Method and system for determining minimum sample size of aviation equipment quality characteristic evaluation

Abstract

The invention belongs to the technical field of aviation equipment quality judgment, and particularly relates to a minimum sample size determination method and system for aviation equipment quality characteristic assessment, and the method comprises the steps: S1, carrying out the normality test of the sample size data for aviation equipment quality characteristic assessment, and determining the minimum sample size; s2, skewness detection is carried out on the sample size data of aviation equipment quality characteristic evaluation; s3, correcting the minimum sample size of the aviation equipment quality characteristic evaluation according to the sample data skewness judgment parameter; and S4, constructing a center limit theorem effect taking principle under small skewness to judge and determine the minimum sample size for evaluating the quality characteristics of the aeronautical equipment. According to the method, skewness is used for measuring data of different distributions in a unified mode, the center limit theorem is used for approaching the number of samples in normal distribution, it is not needed to distinguish which distribution the sample quantity specifically comes from when the sample quantity is calculated, use is more visual, and particularly, a calculation result with statistical significance and reference value can be more effectively given under the condition of small samples.

Description

Technical Field

[0001] The present invention belongs to the technical field of aviation equipment quality, and in particular relates to a method and a system for determining a minimum sample size for aviation equipment quality characteristic evaluation. Background Art

[0002] The quality characteristic data of aviation equipment during flight are field data, which need to reflect the product's conditions under actual use environment and maintenance conditions. However, the sample size is small and the data fluctuates greatly. When processing, it should be classified according to different situations and processing requirements. Quality characteristic evaluation often cannot be completed due to insufficient sample size. Therefore, the number of tests and the sample size of the test should be clarified to ensure the accuracy and rationality of the field evaluation.

[0003] At present, the methods for calculating the minimum sample size all rely on the empirical value of 30. Especially when the minimum sample size calculated by other methods is less than 30, it is still recommended to evaluate the quality characteristic parameters when the sample size reaches 30. This is somewhat conservative. When the sample size is small in a flight environment, it may be difficult to reach the recommended empirical value of 30. In addition, the other main method requires that the sample obeys a specific distribution. In most cases, it is difficult to determine which distribution the data obeys. In the flight process environment, the amount of actual data is small, which further increases the difficulty of determining that the sample obeys the distribution. Therefore, when evaluating the quality characteristics of the near-flight process environment with a small sample size and large data fluctuations, traditional methods often cannot provide statistically significant and reference-worthy results. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a method and system for determining the minimum sample size for evaluating the quality characteristics of aviation equipment. The method uses skewness to uniformly measure data of different distributions, and uses the central limit theorem to approximate the number of samples of a normal distribution. When calculating the sample size, there is no need to distinguish the specific distribution from which the sample size comes, and the method is more intuitive to use. Especially in the case of a small sample, the method can more effectively provide a calculation result with statistical significance and reference value.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for determining the minimum sample size for evaluating the quality characteristics of aviation equipment, comprising:

[0006] S1: Conduct normality test on sample size data of aviation equipment quality characteristic assessment and determine the minimum sample size;

[0007] Obtain sample data X for aviation equipment quality characteristics assessment i , …, x n ), conduct normality test and determine the minimum sample size n for aviation equipment quality characteristic evaluation s for:

[0008]

[0009] Among them, n s Minimum sample size for the evaluation of quality characteristics of aviation equipment; Z a / 2 is the critical value of the standard normal distribution corresponding to the confidence level α; s is the standard deviation of the sample size data X; E is the set error range; α is the set confidence level;

[0010] S2: skewness test of sample size data for aviation equipment quality characteristics assessment;

[0011] The skewness is used to evaluate the symmetry of the distribution of sample data for the evaluation of aviation equipment quality characteristics and to determine whether the sample data is skewed. The sample data skewness determination parameter S is:

[0012]

[0013] Among them, S is the sample data skewness determination parameter; x i is the sample data value after the i-th sorting; is the sample size data mean, n is the total amount of sample data; i is the sample data number;

[0014] S3: Correct the minimum sample size n of the aviation equipment quality characteristic evaluation in step S1 according to the sample data skewness determination parameter S in step S2 s ;

[0015] In order to reduce the impact of skewness on the sample mean distribution, the sample size is increased to improve the applicability of the central limit theorem. To ensure the rationality of the sample size, the sample size expression after skewness correction is:

[0016]

[0017] Among them, n s ￠ is the minimum sample size for the revised aviation equipment quality characteristics assessment;

[0018] S4: Construct the principle of the effectiveness of the central limit theorem under small skewness to determine the minimum sample size n for the quality characteristics evaluation of aviation equipment s ￠;

[0019] The quality characteristic data of aviation equipment is obtained, and the normal distribution is used for estimation and calculation according to the central limit theorem; based on the principle of the effectiveness of the central limit theorem under small skewness, the minimum sample size for the evaluation of the quality characteristics of aviation equipment is constructed to determine the sample size:

[0020]

[0021] Among them, E is the expected distribution state of aviation equipment quality characteristic data; X is the sample size data of aviation equipment quality characteristic evaluation; μ is the sample mean of aviation equipment quality characteristic data; S0 is the set sample data skewness; P(α) is the expected value of the pass rate under the confidence level α; P0 is the pass rate under the confidence level α; N0 is the set sample data volume requirement.

[0022] Preferably, the normality test in step S1 is performed to ensure that the sample data used for the evaluation of the quality characteristics of aviation equipment meet statistical rationality, and the statistical index W of the test sample data set is:

[0023]

[0024] Among them, W is the statistical indicator of the test sample size data set; a i is the i-th sample size data parameter; x i is the i-th sample data value after sorting; is the mean of the sample data; n is the total amount of sample data.

[0025] Preferably, the value of the sample data skewness judgment parameter S in step S2 can be used to determine the distribution of the sample data for the aviation equipment quality characteristics evaluation, specifically: when S=0, the sample data for the aviation equipment quality characteristics evaluation is symmetrically distributed; S≠0, the sample data for the aviation equipment quality characteristics evaluation is skewedly distributed.

[0026] The second aspect of the present invention proposes a sample size determination system for aviation equipment quality characteristics evaluation for the aforementioned minimum sample size determination method for aviation equipment quality characteristics evaluation, which includes: a distribution state applicable sample size simulation analysis determination module, an applicable sample size module for aviation equipment quality characteristics evaluation, and a recommended sample size module for aviation equipment quality characteristics evaluation;

[0027] The distribution state applicable sample size simulation analysis module generates a standard comparison chart of the distribution state applicable sample size by simulating and calculating the minimum applicable sample size of data that obeys the set distribution and satisfies the central limit theorem under different skewnesses and obeys the normal distribution, obtains the universal sample size of data with different distributions and skewnesses, and uses the universal sample size as the minimum sample size;

[0028] The applicable sample size module for aviation equipment quality characteristic evaluation can analyze the distribution state applicable sample size standard comparison chart generated by the distribution state applicable sample size simulation analysis module, and summarize the applicable sample size for aviation equipment quality characteristic evaluation in which the central limit theorem is effective according to the applicable sample size variation with skewness of the distribution simulation calculation results;

[0029] The recommended sample size module for constructing the quality characteristic evaluation of aviation equipment is used to provide sample size recommendations for the quality characteristic evaluation of aviation equipment under the condition of small skewness data, and specifically includes: a data processing submodule, a sample size calculation submodule, a normality test submodule, a sample size recommendation submodule, a visualization submodule and a user interface submodule.

[0030] Preferably, the data processing submodule can perform data import, data preprocessing, skewness correction, and clean, skewness correction and normality test on the original data.

[0031] Preferably, the sample size calculation submodule can combine the skewness-corrected data, use the coefficient of variation and the precision parameter, automatically calculate the recommended sample size, and output a calculation report.

[0032] Preferably, the normality inspection submodule provides an inspection function for aviation equipment quality characteristic sample data and automatically generates an inspection report.

[0033] Preferably, the sample size recommendation submodule dynamically adjusts the sample size recommendation value according to the accuracy requirements and data skewness set by the user, to ensure that the recommended sample size can meet both the evaluation accuracy and the data distribution characteristics.

[0034] Preferably, the visualization submodule can provide sample distribution diagrams, comparison diagrams before and after skewness correction, and normality test result diagrams to intuitively display data characteristics and sample size recommendation results.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) The present invention uses skewness to uniformly measure aviation equipment quality characteristic data with different distributions, and uses a simulation method to use skewness as a measurement standard to uniformly use the central limit theorem to approximate the sample size of the normal distribution of data with different distributions. This measurement method does not need to distinguish the specific distribution of the sample size when calculating the sample size. It is not only universal but also more intuitive to use.

[0037] (2) Compared with the traditional method, the present invention is more flexible in application. When the skewness or distribution of specific data is given, a more accurate simulation result of the determined skewness or distribution is given according to the specific setting of the data skewness or distribution in the simulation. Especially in the case of small samples, the present invention can more effectively give calculation results with statistical significance and reference value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flowchart of a method for determining a minimum sample size for evaluating quality characteristics of aviation equipment of the present invention;

[0039] Figure 2It is a schematic diagram of the standard normal distribution of the present invention;

[0040] Figure 3 A distribution state diagram of sample data obtained by random sampling of the present invention;

[0041] Figure 4 The modified sample data distribution state diagram of the present invention;

[0042] Figure 5 This is a framework diagram of the minimum sample size calculation principle of the present invention;

[0043] Figure 6 It is a diagram of simulation calculation results of each distribution when the normality test pass rate p≥0.9 of the present invention;

[0044] Figure 7 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.9 of the present invention;

[0045] Figure 8 It is a diagram of simulation calculation results of each distribution when the normality test pass rate p≥0.8 of the present invention;

[0046] Fig. 9 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.8 of the present invention;

[0047] Fig.10 It is a diagram of simulation calculation results of each distribution when the normality test pass rate p≥0.7 of the present invention;

[0048] Fig.11 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.7 of the present invention;

[0049] Fig.12 It is a flow chart of test data processing of the present invention;

[0050] Fig.13 It is a graph showing the change of the confidence interval with the number of groups of the present invention. DETAILED DESCRIPTION

[0051] The exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0052] The embodiment of the present invention provides a method for determining the minimum sample size for evaluating the quality characteristics of aviation equipment, such as Figure 1As shown, the sample size data of aviation equipment quality characteristics evaluation is tested for normality to determine the minimum sample size; the sample size data of aviation equipment quality characteristics evaluation is tested for skewness; the minimum sample size of aviation equipment quality characteristics evaluation is corrected according to the skewness judgment parameter of the sample data; the central limit theorem effectiveness principle under small skewness is constructed to determine the minimum sample size for aviation equipment quality characteristics evaluation; it includes:

[0053] Step S1: Perform a normality test on the sample size data of aviation equipment quality characteristic assessment to determine the minimum sample size.

[0054] Obtain sample data X for aviation equipment quality characteristics assessment i , …, x n ), a normality test is performed. In order to make the sample size data used for aviation equipment quality characteristics evaluation meet statistical rationality, the statistical index W of the test sample size data set is:

[0055]

[0056] Among them, W is the statistical indicator of the test sample size data set; a i is the i-th sample size data parameter; x i is the i-th sample data value after sorting; is the mean of the sample data; n is the total amount of sample data.

[0057] Determine the minimum sample size n for the evaluation of quality characteristics of aviation equipment s for:

[0058]

[0059] Among them, n s Minimum sample size for the evaluation of quality characteristics of aviation equipment; Z a / 2 is the critical value of the standard normal distribution corresponding to the confidence level α; s is the standard deviation of the sample size data X; E is the set error range; α is the set confidence level.

[0060] S2: Perform skewness test on sample size data for aviation equipment quality characteristics assessment.

[0061] The skewness is used to evaluate the symmetry of the distribution of sample data for the evaluation of aviation equipment quality characteristics and to determine whether the sample data is skewed. The sample data skewness determination parameter S is:

[0062]

[0063] Among them, S is the sample data skewness determination parameter; x i is the sample data value after the i-th sorting; is the sample size data mean, n is the total amount of sample data; i is the sample data number.

[0064] The value of the sample data skewness judgment parameter S can be used to judge the distribution of sample data for aviation equipment quality characteristic evaluation. Specifically, when S=0, the sample data for aviation equipment quality characteristic evaluation is symmetrically distributed; when S≠0, the sample data for aviation equipment quality characteristic evaluation is skewedly distributed.

[0065] S3: Correct the minimum sample size n of the aviation equipment quality characteristic evaluation in step S1 according to the sample data skewness determination parameter S in step S2 s .

[0066] In order to reduce the impact of skewness on the sample mean distribution, the sample size is increased to improve the applicability of the central limit theorem. To ensure the rationality of the sample size, the sample size expression after skewness correction is:

[0067]

[0068] Among them, n s ￠ is the minimum sample size for the revised aviation equipment quality characteristics assessment.

[0069] like Figure 2 The figure shows a schematic diagram of a standard normal distribution according to an embodiment of the present invention; the skewness of the distribution can often reflect the sample size requirement for samples that obey the distribution to make the central limit theorem effective. Figure 3 The sample data distribution diagram obtained by random sampling of the present invention is shown in FIG. 1, where the sample size is 1000; the sample is randomly sampled from samples with an actual skewness of 60 and an actual skewness of 2.5. It can be seen that when the sample size is 1000, Figure 4 The diagram shows the distribution state of the sample data after the correction of the present invention; in the diagram, the small skewness is already quite close to the normal distribution, and it can be determined that it has obeyed the normal distribution at this time, while the large skewness still has a large skewness when the sample size is 1000, that is, the more obvious skewed distribution will greatly increase the sample size requirements. If the central limit theorem of some common distributions can be applied to the sample size for simulation calculation, and it is confirmed from the results that there are certain values ​​that can make the central limit theorem effective for these common distributions within a certain skewness range, it can guide the selection of sample size when the skewness of historical data is relatively close to 0. Because in some cases, the data will still have a large kurtosis when the skewness is close to 0, and affect the effectiveness of the central limit theorem, so when using the simulation results, it is also necessary to pay attention to limiting the range of kurtosis.

[0070] S4: Construct the principle of the effectiveness of the central limit theorem under small skewness to determine the minimum sample size n for the quality characteristics evaluation of aviation equipment s ￠.

[0071] The quality characteristic data of aviation equipment is obtained, and the normal distribution is used for estimation and calculation according to the central limit theorem; based on the principle of the effectiveness of the central limit theorem under small skewness, the minimum sample size for the evaluation of the quality characteristics of aviation equipment is constructed to determine the sample size:

[0072]

[0073] Among them, E is the expected distribution state of aviation equipment quality characteristic data; X is the sample size data of aviation equipment quality characteristic evaluation; μ is the sample mean of aviation equipment quality characteristic data; S0 is the set sample data skewness; P(α) is the expected value of the pass rate under the confidence level α; P0 is the pass rate under the confidence level α; N0 is the set sample data volume requirement.

[0074] The second aspect of an embodiment of the present invention proposes a sample size determination system for aviation equipment quality characteristic evaluation, which includes: a distribution state applicable sample size simulation analysis determination module, an applicable sample size module for aviation equipment quality characteristic evaluation, and a recommended sample size module for aviation equipment quality characteristic evaluation.

[0075] The distribution state applicable sample size simulation analysis module calculates the minimum applicable sample size of data that obeys the set distribution under different skewnesses and satisfies the central limit theorem and obeys the normal distribution through simulation, generates a standard comparison chart of the distribution state applicable sample size, obtains the common sample size for data with different distributions and skewnesses, and takes the common sample size as the minimum sample size.

[0076] like Figure 5 The diagram shows the framework of the minimum sample size calculation principle of the present invention; this embodiment simulates and calculates the applicable sample sizes of common distributions such as Weibull distribution, exponential distribution, chi-square distribution, F distribution, gamma distribution, lognormal distribution, t distribution, uniform distribution, etc. For a large skewed distribution such as exponential distribution, logarithmic processing is performed first, and then simulation operation is performed. The minimum applicable sample size of data obeying different distributions under different skewnesses that satisfies the central limit theorem and obeys normal distribution is calculated by simulation, and the obtained results are plotted into a graph to obtain the universal sample size of data with different distributions and skewnesses, and the universal sample size is used as the minimum sample size of the skewed data. The specific steps are:

[0077] Step S51: determine a target distribution with certain parameters, and calculate the skewness of the distribution under the parameters.

[0078] Step S52: Take an initial sample size n=2, generate n random numbers of the distribution, and calculate the mean.

[0079] Step S53: Generate m=1000 groups of such random numbers in total, and perform a normality test on the m means (taking the default significance level of 5%).

[0080] Step S54: Repeat steps S52 to S53, set k = 200 times, calculate the normality test pass rate p, if the pass rate p ≥ 0.9, then n is the applicable sample size, if the pass rate p < 0.9, then the sample size n increases by 1, and repeat steps S52 to S54.

[0081] The applicable sample size module for aviation equipment quality characteristic assessment can analyze the standard comparison chart of applicable sample size for distribution status generated by the applicable sample size simulation analysis module for distribution status, and summarize the applicable sample size for aviation equipment quality characteristic assessment for which the central limit theorem is effective based on the change of applicable sample size with skewness of distribution simulation calculation results.

[0082] The recommended sample size module for aviation equipment quality characteristic evaluation is constructed to provide sample size recommendations for aviation equipment quality characteristic evaluation under the condition of small skewness data, which specifically includes: data processing submodule, sample size calculation submodule, normality test submodule, sample size recommendation submodule, visualization submodule and user interface submodule. The data processing submodule can import data, preprocess data, correct skewness, clean the original data, correct skewness and perform normality test. The sample size calculation submodule can automatically calculate the recommended sample size by combining the skewness-corrected data, using the coefficient of variation and precision parameters, and output the calculation report. The normality test submodule provides the test function of the sample data of aviation equipment quality characteristics and automatically generates a test report. The sample size recommendation submodule dynamically adjusts the sample size recommendation value according to the accuracy requirements set by the user and the data skewness, ensuring that the recommended sample size can meet the evaluation accuracy and take into account the data distribution characteristics. The visualization submodule can provide sample distribution diagrams, comparison diagrams before and after skewness correction, and normality test result diagrams to intuitively display data characteristics and sample size recommendation results. The user interface submodule can provide users with a friendly interactive interface, supporting parameter input, data import and result output.

[0083] The simulation calculation results of each distribution in the embodiment of the present invention are as follows. The figure shows the change of the applicable sample size with skewness under different parameters. Figure 6 The figure is a simulation calculation result diagram of each distribution when the normality test pass rate p≥0.9 of the present invention; the results show that when the data sample skewness is in the range of ±0.15, the sample size is greater than 5, and the sample mean can pass the normality test with a significance level of 5% with a probability of 90%, thereby satisfying the central limit theorem. Figure 7 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.9 of the present invention; when the data sample skewness is in the range of ±0.5, the sample size is greater than 30, and the sample mean can pass the normality test with a significance level of 5% with a probability of 90%, thereby satisfying the central limit theorem. And for large skewed distributions such as exponential distribution, this judgment condition is not applicable.

[0084] In the embodiment of the present invention, considering that p≥0.9 is too high in some cases in actual use, a corresponding simulation is also performed for the case of p≥0.8 in the simulation step in combination with the commonly used value 0.8. Figure 8 The figure is a simulation calculation result diagram of each distribution when the normality test pass rate p≥0.8 of the present invention; the results show that when the data sample skewness is in the range of ±0.2, the sample size is greater than 5, and the sample mean can pass the normality test with a significance level of 5% with a probability of 80%, thereby satisfying the central limit theorem; Fig. 9 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.8 of the present invention; when the data sample skewness is in the range of ±0.5, the sample size is greater than 20, which enables the sample mean to pass the normality test with a significance level of 5% with a probability of 80%, thereby satisfying the central limit theorem.

[0085] The present invention uses the same method to calculate the result of p≥0.7; Fig.10 The figure is a simulation calculation result diagram of each distribution when the normality test pass rate p≥0.7 of the present invention; the results show that when the data sample skewness is in the range of ±0.3, the sample size is greater than 5, and the sample mean can pass the normality test with a significance level of 5% with a probability of 70%, thereby satisfying the central limit theorem; Fig.11 This is an enlarged diagram of the simulation calculation results of each distribution when the normality test pass rate p≥0.7 of the present invention; when the data sample skewness is in the range of ±0.5, the sample size is greater than 15, which enables the sample mean to pass the normality test with a significance level of 5% with a probability of 70%, thereby satisfying the central limit theorem.

[0086] From the above conclusions, it can be seen that the applicable sample size increases with the increase of skewness. The reference table of the applicable sample size of the central limit theorem is summarized as shown in Table 1:

[0087] Table 1 Reference table of applicable sample size models for aviation equipment quality characteristics assessment

[0088]

[0089]

[0090] From the simulation calculation results with the default value of 5% for the significance level, it can be seen that it is reasonable to take the minimum sample size of 30 as the empirical value. Under the default significance level, taking the minimum sample size of 30 can ensure that when the data skewness is maintained at ±0.5, the sample mean can pass the normality test with a significance level of 5% with a probability of 90%, thereby satisfying the central limit theorem. That is, taking a sample size of 30 at this time has a high statistical significance, and the sample size can also be directly used to replace the population for relevant calculations.

[0091] The embodiment of the present invention uses the calculation results obtained in Table 1 to analyze the actual aviation equipment quality characteristic data, such as Fig.12 The test data processing flow chart of the present invention is shown; the test data processing process is as follows:

[0092] Step S61: Obtain aviation equipment test data and remove abnormal values.

[0093] Step S62: Determine the type of aviation equipment test data.

[0094] Step S63: When the test data is a continuous parameter and involves the central limit theorem, in addition to theoretically calculating the sample size value, the minimum sample size for statistical significance should also be determined according to step S64.

[0095] Step S64: Determine the minimum sample size.

[0096] Step S641: Calculate the kurtosis and skewness of this type of data in combination with historical data. If the kurtosis is large (the kurtosis of data that completely obeys the normal distribution is 3, and the kurtosis of related data should not be much higher than this value) or the skewness value is far from 0 (such as exponential distribution, this method cannot be used), it is necessary to consider special analysis of sample size requirements.

[0097] Step S642: When the confidence level of the normality test is 95% and the pass rate of the normality test is p≥0.9, when the skewness is in the range of ±0.5, the minimum sample size is 30; when the skewness is in the range of ±0.15, the minimum sample size is 5 (the results when p≥0.8 and p≥0.7 can also be referred to in combination with actual conditions).

[0098] Step S643: When the sample size of the test data is not less than the minimum sample size, continue to execute step S65. When it is less than the minimum sample size, continue the test to obtain more data.

[0099] Step S65: Take the larger value of the two.

[0100] In this case, the failure interval of a certain equipment follows a Weibull distribution with a shape parameter of 3 and a scale parameter of 2. There are 7 groups of data, see Table 2. Each group of data has only five samples due to the limitation of test time. Try to give the confidence interval of the mean failure interval of the equipment at a 95% confidence level.

[0101] Table 2 Confidence interval table of the mean value of equipment failure interval time at 95% confidence level

[0102] Group 1 2 3 4 5 6 7 2.6505 2.3848 2.1153 2.5304 2.5176 1.0404 1.8749 2.1706 1.9989 1.7555 0.7817 1.0387 2.7042 1.9754 1.6902 1.5539 1.7517 0.7106 1.6339 1.9429 1.2882 0.703 1.2568 1.1722 1.6416 1.6851 2.2091 1.2239 0.6588 2.7187 1.2247 2.8246 2.4907 1.2129 2.3763 Skewness 0.0115 0.0036 0.0243 0.0843 -0.1103 0.0363 0.0518 Mean 1.57462 1.98262 1.60388 1.69778 1.8732 1.8219 1.74774

[0103] The embodiment of the present invention will obey the Weibull distribution with a shape parameter of 3 and a scale parameter of 2, and the mathematical expectation E=2*gamma(1+1 / 3)=2*0.893=1.786. According to Table 3 given by the simulation, at the default significance level, when the data skewness is maintained at ±0.15, only 5 samples are needed for each group of data to make its mean approximately conform to the normal distribution. The following uses 3 to 7 groups of data in turn (the quantiles of the t distribution are too large under two groups of data, resulting in a loss of actual reference value), and the confidence interval of the normal distribution mean at 95% confidence level is calculated and written into Table 3.

[0104] Table 3 Confidence interval table of normal distribution mean at 95% confidence level

[0105] Data Used Number of groups Lower confidence limit Upper confidence limit 1-3 groups 3 1.149 2.284 1-4 groups 4 1.415 2.01 1-5 groups 5 1.525 1.963 Group 1-6 6 1.588 1.925 Group 1-7 7 1.62 1.892

[0106] like Fig.13 The figure shows the change of the confidence interval with the number of groups of the present invention. According to the calculation results, it can be seen that the more sample groups are used, the more accurate the confidence interval is. However, in the case of 4 groups of samples or more, the improvement of the accuracy of the confidence interval by continuing to increase the sample size is limited. Therefore, the confidence interval obtained by using 4 groups of samples already has a certain reference value. Through this method, it is possible to obtain a confidence interval with reference value for the sample mean using 20 samples. Compared with the traditional scheme that requires at least 30 samples to obtain a result with reference value, this scheme obtains a calculation result with statistical significance and reference value in the case of a small sample size of less than 30.

[0107] The beneficial effects of the embodiments of the present invention are as follows: the present invention provides a method for determining the minimum sample size for evaluating the quality characteristics of aviation equipment. The embodiments of the present invention use skewness to uniformly measure the quality characteristic data of aviation equipment with different distributions, and use a simulation method to use skewness as a metric to uniformly use the central limit theorem to approximate the number of samples of a normal distribution for data with different distributions. Compared with traditional methods, it is more flexible in application, and when the skewness or distribution of specific data is given, a more accurate simulation result of determining the skewness or distribution is given, especially in the case of small samples, and a calculation result with statistical significance and reference value can be more effectively given. The verification analysis of the embodiments proves that the method can significantly reduce the demand for data volume in actual application and make decisions quickly based on limited data.

[0108] The embodiments described above are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for determining the minimum sample size for aviation equipment quality characteristic evaluation, characterized in that: It includes: S1: Conduct normality test on sample size data of aviation equipment quality characteristic assessment and determine the minimum sample size; Obtain sample data X for aviation equipment quality characteristics assessment i , …, x n ), conduct normality test and determine the minimum sample size n for aviation equipment quality characteristic evaluation s for: Among them, n s Minimum sample size for the evaluation of quality characteristics of aviation equipment; Z a / 2 is the critical value of the standard normal distribution corresponding to the confidence level α; s is the standard deviation of the sample size data X; E is the set error range; α is the set confidence level; S2: skewness test of sample size data for aviation equipment quality characteristics assessment; The skewness is used to evaluate the symmetry of the distribution of sample data for the evaluation of aviation equipment quality characteristics and to determine whether the sample data is skewed. The sample data skewness determination parameter S is: Among them, S is the sample data skewness determination parameter; x i is the sample data value after the i-th sorting; is the sample size data mean, n is the total amount of sample data; i is the sample data number; S3: Correct the minimum sample size n of the aviation equipment quality characteristic evaluation in step S1 according to the sample data skewness determination parameter S in step S2 s ; Increasing the sample size is used to improve the applicability of the central limit theorem. The sample size expression after skewness correction is: Among them, n s ￠ is the minimum sample size for the revised aviation equipment quality characteristics assessment; S4: Construct the principle of the effectiveness of the central limit theorem under small skewness to determine the minimum sample size n for the quality characteristics evaluation of aviation equipment s ￠; The quality characteristic data of aviation equipment is obtained, and the normal distribution is used for estimation and calculation according to the central limit theorem; based on the principle of the effectiveness of the central limit theorem under small skewness, the minimum sample size for the evaluation of the quality characteristics of aviation equipment is constructed to determine the sample size: Among them, E is the expected distribution state of aviation equipment quality characteristic data; X is the sample size data of aviation equipment quality characteristic evaluation; μ is the sample mean of aviation equipment quality characteristic data; s0 is the set sample data skewness; P(α) is the expected value of the pass rate under the confidence level α; P0 is the pass rate under the confidence level α; N0 is the set sample data size requirement.

2. The method for determining the minimum sample size for aviation equipment quality characteristic evaluation according to claim 1 is characterized in that: The normality test in step S1 is to ensure that the sample data used for the quality characteristics assessment of aviation equipment meets statistical rationality. The statistical index W of the test sample data set is: Among them, W is the statistical indicator of the test sample size data set; a i is the i-th sample size data parameter; x i is the i-th sample data value after sorting; is the mean of the sample data; n is the total amount of sample data.

3. The method for determining the minimum sample size for aviation equipment quality characteristic evaluation according to claim 1, characterized in that: The value of the sample data skewness judgment parameter S in step S2 can be used to judge the distribution of the sample data for aviation equipment quality characteristics evaluation, specifically: when S=0, the sample data for aviation equipment quality characteristics evaluation is symmetrically distributed; S≠0, the sample data for aviation equipment quality characteristics evaluation is skewedly distributed.

4. A sample size determination system for aviation equipment quality characteristic evaluation used in the minimum sample size determination method for aviation equipment quality characteristic evaluation according to any one of claims 1 to 3, characterized in that: It includes: a distribution state applicable sample size simulation analysis determination module, an applicable sample size module for aviation equipment quality characteristic evaluation, and a recommended sample size module for aviation equipment quality characteristic evaluation; The distribution state applicable sample size simulation analysis module generates a standard comparison chart of the distribution state applicable sample size by simulating and calculating the minimum applicable sample size of data that obeys the set distribution and satisfies the central limit theorem under different skewnesses and obeys the normal distribution, obtains the universal sample size of data with different distributions and skewnesses, and uses the universal sample size as the minimum sample size; The applicable sample size module for aviation equipment quality characteristic evaluation can analyze the distribution state applicable sample size standard comparison chart generated by the distribution state applicable sample size simulation analysis module, and summarize the applicable sample size for aviation equipment quality characteristic evaluation in which the central limit theorem is effective according to the applicable sample size variation with skewness of the distribution simulation calculation results; The recommended sample size module for constructing the quality characteristic evaluation of aviation equipment is used to provide sample size recommendations for the quality characteristic evaluation of aviation equipment under the condition of small skewness data, and specifically includes: a data processing submodule, a sample size calculation submodule, a normality test submodule, a sample size recommendation submodule, a visualization submodule and a user interface submodule.

5. The sample size determination system for aviation equipment quality characteristic evaluation according to claim 4, characterized in that: The data processing submodule can perform data import, data preprocessing, skewness correction, and clean the original data, skewness correction and normality test.

6. The sample size determination system method for aviation equipment quality characteristic evaluation according to claim 4 is characterized by: The sample size calculation submodule can combine the skewness-corrected data, use the coefficient of variation and precision parameters, automatically calculate the recommended sample size, and output a calculation report.

7. The sample size determination system for aviation equipment quality characteristic evaluation according to claim 4, characterized in that: The normality test submodule provides a test function for the sample data of the quality characteristics of aviation equipment and automatically generates a test report.

8. The sample size determination system for aviation equipment quality characteristic evaluation according to claim 4, characterized in that: The sample size recommendation submodule dynamically adjusts the sample size recommendation value according to the accuracy requirements and data skewness set by the user.

9. The sample size determination system for aviation equipment quality characteristic evaluation according to claim 4, characterized in that: The visualization submodule can provide sample distribution diagrams, comparison diagrams before and after skewness correction, and normality test result diagrams to intuitively display data characteristics and sample size recommendation results.

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