A method for evaluating the performance stability of small-batch civil aircraft materials

Abstract

The present invention discloses a method for evaluating and analyzing the stability of small-batch civil aircraft material performance. The method comprises the following steps: S1, collecting sample data of small-batch civil aircraft material performance, a total of m batches, and recording n material performance data points in each batch; S2, performing a normality test on the sample data; S3, calculating a variable control line according to the change in the data volume; S4, calculating a material performance baseline based on statistics, and forming a dual criterion with the variable control line. The present invention can reduce the probability of misreporting and omission, and the stability evaluation of material performance data is highly accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of civil aircraft airworthiness, and in particular relates to a method for evaluating and analyzing the performance stability of materials for small batches of civil aircraft. Background Art

[0002] At present, the performance stability analysis of civil aircraft materials is mainly evaluated by statistical process control methods. "Statistical process control" is one of the most popular and effective quality improvement methods today. It mainly refers to the use of Shewhart's process control theory, namely control charts, to monitor the various stages of the product production process. According to the distribution of points on the control chart, the trend of quality characteristics is analyzed, and preventive measures are taken to ensure that the production process is in a state of statistical control, so as to achieve the purpose of improvement and quality assurance. However, the traditional Shewhart control chart requires at least 25 batches of data, and at least 5 data per batch to meet the calculation accuracy requirements. Directly using statistical process control methods to evaluate the batch stability of small batches of civil aircraft materials is prone to misreporting and omissions, which not only increases the risk of product suspension inspection due to misreporting, but also poses a hidden danger to civil aircraft safety due to omissions. Summary of the invention

[0003] The present invention aims at solving the above problems and proposes a method for evaluating and analyzing the stability of material performance of small batch civil aircraft. The present invention can reduce the probability of misreporting and underreporting, and the stability evaluation of material performance data is highly accurate.

[0004] Technical solution: A method for evaluating and analyzing the performance stability of small-batch civil aircraft materials, comprising the following steps:

[0005] S1. Collect sample data of small batches of civil aircraft material properties, totaling m batches, and record n ​​material performance data points for each batch;

[0006] S2. Perform normality test on sample data;

[0007] S3, calculating a variable control line according to the change in data volume;

[0008] S4. Calculate the statistical material performance baseline and the variable control line to form a dual criterion.

[0009] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, in step S1, 3≤m<25, n≥5.

[0010] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, the step S2 is specifically as follows:

[0011] 2a) Calculate the Anderson-Darling normality test statistic AD:

[0012]

[0013] Where F0 is the cumulative distribution function of the standard normal distribution of the random variable Z, where x (i) is the i-th minimum sample observation value, is the sample mean, s is the sample standard deviation;

[0014] 2b) If AD>ADC=0.752 / (1+0.75 / N+0.75 / N 2 ), it can be inferred that the data sample does not conform to the normal distribution; otherwise, the assumption that the data sample conforms to the normal distribution holds.

[0015] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, in step S3, before the variable control line is calculated, the sample data that conforms to the normal distribution is processed as follows:

[0016] If the sample is normally distributed, calculate unbiased estimates of the sample mean and standard deviation and

[0017]

[0018]

[0019]

[0020] Among them, F is the unbiased estimate adjustment factor of the standard deviation, and its calculation formula is:

[0021]

[0022] It is the gamma function of the batch size m and the data size n in each batch.

[0023] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, in step S3, the probability of ensuring that the data falls within the variable control line is 99.73%.

[0024] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, the specific process of step S3 is as follows:

[0025] Establish a variable control line, introduce an adjustment factor D that changes with the batch m and the amount of data per batch n, and calculate the upper and lower control line values ​​UCL x With LCL x :

[0026]

[0027]

[0028] in,

[0029] Where tα / 2[m(n-1)] is the upper α / 2 quantile with m(n-1) degrees of freedom.

[0030] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, step S4 is specifically as follows:

[0031] Calculate the upper and lower limits of material properties based on statistics to form the baseline UAL x With LAL x , UAL x With LAL x refers to the 95% upper or lower confidence limit, respectively, for the first percentile of the specified population of measurements, is the overall sample mean, and s is the overall sample standard deviation:

[0032]

[0033]

[0034] Among them, k 99 is the one-sided tolerance coefficient, which is calculated as follows, N is the total number of samples;

[0035]

[0036] in To obey the freedom The noncentrality parameter is The non-central t distribution of k can be calculated from this 99 ; One-sided tolerance parameter k 99 is the coefficient related to the total sample size N.

[0037] The aforementioned small batch civil aircraft material performance stability evaluation and analysis method also includes:

[0038] Step S5: Referring to the drawing method of the Shewhart control chart, the variable control line that changes with the sample quantity and the material performance allowable value baseline as well as the single point value and mean value of each batch of samples are drawn into the control chart;

[0039] Step S6: Determine whether the performance of civil aircraft materials is stable and whether it meets the airworthiness requirements of civil aircraft materials based on the control chart obtained in step S5: If the single point value and the mean are both within the control line and the baseline, the material production process and performance are stable and can meet the requirements for civil aircraft use; If the single point value and the mean are between the control line and the baseline, check whether the material production process is abnormal. If there is no obvious abnormality, continue production and conduct analysis as production continues; If the single point value and the mean are outside the control line and the baseline, production should be stopped for inspection, and the reasons should be analyzed through experiments. In addition, the application of this batch of materials in civil aircraft poses a safety risk and the materials should be rejected.

[0040] In the aforementioned small batch civil aircraft material performance stability evaluation and analysis method, step S5 is specifically as follows:

[0041] 6a) Create a new plane rectangular coordinate system XY, and draw the control line value UCL obtained in step (4) and step (5) in XY x With LCL x Material performance baseline UAL x With LAL x ;

[0042] 6b) The single point value x of each batch of sample data obtained in step 1 ij With the mean Mark them on the XY coordinate system in batch order, and then connect the means in order with a broken line.

[0043] Beneficial effects: In order to reduce the probability of misreporting and omission, a highly accurate material performance data stability evaluation method is obtained. Starting from the principle of statistical process control (SPC) method, the present invention obtains variable control lines of different data amounts and data characteristics by calculation, establishes a batch stability evaluation method based on different data characteristics, and combines the actual design requirements of the material to establish a reference value control line that meets the 99% probability requirement and has a confidence level of 95%, that is, a baseline. Finally, by adopting the dual control line method of variable control line and baseline, the high reliability of the control chart is guaranteed, the production cost of frequent inspections of the production line due to misreporting is reduced, the use safety risk caused by omissions is reduced, and a reference basis for the acceptance of civil aircraft materials is provided. This method can meet the stability evaluation requirements of small batch material performance, significantly shorten the development cycle, reduce development risks, and reduce development costs.

[0044] The method for evaluating the stability of performance data of civil aircraft materials of the present invention can accurately evaluate the material performance during the development of civil aircraft materials, improve the performance quality of civil aircraft materials, and ensure the safety of use of civil aircraft materials.

[0045] The present invention is suitable for small batch (3-24 batches) data stability analysis, has a wider scope of application, and can be used to identify batch production anomalies and improve processes in the early stages of batch development of civil aircraft materials, helping to accelerate the formation of mature material products.

[0046] Compared with the traditional Shewhart control chart analysis of small batch data, which generates a large number of false alarms, the method of the present invention can more accurately analyze the stability of small batch civil aircraft material performance data.

[0047] The reference of the material performance baseline calculation method of the present invention can effectively identify the use risks of civil aircraft materials and ensure the safety of civil aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1It is a flow chart of the implementation of the present invention;

[0049] Figure 2 It is a control chart with double control lines drawn according to the collected samples in the present invention. DETAILED DESCRIPTION

[0050] In order to make the implementation process of the present invention clearer, the technical scheme in the embodiment of the present invention will be described in more detail below in conjunction with the drawings in the embodiment of the present invention. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of the present invention, not all of them, and the undetailed parts are all conventional technologies. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limitations on the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0051] Embodiment 1. A method for evaluating the performance stability of small batch civil aircraft materials, characterized by comprising the following steps:

[0052] (1) Sample collection:

[0053] Collect civil aircraft material performance data, a total of m batches, and record n ​​material performance data points in each batch;

[0054] Let the jth data of the i-th batch be x ij , where i = 1, 2, ..., m, j = 1, 2, ..., n, 3 ≤ m < 25, n ≥ 5;

[0055] (2) Obtain a data sample according to step (1), perform an Anderson-Darling normality test on the sample, and determine whether the sample obeys a normal distribution;

[0056] (3) If the sample follows a normal distribution, calculate the unbiased estimate of the sample mean and standard deviation and

[0057] Where F is the unbiased estimate adjustment factor of the standard deviation, and its calculation formula is:

[0058]

[0059] It is the gamma function of the batch size m and the data size n in each batch;

[0060] (4) Establish a variable control line, introduce an adjustment factor D that changes with batch m and the amount of data per batch n, and calculate the upper and lower control line values ​​UCLx With LCL x :

[0061] in

[0062] Where tα / 2[m(n-1)] is the upper α / 2 quantile with m(n-1) degrees of freedom;

[0063] (5) Calculate the upper and lower limits of material performance based on statistics to form the baseline UAL x With LAL x , refers to the 95% upper or lower confidence limit for the first percentile of the specified population of measurements, is the overall sample mean, and s is the overall sample standard deviation:

[0064]

[0065] where k 99 is the one-sided tolerance coefficient, which is calculated as follows, N is the total number of samples;

[0066]

[0067] in To obey the freedom The noncentrality parameter is The non-central t distribution of k can be calculated from this 99 . One-sided tolerance parameter k 99 is the coefficient related to the total sample size N;

[0068] (6) Referring to the drawing method of the Shewhart control chart, the variable control line that changes with the sample quantity calculated in step (4), the material performance allowable value baseline obtained in step (5), and the single point value and mean value of each batch of samples are drawn on the control chart;

[0069] (7) Based on the control chart obtained in step (6), determine whether the performance of civil aircraft materials is stable and whether it meets the airworthiness requirements of civil aircraft materials: if the single point value and the mean are both within the control line and the baseline, the material production process and performance are stable and can meet the requirements for civil aircraft use; if the single point value and the mean are between the control line and the baseline, check whether the material production process is abnormal. If there is no obvious abnormality, continue production and conduct analysis as production continues; if the single point value and the mean are outside the control line and the baseline, stop production for inspection, analyze the reasons through experiments, and the use of this batch of materials in civil aircraft poses a safety risk, so the materials should be rejected.

[0070] The step (2) is carried out according to the following steps:

[0071] 2a) Calculate the Anderson-Darling normality test statistic AD.

[0072]

[0073] Where F0 is the cumulative distribution function of the standard normal distribution of the random variable Z. (i) is the i-th minimum sample observation value, is the sample mean, and s is the sample standard deviation.

[0074] 2b) If AD>ADC=0.752 / (1+0.75 / N+0.75 / N 2 ), we can infer (with a 5% risk of misjudgment) that the data sample does not conform to the normal distribution. Otherwise, the assumption that the data sample conforms to the normal distribution holds.

[0075] The step (6) is carried out according to the following steps:

[0076] 6a) Create a new plane rectangular coordinate system XY, and draw the control line value UCL obtained in step (4) and step (5) in XY x With LCL x Material performance baseline UAL x With LAL x ;

[0077] 6b) The single point value x of each batch of sample data obtained in step 1 ij With the mean Mark them on the XY coordinate system in batch order, and then connect the means in order with a broken line.

[0078] Example 2. Reference Figure 1 , the implementation steps of this example are as follows:

[0079] Step 1: Collect samples.

[0080] According to the material tensile performance testing standard, 15 batches of material tensile performance tests were carried out on a certain civil aircraft aluminum alloy material. Five tensile strength performance data were recorded for each batch, and a total of 75 data points were obtained. The sample data are shown in Table 1. The data of the jth data of the i-th batch is x. ij , where i=1,2,…15,j=1,2,…5,m=15,n=5.

[0081] Table 1 Tensile strength data of aluminum alloy materials

[0082]

[0083]

[0084] Step 2: According to the data in Table 1, perform the Anderson-Darling normality test on the sample to determine whether the sample obeys the normal distribution; the Anderson-Darling normality test statistic AD is calculated to be 0.6674, and

[0085] ADC=0.752 / (1+0.75 / 75+0.75 / 75 2 )=0.7443;

[0086] The AD value is smaller than the ADC value, so it can be inferred that the assumption that the data sample conforms to the normal distribution holds true.

[0087] Step 3: Based on the data in Table 1, calculate the unbiased estimates of the sample mean and standard deviation and

[0088]

[0089] In order to show the dynamic change trend of the control line and the baseline with batch m, the control line and the baseline of batches 3-15 are calculated in the order of production time. Table 2 shows the changes of sample mean and standard deviation as the batches increase:

[0090] Table 2 Unbiased estimates of sample mean and standard deviation and

[0091]

[0092] Step 4: Based on the data in Table 1, calculate the adjustment factor D that varies with batch m.

[0093] Combined with the unbiased estimate in Table 2 and As a result, calculate the upper and lower control line values ​​LCL x With LCL x :

[0094]

[0095] The data results are shown in Table 3:

[0096] Table 3 Adjustment factors and upper and lower control lines

[0097] m 3 4 5 6 7 8 9 10 11 12 13 14 15 D 1.45 1.32 1.25 1.20 1.17 1.15 1.13 1.12 1.11 1.10 1.09 1.08 1.08 UCLx 211.29 209.53 208.28 207.40 206.70 206.18 205.75 205.59 205.85 206.41 206.37 206.31 206.15 LCLx 192.37 193.28 193.61 193.04 193.38 193.59 193.68 193.46 193.63 191.04 191.34 191.53 191.78

[0098] Step 5: First calculate the single-sided tolerance factor k 99 , and then calculate the upper and lower limits of material performance according to the following formula

[0099] UAL x With LAL x, is the overall sample mean, and S is the overall sample standard deviation:

[0100]

[0101] The calculation results are shown in Table 4:

[0102] Table 4 One-side tolerance factor and baseline

[0103] m 3 4 5 6 7 8 9 10 11 12 13 14 15 k99 3.52 3.30 3.16 3.06 3.00 2.94 2.90 2.86 2.83 2.81 2.79 2.77 2.75 UAL 218.96 216.51 214.76 213.83 212.72 211.88 211.22 211.09 211.40 213.37 213.17 212.98 212.62 Lx 184.70 186.30 187.13 186.61 187.36 187.88 188.21 187.96 188.08 184.07 184.54 184.86 185.31

[0104] Step 6: Referring to the drawing method of the Shewhart control chart, draw the variable control line calculated in step 4 that changes with the sample quantity, the material performance allowable value baseline obtained in step 5, and the mean of each batch of samples into the control chart; proceed as follows:

[0105] 6a) Create a new plane rectangular coordinate system XY, and draw the control line value UCL obtained in steps 4 and 5 in XY. x With LCL x Material performance baseline UAL x With LAL x ;

[0106] 6b) The single point value x of each batch of sample data obtained in step 1 ij With the mean Mark them on the XY coordinate system in batch order, and then connect the means in order with a broken line.

[0107] See attached for the results Figure 2 .

[0108] Step 7: Based on the control chart obtained in step 6, determine whether the performance of civil aircraft materials meets the airworthiness requirements of civil aircraft materials:

[0109] If both the single-point value and the mean are within the control line and the baseline, the material production process and performance are stable and can meet the requirements for civil aircraft use; if the single-point value and the mean are between the control line and the baseline, check whether the material production process is abnormal. If there is no obvious abnormality, continue production and conduct analysis as production continues; if the single-point value and the mean are outside the control line and the baseline, production should be stopped for inspection, and the reasons should be analyzed through experiments. In addition, the use of this batch of materials in civil aircraft poses a safety risk and the materials should be rejected.

[0110] From the attached Figure 2 It can be seen that the single point value and the mean of the 12th batch exceeded the control line and the baseline, so the control chart is abnormal, indicating that the production process of the 12th batch of materials is out of control, the materials do not meet the requirements for civil aircraft use, and production needs to be stopped. The reasons are analyzed through experiments, and the application of the 12th batch of materials in civil aircraft has safety risks, so this batch of materials should be rejected.

[0111] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for evaluating the performance stability of small batch civil aircraft materials. It is characterized in that The steps include: S1. Collect sample data of small batches of civil aircraft material properties, a total of m batches, and record n ​​material performance data points for each batch; the jth data of the i-th batch is x ij , where i = 1, 2, ..., m, j = 1, 2, ..., n, S2. Perform normality test on sample data; S3. Calculate the variable control line according to the change of data volume. Before calculating the variable control line, perform the following processing on the sample data that conforms to the normal distribution: If the sample is normally distributed, calculate unbiased estimates of the sample mean and standard deviation and Among them, F is the unbiased estimate adjustment factor of the standard deviation, and its calculation formula is: It is the gamma function of the batch size m and the data size n in each batch; The specific process of step S3 is as follows: Establish a variable control line, introduce an adjustment factor D that changes with the batch m and the amount of data per batch n, and calculate the upper and lower control line values ​​UCL x With LCL x : in, Where, t α / 2 [m(n-1)] is the upper α / 2 quantile with m(n-1) degrees of freedom; S4, calculating the material performance baseline based on statistics, and forming a dual criterion with the variable control line; Step S4 is as follows: Calculate the upper and lower limits of material properties based on statistics to form the baseline UAL x With LAL x , UAL x With LAL x refers to the 95% upper or lower confidence limit, respectively, for the first percentile of the specified population of measurements, is the overall sample mean, and s is the overall sample standard deviation: Among them, k 99 is the one-sided tolerance coefficient, which is calculated as follows, N is the total number of samples; in To obey the freedom The noncentrality parameter is The non-central t distribution of k is calculated from this 99 ; One-sided tolerance parameter k 99 is the coefficient related to the total sample size N.

2. The method for evaluating and analyzing the performance stability of small batch civil aircraft materials according to claim 1, It is characterized in that In step S1, 3≤m<25, n≥5.

3. The method for evaluating and analyzing the performance stability of small batch civil aircraft materials according to claim 2, It is characterized in that The step S2 is specifically as follows: 2a) Calculate the Anderson-Darling normality test statistic AD: In the formula, F 0 is the cumulative distribution function of the standard normal distribution of the random variable Z, where x (i) is the i-th minimum sample observation value, is the sample mean, s is the sample standard deviation; 2b) If AD>ADC=0.752 / (1+0.75 / N+0.75 / N 2 ), then it is inferred that the sample data does not conform to the normal distribution; otherwise, the assumption that the data sample conforms to the normal distribution holds.

4. The method for evaluating and analyzing the performance stability of small batch civil aircraft materials according to claim 1, It is characterized in that In step S3, the probability of ensuring that the data falls within the variable control line is 99.73%.

5. The method for evaluating and analyzing the performance stability of small batch civil aircraft materials according to claim 1, It is characterized in that Also includes: Step S5: Referring to the drawing method of the Shewhart control chart, the variable control line that changes with the sample quantity and the material performance allowable value baseline as well as the single point value and mean value of each batch of samples are drawn into the control chart; Step S6: Determine whether the performance of civil aircraft materials is stable and whether it meets the airworthiness requirements of civil aircraft materials based on the control chart obtained in step S5: If the single point value and the mean are both within the control line and the baseline, the material production process and performance are stable and meet the requirements for civil aircraft use; If the single point value and the mean are between the control line and the baseline, check whether the material production process is abnormal. If there is no obvious abnormality, continue production and conduct analysis as production continues; If the single point value and the mean are outside the control line and the baseline, production should be stopped for inspection, and the reasons should be analyzed through experiments. In addition, the application of this batch of materials in civil aircraft poses a safety risk and the materials should be rejected.

6. The method for evaluating and analyzing the performance stability of small batch civil aircraft materials according to claim 5, It is characterized in that Step S5 is specifically as follows: 5a) Create a new plane rectangular coordinate system XY, and draw the control line value UCL obtained in step S3 and step S4 in XY x With LCL x Material Performance Baseline UAL x With LAL x ; 5b) The single point value x of each batch of sample data obtained in step S1 is ij With the mean Mark them on the XY coordinate system in batch order, and then connect the means in order with a broken line.

Images