Equipment testability test sampling and evaluation method based on three-dimensional fault data fusion

Abstract

This invention discloses a sampling and evaluation method for equipment testability testing based on three-dimensional fault data fusion, belonging to the technical field of equipment testability testing and evaluation. It includes: acquiring three-dimensional evaluation data for all fault modes of the equipment; normalizing the data to obtain a normalized three-dimensional feature vector for each fault mode; performing weighted fusion using weight coefficients to obtain initial fusion weights; revising the lower limit of the initial fusion weights to obtain final fusion weights; obtaining the three-dimensional fusion weighted sampling probability for each fault mode after normalization; calculating the total sample size of the test; performing PPS sampling allocation using forced sample position allocation and low-difference sequences respectively; conducting physical fault injection tests based on sample allocation; calculating the unbiased estimate of the fault detection rate and the one-sided confidence lower limit of the fault detection rate; and completing the equipment testability evaluation. This invention can improve the scientific rigor of equipment testability evaluation.

Description

Technical Field

[0001] This invention relates to the field of equipment testability testing and evaluation technology, specifically to a sampling and evaluation method for equipment testability testing based on three-dimensional fault data fusion. Background Technology

[0002] Equipment testability testing and evaluation is a core component in verifying equipment's fault detection and isolation capabilities, and a crucial basis for testability control throughout the equipment's lifecycle. In current engineering applications, the sampling method for fault modes based on the failure rate proportion, as outlined in GJB 8895-2017 "Equipment Testability Testing and Evaluation," often uses the predicted failure rate of the fault mode as the sole sampling criterion for PPS sampling. However, the PPS sampling method, which uses a single dimension of failure rate as input, suffers from three unavoidable core flaws: First, the data dimension is too narrow, and there is a significant discrepancy between theory and reality. The sampling is based solely on the theoretically predicted failure rate obtained from the GJB299C standard. This value is derived from a general failure rate database and stress model, which naturally deviates from the actual failure characteristics and mission risk characteristics of equipment in actual field use. This directly results in the sampling results failing to effectively cover the frequent failure modes in the field.

[0003] Second, high-risk failure modes are easily overlooked, posing fatal safety hazards. Although some failure modes are theoretically expected to have a low failure rate, their severity level is high. Once they occur, they will lead to catastrophic consequences such as equipment damage, mission failure, and personnel casualties. In traditional methods, the sampling probability of such failure modes is extremely low, making them very easy to be missed in the sampling and not included in the assessment. As a result, the evaluation results cannot reflect the true testability level of the equipment, laying fatal engineering safety hazards for the entire life cycle of the equipment.

[0004] Third, unequal probability sampling leads to estimation bias and invalidates the statistical premise. The fault detection rate estimation formula specified in the traditional national military standard is naturally unbiased only in the case of proportional PPS sampling where "the sampling probability is proportional to the inherent failure rate of the fault mode". If the sampling weight is adjusted to cover high-risk modes and unequal probability sampling is carried out, the conventional formula will produce systematic estimation bias, which will ultimately cause the statistical premise of the Clopper-Pearson method confidence lower limit calculation to fail, and the evaluation results will not be valid.

[0005] Existing research mainly focuses on optimizing sampling size and improving random sampling sequences, such as introducing low-discrepancy sequences like Halton and Sobol to improve sampling uniformity. However, none of these studies have broken through the limitations of a single failure rate dimension, nor have they established a fusion system for multi-dimensional engineering data. They cannot correct the deviation between theoretically predicted failure rates and actual operating conditions, nor can they fundamentally solve the problem of sampling omissions of high-risk failure modes. Furthermore, they have not solved the problem of unbiased estimation under unequal probability sampling, and thus cannot meet the engineering practice and risk management needs of equipment test field evaluation. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention aims to provide a sampling and evaluation method for equipment testability based on three-dimensional fault data fusion. This method is fully compatible with the core specifications of the GJB 8895-2017 National Military Standard. It scientifically constructs a three-dimensional fusion system of three core engineering data—failure rate, severity, and field failure frequency—using the Analytic Hierarchy Process (AHP) to correct the deviation between theoretical data and actual operating conditions. Through the design of weighted lower limits and forced sample positions, it achieves full coverage of sampling for high-risk failure modes. By using the Horvitz-Thompson unbiased estimator, it solves the estimation bias problem under weighted unequal probability sampling. Without significantly increasing the test sample size, it significantly improves the scientific rigor, compliance, and engineering safety of equipment testability field evaluation.

[0007] Specifically, the present invention provides a sampling and evaluation method for equipment testability tests based on three-dimensional fault data fusion, which includes the following steps: S1: Obtain the three-dimensional evaluation data of the i fault modes of the equipment to be tested and perform normalization processing to obtain the normalized three-dimensional feature vector of each fault mode. The three-dimensional assessment data includes the predicted failure rate. Severity level and field failure frequency level ; S2: Determine separately The weighting coefficient α The weighting coefficient β and The weighting coefficient γ, through the weighting coefficient to We perform weighted fusion to obtain the initial fusion weights for each failure mode. ; S3: Enables all fault modes For the final fusion weights, and among them The final fusion weights of failure modes that are greater than or equal to the calibrated risk level are lowered and revised to obtain the final fusion weights of all failure modes. S4: Normalize the final fusion weights of the i fault modes to obtain the three-dimensional fusion weighted sampling probability of each fault mode, thereby realizing the mapping of the three-dimensional fusion data to the one-dimensional sampling probability space. S5: Calculate the minimum sample size for the basic experiment. and The number of failure modes greater than or equal to the calibrated risk level The sum of these values ​​yields the total sample size; the total sample size is then divided into... Each forced sample bit is assigned one-to-one to each Failure modes greater than or equal to the calibrated risk level; remaining Each sample is allocated using a three-dimensional fusion weighted sampling probability and a Halton low-discrepancy sequence for PPS sampling. S6: Conduct physical fault injection tests based on the sample allocation results of S5, record the number of detection failures for each fault mode, calculate the unbiased estimate of the fault detection rate using the inverse probability weighting method, and calculate the one-sided confidence lower limit of the fault detection rate using the binomial distribution precise one-sided confidence limit method to complete the equipment testability evaluation.

[0008] Furthermore, S1 includes the following steps: S11. Obtain three-dimensional evaluation data for the i failure modes of the equipment to be tested. The three-dimensional evaluation data includes the expected failure rate. Severity level and field failure frequency level .

[0009] S12. Normalize the three-dimensional assessment data to obtain the normalized value of the three-dimensional assessment data for each fault mode. This is used to eliminate the dimensional differences between different feature data and provide a unified data scale basis for subsequent multi-source data fusion. S13. Based on the normalized values ​​of the three-dimensional evaluation data for each fault mode, construct a normalized three-dimensional feature vector corresponding to each fault mode. For the first Normalized predicted failure rates for each failure mode. For the first Normalized values ​​of severity level for each failure mode. For the first Normalized values ​​of field failure frequency levels for each failure mode.

[0010] Furthermore, in S12, the three-dimensional evaluation data are normalized, including: Normalized expected failure rate: ; in, For the first Normalized predicted failure rates for each failure mode. For the first The expected failure rate for each failure mode. The total number of failure modes to be tested for the equipment; Severity level normalization: ; in, For the first Normalized values ​​of severity level for each failure mode. For the first Severity levels for each failure mode; refer to the severity definitions of Class I, II, III, and IV in GJB / Z1391-2006. These correspond to the assigned weights of levels 4, 3, 2, and 1, respectively. Field failure frequency level normalization: ; in, For the first Normalized values ​​of field failure frequency levels for each failure mode. For the first Field failure frequency levels for each failure mode; According to the The actual frequency of each failure mode in the field is divided into levels 1 to 4.

[0011] Furthermore, the weighting coefficients α, β, and γ for the three types of data in S2—predicted failure rate, severity level, and field failure frequency level—can be selected based on the task scenario: Recommended values ​​for general scenarios: α=0.5, β=0.3, γ=0.2; Recommended values ​​for high-risk management priority scenarios: α=0.45, β=0.35, γ=0.2; Recommended values ​​for scenarios prioritizing adaptation to outdoor working conditions: α=0.45, β=0.25, γ=0.3; Furthermore, the formula for calculating the initial fusion weights in step S2 is as follows: , For the first Normalized predicted failure rates for each failure mode. For the first Normalized values ​​of severity level for each failure mode. For the first Normalized values ​​of field failure frequency levels for each failure mode.

[0012] Furthermore, S3 specifically refers to: Get all The initial fusion weight of the fault mode is greater than or equal to the risk level of the fault mode. If it is lower than the lower threshold, the lower threshold is determined as the final fusion weight of the fault mode; otherwise, the initial fusion weight of the fault mode is determined as the final fusion weight. The initial fusion weight of the remaining fault modes is determined as the final fusion weight of the fault mode.

[0013] Furthermore, the formula for adjusting the fusion weights in S3 for lower limit revision is as follows: ,in ≥0.05, These are the initial fusion weights.

[0014] Furthermore, the formula for calculating the 3D fusion weighted sampling probability in S4 is as follows: ; in, The final fusion weights for the failure modes. The total number of failure modes, and satisfying the normalization constraint. .

[0015] Furthermore, the specific steps of PPS sampling allocation based on Halton low-difference sequences in step S54 are as follows: S541: Generation length is One-dimensional Halton low-difference sequences , where sequence elements The basis of the sequence is selected from distinct prime numbers; S542: Calculate the cumulative probability interval for the 3D fusion weighted sampling probability: Set the initial cumulative probability. , No. The cumulative probability of each failure mode This forms a continuous probability interval. ; S543: For each Halton sequence element Determine the cumulative probability interval to which the sample belongs, and assign the sample to the corresponding fault mode within that interval. S544: For all high-risk failure modes, add one forced sample to the above sampling allocation results to obtain the final sample size allocation result. ,satisfy .

[0016] Furthermore, the formula for calculating the unbiased estimate of the fault detection rate in step S6 is as follows: ; in: For the first The sampling probability of each failure mode calculated based on the expected failure rate. For detectability indicator function, As an indicator variable for the sample, This represents the first-order sample probability. The weighted sampling probability for 3D fusion.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention employs a sampling method that differs from traditional methods that rely solely on the predicted failure rate. It constructs a three-dimensional failure mode data fusion system, selecting three types of failure information—the predicted failure rate of the failure mode, the severity level of the failure mode, and the frequency level of the failure in the field—and fusing them to generate sampling weights. This allows the sampling probability to simultaneously reflect the likelihood of failure occurrence, the risk level, and the actual field conditions. This improves the ability of the sampling results to represent real engineering risks and reduces the deviation caused by inconsistencies between theoretical data and actual usage.

[0018] 2. The present invention calculates the minimum sample size for the experimental basis. Count the number of high-risk failure modes Determine the total sample size of the experiment. This makes the sample size controllable and has strong engineering adaptability: the total sample size is only increased by the number of high-risk failure modes (usually accounting for <10%) on the basis of the national military standard, which significantly reduces the cost and workload of large-scale testing.

[0019] 3. This invention will include a portion of the total experimental sample size. One mandatory sample bit is assigned one-to-one to high-risk failure modes; the remaining... Each sample is allocated using a three-dimensional fusion-weighted sampling probability and Halton low-discrepancy sequences for PPS sampling. For high-risk failure modes, a weighted lower limit is set to increase their sampling probability, and a mandatory sample position is assigned to ensure they are included at least once. This approach avoids missing high-risk, low-probability failure modes from both probability correction and deterministic coverage perspectives, significantly enhancing the risk coverage capability of test trials.

[0020] 4. This invention, after employing fusion-weighted sampling, further introduces Horvitz-Thompson unbiased estimation and Clopper-Pearson one-sided confidence lower bound calculation, forming a complete closed loop for sampling scheme design, experimental data collection, and experimental result evaluation. This solves the problem of estimation bias easily generated by traditional statistical methods under unequal probability sampling, and improves the statistical validity of the evaluation results. Attached Figure Description

[0021] Figure 1 This is a flowchart of the equipment test sampling and evaluation method based on three-dimensional fault data fusion according to the present invention. Detailed Implementation

[0022] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0023] As attached Figure 1 As shown, this invention provides a sampling and evaluation method for equipment testability testing based on three-dimensional fault data fusion, comprising the following steps: S1: Obtain the three-dimensional evaluation data of the i fault modes of the equipment to be tested and perform normalization processing to obtain the normalized three-dimensional feature vector of each fault mode. The three-dimensional assessment data includes the predicted failure rate. Severity level and field failure frequency level .

[0024] S11. Obtain three-dimensional evaluation data for the i failure modes of the equipment to be tested. The three-dimensional evaluation data includes the expected failure rate. Severity level and field failure frequency level .

[0025] Acquire three-dimensional evaluation data for i failure modes of the equipment to be tested, namely, three types of core engineering data, and construct a three-dimensional fusion evaluation system for failure modes. The three-dimensional evaluation data includes: Expected failure rate : Based on compliance data, the expected failure mode failure rate in the GJB 299C standard.

[0026] GJB 299C is a Chinese national military standard, officially titled "Reliability Prediction Manual for Electronic Equipment". This standard allows users to find the predicted failure mode failure rates.

[0027] Severity level For risk management data, it is divided into categories I, II, III, and IV with reference to GJB / Z 1391-2006 and assigned weights of 4, 3, 2, and 1 respectively, as shown in Table 1, reflecting the engineering hazard level of the failure mode and highlighting the risk management orientation.

[0028] Currently, the widely adopted standard in China is mainly based on GJB / Z 1391-2006 "Guideline for Failure Mode, Effects and Hazard Analysis". Section 4.2.8 of this guideline provides a mature qualitative classification standard, dividing the severity into four categories corresponding to the weights of 1-4 in this invention: Category I: corresponding to weight 4, catastrophic severity, resulting in death or destruction of products (such as aircraft, tanks, missiles, and ships), and significant environmental damage. Category II: corresponding to weight 3, lethal severity, resulting in serious injury to personnel or significant economic loss or mission failure, serious product damage, and serious environmental damage. Category III: corresponding to weight 2, moderate severity, resulting in moderate injury to personnel or moderate economic loss or mission delay or downgrade, moderate product damage, and moderate environmental damage. Category IV: corresponding to weight 1, mild severity, resulting in consequences insufficient to cause injury to personnel or minor economic loss or minor product damage and environmental damage, but leading to unplanned maintenance or repair.

[0029] Field Failure Frequency Level The data is used to correct operating conditions. Based on historical field usage data of the equipment, it is divided into 1 to 4 levels as shown in Table 1 to correct the deviation between the theoretically predicted failure rate and the actual operating conditions. One method is to statistically analyze the percentage of a specific failure mode occurring within a certain period of time out of the total number of failures of the same product, and compare it with a standard threshold to determine the level, with levels 1 to 4: >20%, 10-20%, 1-10%, and 0.1-1%.

[0030] S12. Normalize the three-dimensional assessment data to obtain the normalized value of the three-dimensional assessment data for each fault mode. This is used to eliminate the dimensional differences between different feature data and provide a unified data scale basis for subsequent multi-source data fusion.

[0031] The three-dimensional assessment data were normalized, including: Normalized expected failure rate: ; in, For the first Normalized predicted failure rates for each failure mode. For the first The expected failure rate for each failure mode. This represents the total number of fault modes to be tested for the equipment.

[0032] Severity level normalization: ; in, For the first Normalized values ​​of severity level for each failure mode. For the first Severity levels for each failure mode; refer to the severity definitions of Class I, II, III, and IV in GJB / Z1391-2006. These correspond to the assigned weights of level 4, 3, 2, and 1, respectively.

[0033] Field failure frequency level normalization: ; in, For the first Normalized values ​​of field failure frequency levels for each failure mode. For the first Field failure frequency levels for each failure mode; According to the The actual frequency of each failure mode in the field is divided into levels 1 to 4.

[0034] S13. Based on the normalized values ​​of the three-dimensional evaluation data for each fault mode, construct a normalized three-dimensional feature vector corresponding to each fault mode. .

[0035] After normalization, the first The three-dimensional feature vectors of each fault mode are ,and That is, all eigenvalues ​​are mapped to the interval [0,1].

[0036] Advantages: Unlike traditional sampling methods that rely solely on predicted failure rates, this invention constructs a three-dimensional fusion assessment system for failure modes. It integrates failure information from three dimensions to generate sampling weights, allowing the sampling probability to simultaneously reflect the likelihood of failure, risk level, and actual field conditions. This improves the ability of sampling results to represent real engineering risks and reduces deviations caused by inconsistencies between theoretical data and actual usage.

[0037] S2: Determine separately The weighting coefficient α The weighting coefficient β and The weighting coefficient γ, through the weighting coefficient to We perform weighted fusion to obtain the initial fusion weights for each failure mode. .

[0038] S21: Determine the following using the Analytic Hierarchy Process (AHP): The weighting coefficient α The weighting coefficient β and The weighting coefficient γ.

[0039] Determining the expected failure rate using the Analytic Hierarchy Process (AHP) Severity level Field Failure Frequency Level The weighting coefficients α, β, and γ for the three types of data must satisfy the weight normalization constraint α + β + γ = 1, and the expected failure rate weight α must be the maximum value among the three weights. This method can transform qualitative engineering experience in equipment testability evaluation into quantitative weights, avoiding the arbitrariness of subjective assignment, ensuring the scientific nature and reproducibility of weight allocation, and meeting the rigorous requirements of military equipment evaluation.

[0040] Based on the engineering requirements of different equipment types and mission scenarios, three sets of recommended engineering weight values ​​are set: Recommended values ​​for general scenarios: α=0.5, β=0.3, γ=0.2; Applicable scope: routine test scenarios such as type approval and commissioning acceptance of land-based equipment, serving as a basic general solution.

[0041] Recommended values ​​for high-risk management priority scenarios: α=0.45, β=0.35, γ=0.2; Applicable scope: scenarios with extremely high requirements for fault risk management, such as aviation, ships, and aerospace. Appropriately increase the severity level weight to further strengthen the sampling coverage of high-hazard fault modes.

[0042] Recommended values ​​for field condition adaptation scenarios: α=0.45, β=0.25, γ=0.3; Applicable scenarios: field assessment of the entire life cycle of equipment after deployment, maintainability assessment of in-service equipment, etc., appropriately increase the weight of field failure frequency to maximize the correction of the deviation between theoretical predictions and actual field conditions.

[0043] S22: Based on the determined weight coefficients, the three-dimensional feature vectors are... Perform weighted fusion and calculate the initial fusion weights: ,in , , The first Normalized values ​​of three types of data for each fault mode.

[0044] The input for this step is [α,β,γ], representing the 3D fusion weights, [v i1 ,v i2 ,v i3 The three-dimensional feature vector representing the i-th fault mode is fused by weighting the scores of these three dimensions according to their respective weights through the dot product, resulting in a fused weight. .

[0045] S3: Enables all fault modes For the final fusion weights, and among them The final fusion weights of failure modes that are greater than or equal to the calibrated risk level are revised with a lower limit to obtain the final fusion weights of all failure modes.

[0046] Get all The initial fusion weight of the fault mode is greater than or equal to the risk level of the fault mode. If it is lower than the lower threshold, the lower threshold is determined as the final fusion weight of the fault mode; otherwise, the initial fusion weight of the fault mode is determined as the final fusion weight. The initial fusion weight of the remaining fault modes is determined as the final fusion weight of the fault mode.

[0047] The lower bound revision aims to fundamentally increase the sampling probability of high-risk failure modes by setting a weighted lower bound. For high-risk fault modes with a severity level of ≥0.05, the fusion weight is forced to be no less than the lower limit. The correction formula is as follows: The lower limit of 0.05 is a protection threshold set based on engineering risk management experience. It aims to prevent high-risk failure modes from being missed in the sampling due to their extremely low theoretical failure rate, ensuring sufficient statistical significance in the 3D fusion system to support the subsequent mandatory sampling mechanism. This value can be adaptively adjusted according to the characteristics of the assessment object; the value given here is a recommended value covering most cases.

[0048] A lower limit for the weights of high-risk fault modes with a severity level higher than Class II is set. After adjusting the initial fusion weights of high-risk fault modes by the lower limit, the final fusion weights of each fault mode are obtained.

[0049] S4: Normalize the final fusion weights of the i fault modes to obtain the three-dimensional fusion weighted sampling probability of each fault mode, thereby realizing the mapping of the three-dimensional fusion data to the one-dimensional sampling probability space.

[0050] The final fusion weights, after correcting for all fault modes, are normalized to obtain the 3D fusion weighted sampling probability for each fault mode. This achieves an accurate mapping of the 3D fusion data to a one-dimensional sampling probability space. The formula is as follows:

[0051] in, For the first The mapping value of the one-dimensional sampling probability space of each failure mode. For the first The fusion weights of each failure mode The sampling probability represents the total number of failure modes and satisfies the normalization constraint of the one-dimensional probability space. .

[0052] S5: Calculate the minimum sample size for the basic experiment. and The number of failure modes greater than or equal to the calibrated risk level The sum of these values ​​yields the total sample size; the total sample size is then divided into... Each forced sample bit is assigned one-to-one to each Failure modes greater than or equal to the calibrated risk level; remaining Each sample is allocated using a three-dimensional fusion weighted sampling probability and a Halton low-discrepancy sequence for PPS sampling.

[0053] This step uses the minimum acceptable sample size determination method, while setting a high-risk pattern to force sample positions, and combines Halton low-discrepancy sequences to achieve optimized sampling. Specifically: S51. Calculate the minimum sample size for the basic experiment. .

[0054] Basic minimum sample size The calculation formula is the official standard formula of GJB 8895-2017, which calculates the minimum sample size to meet the minimum acceptable value of fault detection rate and the orderer's risk requirements. : ; in, Summation symbol This represents the number of missed faults (d) ranging from 0 to the pass / fail count (A). c Accumulate and combine. The inequality ≤ represents the probability of "missed detection". This indicates that the cumulative probability does not exceed the orderer's risk. , This is the number of passes / failes. This represents the lowest acceptable failure detection rate.

[0055] calculate First, determine the number of qualified samples. (Maximum number of undetected faults allowed in the test), minimum acceptable fault detection rate (Minimum fault detection capability required by the system), Purchaser's risks (The maximum probability that a system that does not meet the actual detection rate standard is allowed to be mistakenly judged as qualified is usually taken as 0.2).

[0056] Then from smaller positive integers Begin (e.g.) ), increasing sequentially Then calculate the cumulative probability mentioned above, find the first smallest positive integer n that satisfies the inequality, and this value is the basic minimum sample size. S52. Statistics The number of failure modes greater than or equal to the calibrated risk level .

[0057] The number of high-risk failure modes with severity levels I and II in statistical equipment. For each high-risk failure mode, one mandatory sample bit is assigned (e.g., in Table 1 of Section 4.1, the severity level weight for Class I is 4, and the severity level weight for Class II is 3, with a total of 4 for these two types of failure modes). That is, for each severity level with a weight of 4 and 3, a mandatory sample bit is set, and the sample size is... This is the sum of the number of all failure modes with a severity level weight of 4 and 3.

[0058] S53. Calculate the minimum sample size for the basic experiment. and The number of failure modes greater than or equal to the calibrated risk level The sum of these values ​​yields the total sample size of the experiment.

[0059] Total sample size of the experiment .

[0060] S54. The total sample size of the experiment... Each forced sample bit is assigned one-to-one to each Failure modes greater than or equal to the calibrated risk level; remaining Each sample is allocated using a three-dimensional fusion weighted sampling probability and a Halton low-discrepancy sequence for PPS sampling.

[0061] Sample size allocation: For mandatory sample sizes, Each forced sample bit is assigned one-to-one Fault modes with a severity level greater than or equal to the calibrated risk level, i.e., each severity level with a weight of 3 or 4, are assigned a sample size to completely eliminate missed risks; for the basic minimum sample size Based on the three-dimensional fusion weighted sampling probability, the Halton low-difference sequence is used to complete the PPS sampling allocation.

[0062] The specific steps of PPS sampling allocation based on Halton low-difference sequences in step S54 are as follows: S541: Generation length is One-dimensional Halton low-difference sequences , where sequence elements The basis of the sequence is selected from distinct prime numbers.

[0063] S542: Calculate the cumulative probability interval for the 3D fusion weighted sampling probability: Set the initial cumulative probability. , No. The cumulative probability of each failure mode This forms a continuous probability interval. .

[0064] S543: For each Halton sequence element Determine the cumulative probability interval to which the sample belongs, and assign the sample to the corresponding fault mode of the interval.

[0065] S544: For all high-risk failure modes, add one forced sample to the above sampling allocation results to obtain the final sample size allocation result. ,satisfy .

[0066] Advantages: For high-risk failure modes, a weighted lower limit is set to increase their sampling probability, and mandatory sample positions are assigned to ensure they are sampled at least once. This avoids omitting high-risk, low-probability failure modes from both probability correction and deterministic coverage perspectives, significantly enhancing the risk coverage capability of test experiments. Furthermore, it offers excellent sampling uniformity and strong result stability: using Halton low-discrepancy sequences instead of traditional pseudo-random sequences effectively avoids sampling clustering, and the sample allocation more closely matches theoretical probabilities, satisfying the convergence requirements of Bernoulli's law of large numbers and Khinchin's law of large numbers. Multiple evaluations show strong consistency, reducing evaluation bias caused by sampling randomness.

[0067] S6: Conduct physical fault injection tests based on the sample allocation results of S5, record the number of detection failures for each fault mode, calculate the unbiased estimate of the fault detection rate using the inverse probability weighting method, calculate the one-sided confidence lower limit of the fault detection rate using the binomial distribution precise one-sided confidence limit method, and complete the equipment testability evaluation.

[0068] Physical fault injection tests based on the above sample allocation results are conducted on the physical prototype or equivalent hardware-in-the-loop simulation platform of the equipment to be evaluated. The equipment response is captured by sensors and a test system, and the number of detection failures for each fault mode is recorded. The Horvitz-Thompson (HT) unbiased estimator is introduced to calculate the unbiased point estimate of the fault detection rate. The Clopper-Pearson binomial distribution exact one-sided confidence limit method is used to calculate the one-sided confidence lower limit of the fault detection rate, completing the equipment testability evaluation. Specific steps include: S61: Conduct physical fault injection tests based on the above sample allocation results on the physical prototype or equivalent hardware-in-the-loop simulation platform of the equipment to be evaluated, capture the equipment response through sensors and test systems, and record the number of detection failures for each fault mode.

[0069] S62: Unbiased Estimation Calculation: The Horvitz-Thompson unbiased estimator is introduced to solve the estimation bias problem under 3D fusion weighted unequal probability sampling. The formula for unbiased estimation of fault detection rate is:

[0070] in, For the first The sampling probability of a fault mode calculated based on its expected failure rate, which is the proportion of the expected failure rate of the current fault mode relative to the failure rate of the entire fault set. For detectability indicator functions, the first... When each failure mode can be successfully detected When undetectable The result is determined by the fault injection test. For the sample indicator variable, the first When each failure mode is assigned at least one sample When no sample is assigned ; First-order sample entry probability, high-risk failure mode Low-risk failure mode , The weighted sampling probability for 3D fusion.

[0071] S63: Calculation of the lower confidence limit: The Clopper-Pearson binomial distribution exact one-sided lower confidence limit method is used to calculate the one-sided lower confidence limit. Substituting the total sample size, the number of trial failures, and the confidence level, the lower confidence limit is obtained. :

[0072] in: This represents the one-sided lower confidence limit for the fault detection rate. This represents the total number of failed detections. This represents the total sample size. For confidence level, a value of 0.8 to 0.95 is recommended.

[0073] Advantages: By employing fusion-weighted sampling, the Horvitz-Thompson unbiased estimation and Clopper-Pearson one-sided confidence lower bound calculation are further introduced, forming a complete closed loop for sampling scheme design, experimental data collection, and experimental result evaluation. This solves the problem of estimation bias that traditional statistical methods are prone to produce under unequal probability sampling, and improves the statistical validity of the evaluation results.

[0074] The following examples use the power transmission system of a certain type of tracked armored equipment as the test and evaluation object.

[0075] The basic parameters are as follows: The system contains a total of unassessed fault modes. Among them, the number of high-risk failure modes with severity levels of I and II, i.e., weights of 4 and 3, is... Minimum acceptable failure detection rate Buyer risk Number of qualified judgments Confidence level .

[0076] Selection of general scenario recommendation weights: estimated failure rate Severity level Field Failure Frequency Level Lower bound of weights for high-risk failure modes .

[0077] Detailed data on the expected failure rate, severity level, and field failure frequency level for the 30 failure modes are shown in Table 1 below: Table 1: Detailed Table of 3D Data for Failure Modes

[0078] Step 1: Normalization of 3D Fault Data Taking the high-risk fault mode FM03 as an example, complete the normalization calculation of three-dimensional fault data: 1. Total expected failure rate for all 30 failure modes .

[0079] 2. Normalized expected failure rate: .

[0080] 3. Severity level normalization: .

[0081] 4. Field Fault Frequency Level Normalization: .

[0082] 5. The normalized three-dimensional eigenvector of FM03 is .

[0083] Following the same method, the three-dimensional fault data of all 30 fault modes were normalized to obtain the three-dimensional feature vectors of all fault modes.

[0084] Step 2: Weighted Fusion and Weight Correction of 3D Fault Data Weighted fusion calculation of initial fusion weights: Taking FM03 as an example, the initial fusion weights .

[0085] Correction of lower limit of weight for high-risk modes: The initial fusion weights of the four high-risk failure modes (for high-risk failure modes of severity I and II, corresponding to 4 and 3 in this table) are all greater than the lower limit of weight of 0.05, and no correction is required. The final fusion weights are consistent with the initial values.

[0086] Step 3: Calculation of 3D Fusion Weighted Sampling Probability Calculate the sum of the final fusion weights for all 30 failure modes. Taking FM03 as an example, its 3D fusion weighted sampling probability is: .

[0087] Step 4: Halton sampling allocation with forced sample positions Calculation of the minimum basic sample size: Solution To obtain the basic minimum sample size Total sample size calculation: Number of high-risk failure modes Total sample size .

[0088] Forced sample allocation: One forced sample is allocated to each of the four high-risk fault modes FM03, FM07, FM12 and FM18 to ensure 100% sample input.

[0089] Halton sequence sampling: Using prime number 2 as the basis, a Halton sequence of length 18 is generated. The cumulative probability interval of the three-dimensional fusion weighted sampling probability is calculated, and the 18 Halton points are mapped to the corresponding probability interval to complete the allocation of the remaining samples.

[0090] Final sample allocation results: 2 samples were allocated to each of the 4 high-risk failure modes (1 forced sample + 1 sampled sample), and 14 samples were allocated to the remaining 26 failure modes. All high-risk failure modes were fully covered without omission.

[0091] Step 5: Calculation of testability indicators and pass / fail determination Fault injection test: Physical fault injection test based on the above sample allocation results is carried out on the physical prototype or equivalent semi-physical simulation platform of the equipment to be evaluated. The equipment response is captured by sensors and test system, and the number of detection failures for each fault mode is recorded: total sample size 22, total number of detection failures F=1, number of successful fault detections 21.

[0092] HT unbiased point estimation calculation: Substituting the values ​​of each fault mode , , , The unbiased point estimate is calculated. .

[0093] Finally, the Horvitz-Thompson estimator was introduced, and the unbiased point estimate of the fault detection rate for this high-risk fault mode was calculated to be 0.948.

[0094] This invention introduces the HT estimator and applies a "penalty scaling" to the weights of high-probability samples using the reciprocal of the sampling probability (1 / πi), ultimately restoring an unbiased estimate of 0.948. 0.948 objectively indicates that the true detection capability limit for this fault mode is 94.8%, with the remaining 5.2% blind spot due to the physical limitations of the detection algorithm itself rather than uneven sampling. This precise unbiased quantification result avoids the risk of missing fatal faults due to blind optimism in engineering applications, providing irreplaceable benchmark data for evaluating the true capability of detection systems.

[0095] Clopper-Pearson confidence lower bound calculation: Confidence level C=0.9, total sample size n=22, total number of failures F=1, substitute into the formula to obtain the one-sided confidence lower bound at 90% confidence level. .

[0096] Based on the aforementioned unbiased estimate of the fault detection rate (0.948), the lower one-sided confidence limit PL = 0.84 at 90% confidence level is further obtained.

[0097] In the test evaluation, the point estimate of 0.948 only represents the theoretical expectation, while the one-sided confidence lower bound (PL) of 0.84 is the actual guaranteed performance indicator of the system. Its physical meaning is that there is a 90% certainty that, regardless of the fluctuations in the sample size, the actual detection capability of this failure mode can reach at least 84%.

[0098] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A sampling and evaluation method for equipment testability based on three-dimensional fault data fusion, characterized in that, Includes the following steps: S1: Obtain the three-dimensional evaluation data of the i fault modes of the equipment to be tested and perform normalization processing to obtain the normalized three-dimensional feature vector of each fault mode. The three-dimensional assessment data includes the predicted failure rate. Severity level and field failure frequency level ; S2: Determine separately The weighting coefficient α The weighting coefficient β and The weighting coefficient γ, through the weighting coefficient to We perform weighted fusion to obtain the initial fusion weights for each failure mode. ; S3: Enables all fault modes For the final fusion weights, and among them The final fusion weights of failure modes that are greater than or equal to the calibrated risk level are lowered and revised to obtain the final fusion weights of all failure modes. S4: Normalize the final fusion weights of the i fault modes to obtain the three-dimensional fusion weighted sampling probability of each fault mode, thereby realizing the mapping of the three-dimensional fusion data to the one-dimensional sampling probability space. S5: Calculate the minimum sample size for the basic experiment. and The number of failure modes greater than or equal to the calibrated risk level The sum of these values ​​yields the total sample size; the total sample size is then divided into... Each forced sample bit is assigned one-to-one to each Failure modes greater than or equal to the calibrated risk level; remaining Each sample is allocated using a three-dimensional fusion weighted sampling probability and a Halton low-discrepancy sequence for PPS sampling. S6: Conduct physical fault injection tests based on the sample allocation results of S5, record the number of detection failures for each fault mode, calculate the unbiased estimate of the fault detection rate using the inverse probability weighting method, and calculate the one-sided confidence lower limit of the fault detection rate using the binomial distribution precise one-sided confidence limit method to complete the equipment testability evaluation.

2. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, S1 includes the following steps: S11. Obtain three-dimensional evaluation data for the i failure modes of the equipment to be tested. The three-dimensional evaluation data includes the expected failure rate. Severity level and field failure frequency level ; S12. Normalize the three-dimensional assessment data to obtain the normalized value of the three-dimensional assessment data for each fault mode. This is used to eliminate the dimensional differences between different feature data and provide a unified data scale basis for subsequent multi-source data fusion. S13. Based on the normalized values ​​of the three-dimensional evaluation data for each fault mode, construct a normalized three-dimensional feature vector corresponding to each fault mode. For the first Normalized predicted failure rates for each failure mode. For the first Normalized values ​​of severity level for each failure mode. For the first Normalized values ​​of field failure frequency levels for each failure mode.

3. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 2, characterized in that, In S12, the three-dimensional evaluation data are normalized, including: Normalized expected failure rate: ； in, For the first Normalized predicted failure rates for each failure mode. For the first The expected failure rate for each failure mode. The total number of failure modes to be tested for the equipment; Severity level normalization: ； in, For the first Normalized values ​​of severity level for each failure mode. For the first Severity levels for each failure mode; refer to the severity definitions of Class I, II, III, and IV in GJB / Z1391-2006. These correspond to the assigned weights of levels 4, 3, 2, and 1, respectively. Field failure frequency level normalization: ； in, For the first Normalized values ​​of field failure frequency levels for each failure mode. For the first Field failure frequency levels for each failure mode; According to the The actual frequency of each failure mode in the field is divided into levels 1 to 4.

4. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, The weighting coefficients α, β, and γ for the three types of data in S2—expected failure rate, severity level, and field failure frequency level—can be selected based on the task scenario. Recommended values ​​for general scenarios: α=0.5, β=0.3, γ=0.2; Recommended values ​​for high-risk management priority scenarios: α=0.45, β=0.35, γ=0.2; Recommended values ​​for scenarios prioritizing adaptation to outdoor working conditions: α=0.45, β=0.25, γ=0.

3.

5. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, The formula for calculating the initial fusion weights in S2 is: , For the first Normalized predicted failure rates for each failure mode. For the first Normalized values ​​of severity level for each failure mode. For the first Normalized values ​​of field failure frequency levels for each failure mode.

6. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, S3 specifically refers to: Get all If the initial fusion weight of the fault mode is greater than or equal to the calibrated risk level, determine whether it is lower than the lower threshold. If it is, determine the lower threshold as the final fusion weight of the fault mode; otherwise, determine the initial fusion weight of the fault mode as the final fusion weight. Furthermore, the initial fusion weights of the remaining fault modes are determined as the final fusion weights of the fault modes.

7. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 6, characterized in that, The formula for adjusting the fusion weight in S3 is as follows: ,in ≥0.05, These are the initial fusion weights.

8. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 7, characterized in that, The formula for calculating the 3D fusion weighted sampling probability in S4 is: ； in, The final fusion weights for the failure modes. The total number of failure modes, and satisfying the normalization constraint. .

9. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, The specific steps for PPS sampling allocation based on Halton low-difference sequences in S54 are as follows: S541: Generation length is One-dimensional Halton low-difference sequences , where sequence elements The basis of the sequence is selected from distinct prime numbers; S542: Calculate the cumulative probability interval for the 3D fusion weighted sampling probability: Set the initial cumulative probability. , No. The cumulative probability of each failure mode This forms a continuous probability interval. ; S543: For each Halton sequence element Determine the cumulative probability interval to which the sample belongs, and assign the sample to the corresponding fault mode within that interval. S544: For all high-risk failure modes, add one forced sample to the above sampling allocation results to obtain the final sample size allocation result. ,satisfy .

10. The equipment testability sampling and evaluation method based on three-dimensional fault data fusion according to claim 1, characterized in that, The formula for calculating the unbiased estimate of the fault detection rate in S6 is as follows: ； in: For the first The sampling probability of each failure mode calculated based on the expected failure rate. For detectability indicator function, As an indicator variable for the sample, This represents the first-order sample probability. The weighted sampling probability for 3D fusion.

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