is subject to the weibull distribution, the results of the K-S test and the chi-square test are shown in table 42.
From this table, the K-S test obeys the weibull distribution at significance levels of 0.01, 0.02, 0.05, 0.1, 0.2, and the chi-square test does not obey the weibull distribution at significance levels of 0.2 only.
Table 42
(3) Exponential distribution
Assuming that the starter demand obeys an exponential distribution, the results of the K-S test and the chi-square test are shown in table 43.
From this table, it can be seen that the K-S test obeys the exponential distribution at a significance level of 0.01, 0.02, 0.05, and the chi-square test obeys the exponential distribution only at a significance level of 0.01.
Table 43
2) Discrete distribution
(1) Poisson distribution
Assuming that the starter demand is following a poisson distribution, the K-S test is used and the results are shown in table 44.
As can be seen from the table, the starter obeys poisson distribution at significance levels of 0.01, 0.02, 0.05.
Table 44
(2) Negative binomial distribution
Assuming that the starter demand obeys the negative binomial distribution, the K-S test is used, and the results are shown in Table 45.
From the table, the starter obeys binomial distribution only under the conditions of significance level 0.01 and 0.02.
Table 45
In addition, the difference ratio of the negative binomial distribution is larger than 1, the difference ratio of the binomial distribution is smaller than 1, and only one of the two can accept the original assumption, so the starter requirement does not obey the binomial distribution.
The starter has a sample observation period of half a year, and if the observation period is one year, the standard deviation thereof is larger, that is, the fluctuation of the failure sample data thereof is larger or the dispersion degree of the failure number thereof is higher. As can be seen from table 40, a certain number of faults in the number 19 of the equipment fault comparison set are completed in the field, and spare parts are not replaced, that is, the faults do not generate requirements on the spare parts. Because the faults of the equipment are complex and various, and faults which can be removed on site are difficult to predict, the standard formulated by adopting fault data is larger. The equipment security department considers that the proper and larger standard can better ensure that the equipment requirement is met, and the standard which is actually formulated by adopting fault data is reasonable as a whole and basically acceptable. However, there are also equipment that has fewer replacement parts and is on-site and has a large number of faults, and the standard and actual deviation are relatively large. Therefore, when equipment is prepared for raising and supplying standard, the fault data of the quality control room of the large crew of the machine is adopted preferentially, and the repair and payment data of the aviation material strand are adopted.
Comparing K-S test statistics of various distributions, it can be seen that the test statistics of the normal distribution are the smallest and the test statistics of the exponential distribution are the largest in three continuous distributions of the normal distribution, the Weibull distribution and the exponential distribution, which means that the fitting degree of the normal distribution is the highest and the fitting degree of the exponential distribution is the lowest; it can also be seen that the poisson distribution has a higher fitness and the negative binomial distribution has a lower fitness in two discrete distributions, poisson distribution and negative binomial distribution. For the starter, under the condition of the significance level of 0.05, the normal distribution, the Weibull distribution, the Poisson distribution and the index distribution all accept the original assumption, so that the starter can be used for measuring and calculating the equipment requirements.
The fitting curves of the different distributions are shown in fig. 21 and 22, and it can be seen that the exponential distribution is greatly different from the actual distribution, and the poisson distribution, the normal distribution and the weibull distribution are close to the actual distribution, and the poisson distribution, the normal distribution and the weibull distribution are closest to each other.
In addition, as can be seen from fig. 21, the exponential distribution curve is greatly different from the actual, but at a significance level of 0.05, the chi-square test accepts an assumption that obeys the exponential distribution, but the K-S assumption does not accept the assumption. If the P value is greater than 0.05, this means that the failure of the equipment is not in compliance with the exponential distribution, but only that the probability is low.
The above-described embodiments are intended to illustrate the present invention, not to limit it, and any modifications and variations made thereto are within the spirit of the invention and the scope of the appended claims.
Claims (4)
1. A statistical distribution inspection method for the demand of aviation equipment maintenance equipment is characterized by comprising the following steps:
collecting historical fault data of various typical equipment requirements, and manufacturing a historical fault data sample set according to the historical fault data;
drawing a histogram of each typical equipment requirement according to the historical fault data sample set;
obtaining statistical distribution of each typical equipment requirement according to histogram fitting of each typical equipment requirement;
the statistical distribution of the requirements of each typical equipment is checked by adopting a chi-square checking method; the method for checking by adopting the chi-square checking method comprises the following steps:
assume that:
H 0 : the distribution function of X is F 0 (x) (1)
Wherein X is a historical failure data sample set of typical equipment requirements, F 0 (x) A statistical distribution function of typical equipment requirements obtained for the histogram, wherein X is a sample in a historical fault data sample set X;
test statistic χ 2 The method comprises the following steps:
where n is the total number of samples x, n i To observe value equal to x i Is the actual measurement frequency of x i For the ith sample, p i As theoretical probability, np i For theoretical frequency, k is the number of packets;
H 0 the receiving domain is:
χ 2 ≤χ 2 1-α (k-1) (3)
in χ 2 1-α (k-1) is the test statistic χ 2 α is the significance level;
judging whether the actual statistical distribution of the typical equipment demands is subjected to the statistical distribution of the typical equipment demands obtained by the histogram according to the formula (3);
adopting a K-S test method to test the statistical distribution of the requirements of each typical equipment; the method for checking by adopting the K-S checking method comprises the following steps:
assume that:
H 0 ：F(x)＝F 0 (x) (4)
wherein F (x) is the actual statistical distribution of typical equipment requirements;
the test statistic D is:
in the method, in the process of the invention,for the actual cumulative frequency, m i For observations less than or equal to x i A total number of n samples x;
H 0 the receiving domain is:
D≤D α (6)
wherein D is α For the distribution threshold of test statistic D, α is the significance level;
determining whether the actual statistical distribution of the typical equipment demand follows the histogram to obtain the statistical distribution of the typical equipment demand according to formula (6)
Judging the statistical distribution of the requirements of each typical equipment according to the test result of the chi-square test method and the test result of the K-S test method;
when judging the statistical distribution of each typical equipment, if the test result of the chi-square test method is consistent with the test result of the K-S test method, determining that the statistical distribution of the requirements of the typical equipment obeys the statistical distribution obtained according to the histogram; if the test result of the chi-square test method is inconsistent with the test result of the K-S test method, determining that the statistical distribution of the typical equipment requirements does not follow the statistical distribution obtained according to the histogram.
2. The method for checking statistical distribution of aircraft equipment maintenance equipment requirements according to claim 1, wherein when the actual statistical distribution of typical equipment requirements is determined according to the formula (3), if the formula (3) is satisfied, the actual statistical distribution of typical equipment requirements is determined to follow the statistical distribution of typical equipment requirements obtained by the histogram, and if the formula (3) is not satisfied, the actual statistical distribution of typical equipment requirements is determined to not follow the statistical distribution of typical equipment requirements obtained by the histogram.
3. The method for checking statistical distribution of aircraft equipment maintenance equipment requirements according to claim 1, wherein when determining actual statistical distribution of typical equipment requirements according to formula (6), if formula (6) is satisfied, determining that the actual statistical distribution of the typical equipment requirements follows the statistical distribution of the typical equipment requirements obtained by the histogram, and if formula (6) is not satisfied, determining that the actual statistical distribution of the typical equipment requirements does not follow the statistical distribution of the typical equipment requirements obtained by the histogram.
4. A method of testing the statistical distribution of the demand of maintenance equipment for aircraft equipment according to claim 3, wherein, when the statistical distribution of each typical equipment is two or more, if the test result of the chi-square test method and the test result of the K-S test method of each statistical distribution are identical, the statistical distribution with the largest P value is selected as the final statistical distribution of the typical equipment, wherein the P value is represented by the test statistic χ 2 Or test statistic D.
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Inventor after: Guo Feng Inventor after: Zhao Hongqiang Inventor after: Sun Zhonghua Inventor after: Xu Fenglei Inventor after: Zhang Suqin Inventor after: Guo Xingxiang Inventor after: Gao Wei Inventor before: Guo Feng Inventor before: Zhao Hongqiang Inventor before: Sun Zhonghua Inventor before: Xu Fenglei Inventor before: Zhang Suqin Inventor before: Guo Xingxiang Inventor before: Gao Wei |
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