Numerical control machine tool reliability modeling method and system considering fault trend

Abstract

The invention relates to a numerical control machine tool reliability modeling method and system considering a fault trend. The method comprises the following steps: checking the homogeneity of a numerical control machine tool based on the fault trend; constructing an AMSAA model of the multiple samples subjected to truncation at unequal time; evaluating the precision of the reliability model; aiming at the problem of insufficient reliability model precision of a multi-sample condition of a numerical control machine tool, a multi-sample AMSAA model modeling method of the numerical control machine tool considering a fault trend is provided, sample data classification is carried out through trend inspection and homotype inspection, and fault data of same-type machine tools are preprocessed by adopting a fault total time method; adopting a maximum likelihood method to estimate AMSAA model parameters of the same-type machine tool, and using Cramer-Von Mises to test the goodness of fit of the model; evaluating the precision of the reliability model by taking an average absolute percentage error (MAPE) of an instantaneous MTBF point estimation value and an MTBF observation value as an index; compared with a multi-sample AMSAA model established by a direct maximum likelihood method, the method is higher in prediction precision.

Description

A Reliability Modeling Method and System for CNC Machine Tools Considering Failure Trends Technical Field

[0001] This invention belongs to the field of CNC lathe reliability technology, and relates to a CNC machine tool reliability modeling method and system that considers failure trends. Specifically, it involves CNC machine tool homogeneity verification based on failure trends, construction of unequal timing truncated multi-sample AMSAA model, and accuracy evaluation of reliability model. Background Technology

[0002] Equipment failure is an unavoidable performance degradation phenomenon during the operation of CNC machine tools. Its occurrence and exacerbation not only directly lead to the deterioration of key performance indicators such as machine tool positioning accuracy and machining efficiency, but also constitute one of the core factors affecting machining stability and product qualification rate. In the CNC machine tool life cycle management system, building a reliability model and conducting quantitative assessments is a key technical path to ensure production continuity and machining quality.

[0003] By collecting failure data such as product failure time and truncation time, a reliability model can be constructed to describe the evolution of product failures, thereby obtaining the failure rate and mean time between failures (MTBF). Core reliability indicators such as [list of indicators] are used to quantitatively evaluate product reliability levels. However, CNC machine tools are complex repairable systems integrating mechanics, electronics, hydraulics, and optics. Under the influence of fault repair time, the fault interval often shows a trend of increasing or decreasing, resulting in fault data that is not necessarily independently and identically distributed. In this case, the data obtained based on traditional distribution models... The estimated values ​​will deviate significantly from the actual observed values, affecting the accuracy of reliability assessment. Therefore, constructing a reliability growth model for CNC machine tools and improving its prediction accuracy is an important problem that urgently needs to be solved in current research.

[0004] Based on this, a reliability modeling method and system for CNC machine tools that considers failure trends is proposed. The total failure time method is used to preprocess the failure data of the same type of CNC machine tools, and the maximum likelihood estimation method is combined to estimate the model parameters. An unequal time truncated multi-sample AMSAA model is constructed. Compared with the multi-sample AMSAA model constructed by the direct maximum likelihood estimation method, the proposed method can more accurately evaluate the reliability of CNC machine tools. Summary of the Invention

[0005] To address the issue of insufficient prediction accuracy in existing reliability models for CNC machine tools under multi-sample conditions, this invention classifies sample data through trend tests and similarity tests, preprocesses fault data of similar machine tools using the total failure time method, and estimates the AMSAA model parameters of similar machine tools using the maximum likelihood method, in order to achieve instantaneous... Point estimate and Mean absolute percentage error of observations ( To evaluate the accuracy of reliability models, a multi-sample AMSAA model considering failure trends was constructed and the accuracy of reliability models was predicted.

[0006] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution, which is described below with reference to Figure 1:

[0007] A reliability modeling method for CNC machine tools that considers failure trends includes the following steps:

[0008] Step 1: CNC machine tool conformity inspection based on failure trends

[0009] pass The test method performs trend tests on the fault data of each CNC machine tool sample to determine whether there is a monotonic trend; for samples with monotonic trends, a single-sample AMSAA model is established, and the goodness of fit of the model is tested by Cramér-Von Mises; the samples are classified according to the shape parameters of each sample AMSAA model into two categories: reliability increase and reliability decrease. Combining the modified Bartlett likelihood ratio statistic and the likelihood ratio statistic, the isomorphism test is performed on machine tools with the same monotonic trend.

[0010] Step 2: Construction of an Inequal Timing-Cut-Off Multi-Sample AMSAA Model

[0011] Based on the analysis in step one, the fault data of CNC machine tools are classified. The total fault time method is used to preprocess the unequal timing truncated data of the same type of machine tool. The maximum likelihood estimation method is used to estimate the parameters of the multi-sample AMSAA model. An unequal timing truncated multi-sample AMSAA model based on the same type of machine tool is constructed. The Cramér-Von Mises test is used to verify the goodness of fit of the model and the effectiveness of the constructed model.

[0012] Step 3: Reliability Model Accuracy Assessment

[0013] Calculate the instantaneous mean time between failures (MTBF) based on the model constructed in step two. Point estimates, in instantaneous Point estimate and Mean absolute percentage error of observations ( ) is used to evaluate the accuracy of the reliability model. The smaller the value, the higher the model accuracy.

[0014] The CNC machine tool conformity inspection based on failure trends mentioned in step one refers to:

[0015] First, adopt The test method involves performing trend tests on the fault data of each sample.

[0016] The trend test statistics are as follows:

[0017] (1)

[0018] In the formula, For trend test statistics, No. Taiwanese machine tool Time of the fault occurrence For the first The truncation time of the test machine tool. For the first The number of machine tool failures; , .

[0019] At the significance level Below, the critical value of the trend test statistic can be obtained. When the trend test statistic When the time is right, it indicates that the data has a monotonic trend; conversely, when the time is wrong, the fault process has no monotonic trend.

[0020] Secondly, a one-sample AMSAA model is established for samples exhibiting a monotonic trend, with the model scaling parameter... and shape parameters The maximum likelihood estimate is:

[0021] (2)

[0022] In the formula, No. Taiwanese machine tool Time of the fault occurrence For the first The truncation time of the test machine tool. For the first The number of machine tool failures.

[0023] The goodness-of-fit test of the one-sample AMSAA model was performed using the Cramér-Von Mises statistic. The goodness-of-fit test statistic is as follows:

[0024] (3)

[0025] In the formula, The parameters are for goodness-of-fit testing. , The number of product defects; ; Shape parameters Unbiased estimation, .

[0026] At the significance level Below, if the calculated value Not greater than the critical value This indicates that the product's reliability data conforms to the AMSAA model.

[0027] Secondly, based on Shape parameters of a single-sample AMSAA model for a desktop machine tool The samples were classified into two categories: reliability growth and reliability decline. For machine tools with the same monotonic trend, a similarity test was performed, which verified whether the shape parameters and scale parameters of the AMSAA model of each sample were equal. If they were equal, they could be considered as the same type of product.

[0028] The statistical hypothesis was tested using the modified Bartlett likelihood ratio statistic: ; Not all are equal.

[0029] The modified Bartlett likelihood ratio statistic is:

[0030] (4)

[0031] In the formula, The parameters are for goodness-of-fit testing. , , For the first The number of machine tool failures. Number of machine tools; and for and The maximum likelihood estimate can be obtained by iteratively calculating equation (5):

[0032] (5)

[0033] In the formula, For the first Taiwanese machine tool Time of the fault occurrence For the first The truncation time of the test machine tool. For the first The number of machine tool failures. , This refers to the number of machine tools.

[0034] when At the significance level Accept the hypothesis It can be considered Otherwise, refuse. And accept That is to say, it is believed Not all are equal;

[0035] exist Under the premise that the likelihood ratio statistic is used to test the statistical hypothesis: ; Not all are equal.

[0036] The likelihood ratio statistic is:

[0037] (6)

[0038] In the formula, and for and The unconstrained maximum likelihood estimate, , , , and for and The maximum likelihood estimate is obtained from equation (5).

[0039] when At the significance level accept It can be considered Otherwise, refuse. And accept That is to say, it is believed Not all are equal.

[0040] The construction of the unequal-timing truncated multi-sample AMSAA model mentioned in step two refers to:

[0041] First, the total time to failure method is used to preprocess the fault data of the same type of CNC machine tool.

[0042] Taking machine tools 1-3 in Figure 2 as an example, the total failure time for each fault point in the figure is as follows: , , The truncation time after processing using the total fault time method is: In the picture, The time when the malfunction of machine tool No. 1 occurred; and The times of failure for machine tool No. 2 are listed in order. , and These are the cutoff times for machine tools 1-3, respectively.

[0043] Secondly, based on the fault data processed by the total failure time method, a multi-sample AMSAA model is constructed using the maximum likelihood estimation method, with the model scaling parameters... and shape parameters The maximum likelihood estimate is:

[0044] (7)

[0045] In the formula, The total failure time after processing by the total failure time method This is the truncation time after processing with the total failure time method. This represents the total number of faults.

[0046] The Cramér-Von Mises statistic was used to test the goodness of fit of the multi-sample AMSAA model. The goodness of fit test statistic is as follows:

[0047] (8)

[0048] In the formula, To be Sort by size from smallest to largest. Shape parameters of the AMSAA model Conditional unbiased estimation, , The parameters are for goodness-of-fit testing. , For the first Number of product malfunctions.

[0049] At the significance level If The calculated value is less than or equal to critical value This indicates that the product's reliability data conforms to the AMSAA model, and the multi-sample AMSAA model can be used to statistically estimate the product's reliability parameters.

[0050] The reliability model accuracy assessment mentioned in step three refers to;

[0051] Instantaneous Mean Interval Time Estimates Based on the AMSAA Model The function expression:

[0052] (9)

[0053] Mean time between failures (MTBF) observations The following formula can be used for calculation:

[0054] (10)

[0055] In the formula, The number of CNC machine tools to be assessed; For the first Cut-off time for benchtop machine tool testing; For the first time during the assessment period The frequency of malfunctions occurring on the CNC lathe.

[0056] Mean absolute percentage error The calculation formula is:

[0057] (11)

[0058] In the formula, It refers to the number of observation points; For the results obtained based on the AMSAA model Estimated value; for Observed values.

[0059] The errors of the point estimates obtained from different methods are calculated according to formula (11). The smaller the value, the higher the corresponding point estimate. The better the model, the smaller the error.

[0060] A CNC machine tool reliability modeling system considering failure trends includes:

[0061] Module 1: CNC Machine Tool Similarity Inspection Module, used to perform similarity inspection on machine tools that have the same monotonicity trend;

[0062] Module 2: Unequal Timing Truncation Multi-Sample AMSAA Model Construction Module, used to construct an unequal timing truncated multi-sample AMSAA model based on the same type of machine tool, and to verify the effectiveness of the constructed model;

[0063] Module 3: Reliability Model Accuracy Evaluation Module, used to evaluate the accuracy of reliability models.

[0064] The CNC machine tool conformity inspection module described in Module 1 includes:

[0065] Each sample fault data trend test unit is used to employ... The test method is used to perform trend tests on the fault data of each sample;

[0066] The single-sample AMSAA model building unit is used to build a single-sample AMSAA model for samples with a monotonic trend, and uses the maximum likelihood estimation method to estimate the model scaling parameters. and shape parameters Estimates were made, and the Cramér-Von Mises statistic was used to test the goodness of fit of the single-sample AMSAA model;

[0067] The sameness test unit is used to verify whether the shape parameters and dimensional parameters of the AMSAA models of various machine tools with the same monotonic trend are equal. If they are equal, they are considered to be the same type of product.

[0068] The unequal timing truncated multi-sample AMSAA model construction module described in Module 2 includes:

[0069] The fault preprocessing unit is used to preprocess fault data of the same type of CNC machine tool using the total fault time method;

[0070] Maximum likelihood estimation unit, used for model scaling parameters and shape parameters Perform maximum likelihood estimation;

[0071] The goodness-of-fit test unit is used to test the goodness-of-fit of a multi-sample AMSAA model using the Cramér-Von Mises statistic.

[0072] The reliability model accuracy evaluation module described in Module 3 includes:

[0073] The mean time between failures (MTBF) calculation unit is used to estimate the instantaneous time of failure in a multi-sample AMSAA model. Point estimates and Observations;

[0074] The mean absolute percentage error calculation unit is used to calculate based on instantaneous... Point estimate and Mean absolute percentage error of observations .

[0075] Compared with the prior art, the beneficial effects of the present invention are:

[0076] In this invention, sample data are classified using trend tests and similarity tests. Based on this, the total failure time method is used for preprocessing of fault data for similar machine tools. The maximum likelihood method is used to estimate the parameters of the AMSAA model for similar machine tools. The Cramér-Von Mises test is used to assess the model fit, and instantaneous... Point estimate and Mean absolute percentage error of observations ( This method uses indicators to evaluate the accuracy of reliability models, effectively solving the problem of insufficient accuracy in CNC machine tool reliability models under multi-sample conditions. Compared with the multi-sample AMSAA model established by the direct maximum likelihood method, the model established by the proposed method has higher prediction accuracy. Attached Figure Description

[0077] The invention will now be further described with reference to the accompanying drawings:

[0078] Figure 1 is a flowchart of the CNC machine tool reliability modeling method considering failure trends according to the present invention.

[0079] Figure 2 is a schematic diagram of the total fault time calculation principle. Detailed Implementation

[0080] The present invention will now be described in detail with reference to the accompanying drawings:

[0081] Referring to Figure 1, the CNC machine tool reliability modeling method and system considering failure trends of the present invention includes the following steps: CNC machine tool homogeneity verification based on failure trends; construction of an unequal timing truncated multi-sample AMSAA model; and reliability model accuracy evaluation.

[0082] I. CNC Machine Tool Similarity Inspection Based on Failure Trends

[0083] pass The test method performs trend tests on the fault data of each CNC machine tool sample to determine whether there is a monotonic trend; for samples with monotonic trends, a single-sample AMSAA model is established, and the goodness of fit of the model is tested by Cramér-Von Mises; the samples are classified according to the shape parameters of each sample AMSAA model into two categories: reliability increase and reliability decrease. Combining the modified Bartlett likelihood ratio statistic and the likelihood ratio statistic, the isomorphism test is performed on machine tools with the same monotonic trend.

[0084] II. Construction of a Multi-Sample AMSAA Model with Inequal Timing and Truncation

[0085] Based on the analysis in step one, the fault data of CNC machine tools are classified. The total fault time method is used to preprocess the unequal timing truncated data of the same type of machine tool. The maximum likelihood estimation method is used to estimate the parameters of the multi-sample AMSAA model. An unequal timing truncated multi-sample AMSAA model based on the same type of machine tool is constructed. The Cramér-Von Mises test is used to verify the goodness of fit of the model and the effectiveness of the constructed model.

[0086] III. Reliability Model Accuracy Assessment

[0087] Calculate the instantaneous MTBF point estimate based on the model constructed in step two. Use the mean absolute percentage error (MAPE) between the instantaneous MTBF point estimate and the MTBF observation as an indicator to evaluate the reliability of the model accuracy. The smaller the MAPE value, the higher the model accuracy.

[0088] IV. Reliability Modeling System for CNC Machine Tools Considering Failure Trends

[0089] A reliability modeling system for CNC machine tools that considers failure trends is constructed. The system includes a CNC machine tool homogeneity verification module, which is used to perform homogeneity verification on machine tools with the same monotonic trend; an unequal timing truncated multi-sample AMSAA model construction module, which is used to construct an unequal timing truncated multi-sample AMSAA model based on the same type of machine tool and verify the effectiveness of the constructed model; and a reliability model accuracy evaluation module, which is used to evaluate the accuracy of the reliability model.

[0090] This invention provides a CNC machine tool reliability modeling system that considers failure trends, comprising:

[0091] The CNC machine tool conformity inspection module is used to perform conformity inspection on various machine tools that have the same monotonicity trend.

[0092] The CNC machine tool conformity inspection module includes:

[0093] Each sample fault data trend test unit is used to employ... The test method is used to perform trend tests on the fault data of each sample;

[0094] The single-sample AMSAA model building unit is used to build a single-sample AMSAA model for samples with a monotonic trend, and uses the maximum likelihood estimation method to estimate the model scaling parameters. and shape parameters Estimates were made, and the Cramér-Von Mises statistic was used to test the goodness of fit of the single-sample AMSAA model;

[0095] The sameness test unit is used to verify whether the shape parameters and dimensional parameters of the AMSAA models of various machine tools with the same monotonic trend are equal. If they are equal, they are considered to be the same type of product.

[0096] The module for constructing unequal-timing truncated multi-sample AMSAA models is used to construct unequal-timing truncated multi-sample AMSAA models based on the same type of machine tool and to verify the effectiveness of the constructed models.

[0097] The module for building a multi-sample AMSAA model with unequal timing truncation includes:

[0098] The fault preprocessing unit is used to preprocess fault data of the same type of CNC machine tool using the total fault time method;

[0099] Maximum likelihood estimation unit, used for model scaling parameters and shape parameters Perform maximum likelihood estimation;

[0100] The goodness-of-fit test unit is used to test the goodness-of-fit of a multi-sample AMSAA model using the Cramér-Von Mises statistic.

[0101] The reliability model accuracy evaluation module is used to evaluate the accuracy of the reliability model.

[0102] The reliability model accuracy assessment module includes:

[0103] The mean time between failures (MTBF) calculation unit is used to estimate the instantaneous time of failure in a multi-sample AMSAA model. Point estimates and Observations;

[0104] The mean absolute percentage error calculation unit is used to calculate based on instantaneous... Point estimate and Mean absolute percentage error of observations .

[0105] Example

[0106] A field tracking test was conducted on 6 machining centers, and the reliability assessment was performed using the statistical field failure data as an example. The failure data is shown in Table 1.

[0107] Table 1 Machining Center Fault Data

[0108] Machine Tool Number | First Fault Occurrence Time / h | Second Fault Occurrence Time / h | Third Fault Occurrence Time / h | Fourth Fault Occurrence Time / h | Truncation Time / h | 013019861367011080231137470903107268524048214535881390805285327520782.5 | 06611171242.5 surface

[0109] At the significance level Below, trend tests were performed on 1-6 machine tools using equation (1), and the results are shown in Table 2. Trend test statistics All are greater than the critical value This indicates that machine tools 1-6 are at a significance level. All of them show a monotonic trend.

[0110] Table 2. Trend Analysis of Fault Data for Machine Tools 1-6

[0111] Machine tool serial number trend test statistic: Trend test critical value 01 -0.77299 -2.77645 02 -0.14329 -4.30265 03 -1.03380 -4.30265 04 -0.44826 -2.77645 05 -0.13416 -3.18245 06 -154.082 -3.18245 surface

[0112] Substituting the fault data into equation (2), the estimated parameters of the AMSAA model for each machine tool are obtained, as shown in Table 3.

[0113] Table 3. Estimation of AMSAA Model Parameters for Machine Tools 1-6

[0114] Machine tool serial number, shape parameters, dimensional parameters: 01 0.6242 0.0503 021.3664 0.00025 03 0.8853 0.0078 04 0.7575 0.02297 051.3094 0.00049 06 0.2090 0.6766 surface

[0115] At the significance level Below, the goodness-of-fit test was performed on the six machine tools using equation (3), as shown in Table 4. Machine tools 1-5 passed the goodness-of-fit test, and their data conformed to the AMSAA model. The AMSAA model can be used to statistically estimate their reliability parameters; Machine tool 6: The test failed, and the AMSAA model cannot be used to estimate the parameters of machine tool No. 6.

[0116] Table 4. Goodness-of-fit test of AMSAA model for machine tools 1-6

[0117] Machine tool number, goodness-of-fit test statistic, goodness-of-fit test critical value: 0, 10.056, 108, 0.191, 02, 0.154, 560, 0.184, 03, 0.101, 736, 0.184, 04, 0.043, 644, 0.191, 05, 0.1078, 866, 0.184, 06, 0.2038, 67, 0.184 surface

[0118] Machine tools No. 1, 3, and 4 all have shape parameters less than 1, and their reliability shows a monotonically increasing trend. They are classified as similar products and designated as Model 1. Machine tools No. 2 and 5 all have shape parameters greater than 1, and their reliability shows a monotonically decreasing trend. They can be classified as another type of product and designated as Model 2. To verify the effectiveness of the proposed method, isomorphism tests were performed on both types of machine tools. Based on this, a multi-sample AMSAA model was established, and reliability assessment and model accuracy analysis were then completed.

[0119] (1) Construction of the AMSAA model for the first type of machine tool

[0120] For the first type of model, hypothesis testing: ; Not all are equal.

[0121] First, test the hypothesis: ; Not all are equal.

[0122] Due to the modified Bartlett likelihood ratio statistic Therefore, accept ,think .

[0123] Then, test the hypothesis: ; Not all equal

[0124] , The unconstrained maximum likelihood estimate is ;pass The calculation yielded: From equation (5), we can obtain and The maximum likelihood estimate is , .

[0125] Because of likelihood ratio statistic Therefore, accept ,think This means that the three machine tools are considered to be the same type of product.

[0126] The fault data of Model 1 were processed using the total failure time method, and the processed fault data is shown in Table 5.

[0127] Table 5 Fault Data of CNC Machine Tools

[0128] Model Number Fault Occurrence Time / h Truncation Time / h Model 1 90, 246, 321, 435, 594, 804, 1074, 1772, 1864, 2150 2540 surface

[0129] Substituting the fault data from Model 1 into Equation (7), we obtain the parameter estimates for the multi-sample AMSAA model: shape parameters. Scale parameters .

[0130] At the significance level The goodness-of-fit of the multi-sample AMSAA model is then tested using equation (8).

[0131] In the formula, , .

[0132] At the significance level Down, The calculated value is less than its critical value. The product reliability data in Model 1 conforms to the multi-sample AMSAA model.

[0133] (1) Construction of the AMSAA model for the second type of machine tool

[0134] For the second type of model, hypothesis testing: ; .

[0135] First, test the hypothesis: ; They are not equal.

[0136] Due to the modified Bartlett likelihood statistic Therefore, accept ,think .

[0137] Then, test the hypothesis: ; They are not equal.

[0138] , The unconstrained maximum likelihood estimate is: ;pass The calculation yielded: From equation (5), we can obtain and The maximum likelihood estimate is , .

[0139] Because of likelihood ratio statistic Therefore, accept ,think This means that the two machine tools are considered to be the same type of product.

[0140] The fault data of Model 2 were processed using the total failure time method, and the processed fault data is shown in Table 6.

[0141] Table 6 Fault Data of CNC Machine Tools

[0142] Model Number | Fault Occurrence Time / h | Truncation Time / h | Model Two | 570, 622, 654, 748, 1040 | 1491.5 surface

[0143] Substituting the fault data from Model 2 into Equation (7), we obtain the parameter estimates for the multi-sample AMSAA model: shape parameters. Scale parameters .

[0144] At the significance level The goodness-of-fit of the multi-sample AMSAA model is then tested using equation (8).

[0145] .in, , .

[0146] At the significance level Down, The calculated value is less than its critical value. The product reliability data in Model 2 conforms to the multi-sample AMSAA model.

[0147] (3) Reliability model evaluation

[0148] Taking machine tool No. 1 as an example, its failure time point and truncation time are listed, and the results based on the multi-sample AMSAA model are obtained. The point estimates and fault intensity estimates, as shown in Table 7, indicate that the AMSAA model... The point estimate is a dynamic value that increases as the fault intensity decreases, exhibiting a trend and predicting the average fault interval time at the next equipment operating time.

[0149] Table 7. Estimated MTBF values ​​for Machine Tool No. 1

[0150] Time point MTBF estimate / h Fault intensity estimate 30103.12540.009697198173.53860.005762624238.17030.004199670242.88860.0041171108+279.03570.003584 surface

[0151] The truncation time points of machine tools 1-5 are listed. The multi-sample AMSAA model constructed using the method presented in this paper and the multi-sample AMSAA model constructed directly using the maximum likelihood estimation method based on fault observations are calculated respectively. Point estimate, and The observed values ​​are compared, and then the mean absolute percentage error of the two methods is calculated. .in The observed values ​​are obtained by equation (10). The prediction accuracy analysis results of the multi-sample AMSAA model constructed by the method in this paper are shown in Table 8.

[0152] Table 8. Prediction accuracy analysis of the multi-sample AMSAA model based on the proposed method.

[0153] Machine Tool Number Truncation Time / h MTBF Observation Value / h MTBF Point Estimate / h MAPE 011108+277270.03190.73% 03524+262226.966313.37% 04908+227264.125216.35% 02709+354.5287.008619.04% 05782.5+260.67277.34856.40% surface

[0154] Mean absolute percentage error .

[0155] The maximum likelihood estimation method was used to directly estimate the AMSAA model parameters from the fault data observations, resulting in the following parameters for Model 1 and Model 2: ; Substituting the parameter estimation results and fault data into equation (9) yields... Point estimate, and The average absolute percentage error was calculated by comparing the observed values, and the model accuracy analysis results are shown in Table 9.

[0156] Table 9. Prediction accuracy analysis of the multi-sample AMSAA model based on the direct maximum likelihood method.

[0157] Machine Tool Number Truncation Time / h MTBF Observation Value / h MTBF Point Estimate / h MAPE 011108+277372.429334.45% 03524+262303.504015.84% 04908+227352.708555.38% 02709+354.5225.843036.29% 05782.5+260.67218.321316.25% surface

[0158] Mean absolute percentage error .

[0159] In traditional methods, multi-sample AMSAA models built directly using maximum likelihood estimation for fault data not processed by the total failure time method often suffer from limitations in the truncation time. The point estimates deviated significantly from the actual observations, with a mean absolute percentage error of 31.64%; while the multi-sample AMSAA model constructed after processing the fault data using the total fault time method showed a significant deviation in the truncation time. Point estimate and The observation bias is small, with an average absolute percentage error of 11.18%, indicating that the multi-sample AMSAA model constructed by the method in this paper has better predictive performance.

[0160] (4) This invention considers the shortcomings of existing reliability models in the case of multiple samples. Based on the failure trend of CNC machine tools, it proposes a reliability modeling method for the same type of CNC machine tools under multiple sample unequal timing truncated data, and uses instantaneous data as the basis. Point estimate and Mean absolute percentage error of observations ( The accuracy of the reliability model was evaluated using the index, and compared with the model established by directly using the maximum likelihood estimation method. The results showed that the accuracy of the proposed model was better. This method solves the problem of insufficient accuracy of CNC machine tool reliability models in the case of multiple samples, and provides certain guidance for similar studies.

[0161] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be included within the scope of protection of the present invention. Furthermore, all content not described in detail in this specification is prior art known to those skilled in the art.

Claims

1. A reliability modeling method for CNC machine tools that considers failure trends, comprising the following steps: Step 1: Passing the CNC machine tool conformity test based on failure trends The inspection method is used to perform trend inspection on the fault data of each CNC machine tool sample to determine whether there is a monotonic trend; For samples exhibiting a monotonic trend, a single-sample AMSAA model is established, and the Cramér-Von Mises test is used to verify the model's goodness of fit. Based on the shape parameters of each sample's AMSAA model, samples are classified into two categories: reliability growth and reliability decline. Using the modified Bartlett's likelihood ratio statistic and the likelihood ratio statistic, a homogeneity test is performed on machine tools with the same monotonic trend. Step Two: Construction of an unequal-time truncated multi-sample AMSAA model. Based on the classification of CNC machine tool fault data in Step One, the total failure time method is used to preprocess the unequal-time truncated data of the same type of machine tool. The maximum likelihood estimation method is used to estimate the parameters of the multi-sample AMSAA model, constructing an unequal-time truncated multi-sample AMSAA model based on the same type of machine tool. The Cramér-Von Mises test is used to verify the model's goodness of fit and validate its effectiveness. Step Three: Accuracy evaluation of the reliability model. The instantaneous mean time between failures (MTBF) is calculated based on the model constructed in Step Two. Point estimate, in instantaneous Point estimate and Mean absolute percentage error of observations To evaluate the accuracy of the reliability model for the indicators, The smaller the value, the higher the model accuracy.

2. The CNC machine tool reliability modeling method considering failure trends according to claim 1, characterized in that: The CNC machine tool conformity inspection based on failure trends described in Step 1 specifically includes the following steps: First, using... The trend test method is used to perform trend tests on the fault data of each sample. The trend test statistic is: (1) In the formula, This is a trend test statistic; For the first Taiwanese machine tool Time of occurrence of the fault For the first The truncation time of the test machine tool. For the first The number of machine tool failures; ， At the significance level Below, the critical value of the trend test statistic is obtained. When the statistic When the trend is constant, it indicates that the data has a monotonic trend; conversely, the fault process does not have a monotonic trend. Secondly, a single-sample AMSAA model is constructed. A single-sample AMSAA model is established for samples exhibiting a monotonic trend, with the model scale parameter... and shape parameters The maximum likelihood estimate is: (2) In the formula, The Taiwanese machine tool Time of occurrence of the fault For the first The truncation time of the test machine tool. For the first The number of machine tool failures; the goodness-of-fit test of the single-sample AMSAA model was performed using the Cramér-Von Mises statistic, and the goodness-of-fit test statistic is: (3) In the formula, The parameters are for goodness-of-fit testing. ， The number of product defects; ； Shape parameters Unbiased estimation, At the significance level Below, if the calculated value Not greater than the critical value This indicates that the product's reliability data conforms to the AMSAA model; finally, machine tool conformity testing is performed, and after a single-sample AMSAA model goodness-of-fit test is conducted on the product failure data, based on... Shape parameters of a single-sample AMSAA model for a desktop machine tool The samples are classified into two categories: reliability growth and reliability decline. At this point, it is necessary to verify the strength function of each machine tool with the same monotonic trend. The equality check verifies whether the shape and scale parameters of the AMSAA models of each sample are equal. If they are equal, they are considered to be the same type of product; regardless of... To determine if they are equal, first use the modified Bartlett likelihood ratio statistic to test the statistical hypothesis: ； Not all are equal; the corrected Bartlett likelihood ratio statistic is: (4) In the formula, The parameters are for goodness-of-fit testing. ， ， For the first The number of machine tool failures. Number of machine tools; and for and The maximum likelihood estimate is obtained through iterative calculation using equation (5): In formula (5), For the first Taiwanese machine tool Time of occurrence of the fault For the first The truncation time of the test machine tool. For the first The number of machine tool failures. ， For the number of machine tools; when At the significance level Accept the hypothesis It can be considered Otherwise, refuse. And accept That is to say, it is believed Not all are equal; Under the premise that the likelihood ratio statistic is used to test the statistical hypothesis: ； Not all are equal; the likelihood ratio statistic is: In formula (6), and for and The unconstrained maximum likelihood estimate, ， ， ， and for and Maximum likelihood estimation; when At the significance level accept ,think Otherwise, refuse. And accept That is to say, it is believed Not all are equal.

3. The CNC machine tool reliability modeling method considering failure trends according to claim 1, characterized in that: The construction of the unequal-time truncated multi-sample AMSAA model in step two includes the following steps: First, preprocessing the fault data of the same type of CNC machine tool using the total failure time method; second, constructing a multi-sample AMSAA model based on the fault data processed by the total failure time method, using the maximum likelihood estimation method to construct the multi-sample AMSAA model, with the model scaling parameters... and shape parameters The maximum likelihood estimate is: In equation (7), The total failure time after processing by the total failure time method This is the truncation time after processing with the total failure time method. The total number of faults is given. Finally, the Cramér-Von Mises statistic is used to test the goodness of fit of the multi-sample AMSAA model. The goodness of fit test statistic is: In formula (8), To be Sort by size from smallest to largest. Shape parameters of the AMSAA model Conditional unbiased estimation, ， The parameters are for goodness-of-fit testing. ， For the first The number of product failures at the significance level; If The calculated value is less than or equal to critical value This indicates that the product's reliability data conforms to the AMSAA model, and the product reliability parameters are statistically estimated using a multi-sample AMSAA model.

4. The CNC machine tool reliability modeling method considering failure trends according to claim 1, characterized in that: Step three introduces instantaneous Point estimate and Mean absolute percentage error of observations To evaluate the accuracy of the reliability model, the evaluation process is as follows: Estimated instantaneous mean fault interval time points based on the multi-sample AMSAA model. The function expression: (9) Observed values ​​of mean time between failures The following formula can be used for calculation: In equation (10), The number of CNC machine tools to be assessed; For the first The truncation time for the test on the machine tool; For the first time during the assessment period Frequency of malfunctions on CNC lathes; average Absolute percentage error The calculation formula is: In formula (11), It refers to the number of observation points; For the results obtained based on the AMSAA model Estimated value; for Observed values; calculate the error of the point estimates obtained from different methods according to formula (11), The smaller the value, the higher the corresponding point estimate. The better the model, the smaller the error.

5. A CNC machine tool reliability modeling system considering failure trends, comprising: The CNC machine tool conformity inspection module is used to perform conformity inspection on various machine tools that have the same monotonicity trend. The module for constructing unequal-timing truncated multi-sample AMSAA models is used to construct unequal-timing truncated multi-sample AMSAA models based on the same type of machine tool and to verify the effectiveness of the constructed models; the module for evaluating the accuracy of reliability models is used to evaluate the accuracy of reliability models.

6. A CNC machine tool reliability modeling system considering failure trends according to claim 5, characterized in that, The CNC machine tool conformity inspection module includes: a fault data trend inspection unit for each sample, used to employ... The test method performs trend tests on the fault data of each sample; the single-sample AMSAA model building unit is used to build a single-sample AMSAA model for samples with monotonic trends, and the model scaling parameters are estimated using the maximum likelihood method. and shape parameters Estimates were made, and the Cramér-Von Mises statistic was used to test the goodness of fit of the single-sample AMSAA model. The isomorphism test unit was used to verify whether the shape parameters and scale parameters of the AMSAA models of machine tools with the same monotonic trend were equal. If they were equal, they were considered to be the same type of product.

7. A CNC machine tool reliability modeling system considering failure trends according to claim 5, characterized in that, The unequal-time truncated multi-sample AMSAA model construction module includes: a fault preprocessing unit, used to preprocess fault data of the same type of CNC machine tool using the total fault time method; and a maximum likelihood estimation unit, used to estimate the model scaling parameters. and shape parameters Perform maximum likelihood estimation; goodness-of-fit test unit, used to test the goodness-of-fit of multi-sample AMSAA models using the Cramér-Von Mises statistic.

8. A CNC machine tool reliability modeling system considering failure trends according to claim 5, characterized in that, The reliability model accuracy evaluation module includes: a mean time between failures (MTBF) calculation unit, used to estimate the instantaneous time of failure (AMSAA) of the multi-sample AMSAA model. Point estimates and Observations; Mean Absolute Percentage Error (MAPE) calculation unit, used to calculate based on instantaneous... Point estimate and Mean absolute percentage error of observations 。

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