Testability Test and Verification Method for Radar Systems

Abstract

The present invention provides a testability test verification method for a radar system, which includes the following steps. Step 1: Complete the design of the sample space of the radar system. Step 2: Based on the testability fixed-number sampling plan design method of binomial distribution combined with the large-sample small-sampling plan, determine the sample size of the final truncation of the radar system testability test, and complete the test plan design. Step 3: It also includes using the binomial distribution success / failure type truncated sequential method to evaluate the determined truncation value. Through the provided testability test verification method for the radar system, the present invention can effectively improve the efficiency of the radar system testability test, enhance the feasibility of the radar system testability test project development, reduce the uncertain factors in the project development, and provide a theoretical basis for the popularization and application of the testability verification work in various professional fields.

Description

Technical Field

[0001] This application relates to the field of testability test plan design, and specifically to a testability test verification method for a radar system. Background Art

[0002] Testability is a design characteristic of a product that can determine its status in a timely and accurate manner, that is, whether it can work, cannot work, or its performance has declined, etc., and isolate its internal faults. Good testability design can greatly shorten the fault detection and isolation time, reduce the workload of maintenance support, and thus reduce the maintenance time and maintenance personnel. And the testability verification test has always been an important means to promote the improvement of testability capabilities.

[0003] The radar system is one of the typical complex systems. The characteristics of its fault sample space are that the number of fault modes is not only huge, but also the fault modes of the antenna part are constantly repeating. Its main characteristics are:

[0004] 1) The total number of fault modes is large. For a typical radar system encountered currently, the total number of fault modes at the level of field-replaceable units is approximately 5,000 - 8,000, the number of fault modes at the level of in-field replaceable units is approximately 5,000 - 15,000, and the number of fault modes at the functional circuit level is approximately 20,000 - 30,000.

[0005] 2) Most of the fault modes in the fault sample space have the characteristic of "concentrated repetition", that is, there are a large number of repetitive fault modes in the fault mode set. For a certain radar system, the proportion of fault modes of its transceiver (TR) component is as high as 88.72%, and the sum of the failure rates of the radar antenna accounts for 94.40% of the total failure rate of the entire radar.

[0006] At this time, according to the sampling method implemented, due to the absolute proportion of the antenna, the sample will mainly be biased towards the antenna part. In order to increase the coverage, the sampling samples required for the test will be greatly increased, the test cycle will be extended, and the workload will be increased. It is not conducive to engineering promotion. At the same time, as the test progresses, field data will also occur simultaneously. If integrating field data to improve the comprehensive evaluation accuracy is also an important task.

[0007] Therefore, it is necessary to provide a testability test verification method for a radar system to solve the problems existing in the prior art. Summary of the Invention

[0008] To overcome the deficiencies of the prior art, the objective of the present invention is to propose a testability test verification method for a radar system. By selecting the truncation value of the sample size in the radar system testability plan, the total sample quantity required for test verification is greatly reduced, thereby shortening the test cycle and significantly improving the test efficiency, and solving the problems of large workload and long cycle in the current radar system testability test, which lead to difficulties in promoting functions. In addition, an evaluation method based on the truncated sequential test of the binomial distribution is provided to fill the current theoretical gap.

[0009] To achieve the above objective, the solution adopted by the present invention is to provide a testability test verification method for a radar system, which includes the following steps:

[0010] Step 1: Conduct a failure mode and effects analysis for the radar system to obtain the failure modes at each level of the analyzed radar system, and select the failure modes at the required test level from the failure modes at each level of the radar system to design a test sample library;

[0011] Step 2: Based on the testability fixed-sample-size sampling plan design method of the binomial distribution and combined with the large-sample small-sampling plan, determine the final truncated sample size of the radar system testability test to complete the test plan design;

[0012] Step 21: According to the number M of failure modes in the test sample library of the radar system selected in Step 1, based on the binomial distribution theory, determine multiple groups of failure criteria c (FD) and the preliminary sample size n (FD) matched with c (FD) :

[0013]

[0014] where: β (FD) is the user risk; q T1(FD) is the minimum acceptable value of the detection rate; F is a variable; is the combination number of taking F from n (FD) ;

[0015] Among the multiple groups of failure criteria c (FD) and the preliminary sample size n (FD) matched with c (FD) , select the minimum value greater than the number M of failure modes in the test sample library of the radar system as the preliminary test sample size of the radar system testability test;

[0016] Step 22: Conduct tests according to the samples of the radar system determined in Step 21, and perform censoring according to the large-sample small-sampling method to utilize the samples for testing; the large-sample small-sampling method conducts step-by-step analysis on the preliminary test sample size of the radar system testability test, calculates the range results of the confidence lower limit when different censoring values are adopted under different sample sizes, and determines the censoring value that meets the range target value according to the change trend of the range results. Specifically:

[0017] When the preliminary test sample size of the radar system testability test is less than or equal to 10,000, and when the range target value is within 2%, select the censoring value as 2,000;

[0018] When the preliminary test sample size of the radar system testability test is greater than 10,000 and less than or equal to 20,000, and when the range target value is within 2%, select the censoring value as 1,000; when the preliminary test sample size of the radar system testability test is greater than 10,000 and less than or equal to 20,000, and when the range target value is within 1%, select the censoring value as 2,000; or

[0019] When the preliminary test sample size of the radar system testability test is greater than 20,000 and less than or equal to 30,000, and when the range target value is within 2%, select the censoring value as 2,000;

[0020] Step 3: It also includes evaluating the results by using the success / failure type censored sequential method based on the binomial distribution, specifically including the following sub-steps:

[0021] Step 31: Develop a censored sequential test plan for the determined censoring value to obtain a test plan diagram;

[0022] Step 32: Conduct tests according to the test plan diagram obtained in Step 31 to obtain the final test results. Specifically:

[0023] When d ≤ sn s -h, it is accepted;

[0024] When d ≥ sn s +h, it is rejected;

[0025] When sn s -h ≤ d ≤ sn s +h, continue the test;

[0026] In the formula: d is the cumulative number of failures; s is the slope of the acceptance and rejection lines in the test plan diagram; h is the vertical intercept of the test plan diagram; n s is the cumulative number of tests;

[0027] Step 33: Conduct a point estimate evaluation of the censored sequential test according to the final test results obtained in Step 32;

[0028] Step 34: Evaluate the confidence lower limit of the truncated sequential test according to the final test results obtained in Step 32. For the grid point (n F , F) of the test plan diagram obtained for the product in Step 1, truncate, and calculate the confidence lower limit R L of the detection rate according to the confidence level c:

[0029]

[0030] In the formula: n F is the total amount of the last test samples for the detection rate and the sample amount of the successfully detected samples for the isolation rate at the end of the test; F is the number of samples that are not successfully detected and not successfully isolated at the end of the test; is the probability of the product at the i-th point (n i , i); n i is the test sample amount matching i.

[0031] Preferably, the specific steps in Step 1 include the following steps:

[0032] Step 11: Carry out failure mode and effect analysis on the radar system by using the single-factor analysis method to obtain the failure modes of each layer of the analyzed radar system. The layers include: device / component level, functional circuit level, SRU level, LRU / LRM level, and radar subsystem;

[0033] Step 12: Select the failure modes of the required test layer from the failure modes of each layer of the radar system obtained in Step 11;

[0034] Step 13: Screen the failure modes selected in Step 12 and form a testability test sample library by using the screened failure modes;

[0035] The specific screening method is:

[0036] Screen out the failure modes corresponding to the functional circuits that are no longer used after the radar system is finalized; screen out the failure modes corresponding to the functions not included in the current technical state of the radar system; screen out the failure modes corresponding to the redundant unused pins and pins of the radar system; or delete the failure modes of the performance degradation type that exceed the technical agreement of the radar system.

[0037] Preferably, the single-factor analysis method adopted in Step 11 is specifically: starting from the failure modes of the bottommost component layer from bottom to top and ending with the product layer corresponding to the agreed level; using the failure modes of the lower layer as the causes of the failure modes of the upper layer and the failure modes of the upper layer as the effects of the failure modes of the lower layer to establish a connection relationship between layers.

[0038] Preferably, the failure to meet the operating conditions of the radar system testability test in step 3 includes that the existing cycle requirements cannot meet the implementation of the preliminary test sample size of the radar system testability test selected in step 2.

[0039] After the implementation, it can generally be evaluated according to the success / failure type truncated sequential method, or the success / failure type truncated sequential method based on the binomial distribution can be used to evaluate the determined truncation value, specifically referring to step 34, where the calculation method of the truncation lattice points is as follows:

[0040] If the product is finally accepted, the acceptance point will fall into the lattice point

[0041] Solve 0 = sn s -h, and obtain the result n s Round up to obtain n0;

[0042] Solve 1 = sn s -h, and obtain the result n s Round up to obtain n1;

[0043] Solve A = sn s -h, and obtain the result n s Round up to n A , where A is the result of rounding down (sn t -h);

[0044] (nt, t) is the first point upward along the solid line on the right side of the square in the test plan diagram, and t is the result of rounding up (sn t -h);

[0045] Then keep nt unchanged and increase t until the last point n t is the truncation test number; C t is the truncation failure number;

[0046] If the product is finally rejected, the rejection point will fall into the next point of the acceptance point

[0047] In the formula: m i is the critical value when the step occurs, and the value range of i is from to C t ; is the value obtained by rounding up the ordinate intercept h of the test plan diagram;

[0048] Solve (C t -1) = (sns +(h), to obtain the result n s Obtained by rounding down

[0049] Solve (C t - 2) = (sn s +(h), to obtain the result n s Obtained by rounding down

[0050] Solve (C t - 3) = (sn s +(h), to obtain the result n s Obtained by rounding down

[0051] Preferably, step 32 truncates at the grid point (n F , F) in the test plan diagram obtained by the product in step 31, and the point estimate is specifically:

[0052]

[0053] In the formula: Is the point estimate value.

[0054] Preferably, the When i is 0 is:

[0055]

[0056] In the formula: Is the combination number of taking 0 from n0; Is the n0th power of the confidence lower limit.

[0057] Preferably, the When i is 1 is:

[0058]

[0059] In the formula: Is the combination number of taking 1 from n0; Is the (n0 - 1)th power of the confidence lower limit; Is the (n1 - n0)th power of the confidence lower limit.

[0060] Preferably, the When i is 2 is:

[0061]

[0062] In the formula: Is the combination number of taking 2 from n0; Is the (n0 - 2)th power of the confidence lower limit; is the combination number of taking 1 from n1 - n0; is the (n1 - n0 - 1)th power of the lower confidence limit; is the (n2 - n1)th power of the lower confidence limit; is the (n2 - n0)th power of the lower confidence limit.

[0063] Preferably, the when i is 3 is:

[0064]

[0065] wherein: is the combination number of taking 3 from n0; is the (n0 - 3)th power of the lower confidence limit; is the (n3 - n0)th power of the lower confidence limit; is the (n3 - n1)th power of the lower confidence limit; is the combination number of taking 1 from n2 - n1; is the (n2 - n1 - 1)th power of the lower confidence limit; is the (n3 - n2)th power of the lower confidence limit; is the (n1 - n0 - 2)th power of the lower confidence limit; is the combination number of taking 2 from n1 - n0.

[0066] Preferably, the when i is 4 is:

[0067]

[0068] wherein: is the combination number of taking 4 from n0; is the (n0 - 4)th power of the lower confidence limit; is the (n4 - n0)th power of the lower confidence limit; is the (n4 - n1)th power of the lower confidence limit; is the combination number of taking 0 from n1 - n0; is the (n4 - n2)th power of the lower confidence limit; is the combination number of taking 0 from n2 - n0; is the (n2 - n0)th power of the lower confidence limit; is the combination number of taking 1 from n3 - n2; is the (n3 - n2 - 1)th power of the lower confidence limit; is the (n4 - n3)th power of the lower confidence limit; is the combination number of taking 1 from n2 - n1; is the combination number of taking 2 from n2 - n1.

[0069] Preferably, the truncated sequential test plan designed according to the step 31 is specifically: according to the detection rate specified value q0(FD) The minimum acceptable value q of the detection rate 1(FD) Determine four parameters, namely the production risk α and the user risk β, to obtain the test plan diagram. The four parameters include the vertical intercept h of the test plan diagram, the slope s of the acceptance and rejection lines of the test plan diagram, the truncated test number n t and the truncated failure number c t .

[0070] Preferably, the slope s of the acceptance and rejection lines of the test plan diagram is specifically:

[0071]

[0072] The vertical intercept h of the test plan diagram is specifically:

[0073]

[0074] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0075] (1) The "large sample, small sampling" scheme design method proposed by the present invention for the testability test of radar systems solves the problems of long implementation cycle and uncontrollable cost encountered in the current testability test of radar systems, fills the gap in the special applicability research in the current testability test plan design theory of radar systems, and forms a testability test plan design verification method with engineering applicability. It provides a theoretical basis for the subsequent testability tests of various types of radar products, and greatly promotes the in-depth popularization of the testability specialty in various complex subsystems.

[0076] (2) After determining the truncated value, the present invention further conducts the testability test through the truncated sequential scheme of the binomial distribution to ensure the accuracy of the results. First, the test plan diagram, that is, the sequential diagram, is obtained through scheme design, and then the test is carried out to obtain the grid points where the truncation falls. According to the grid points where the truncation of the product falls in the sequential diagram and the required confidence level, the lower confidence limit of the detection rate is calculated, which can solve the problem that the current truncated sequential test based on the binomial distribution cannot give an evaluation result, and will greatly promote the application of the truncated sequential test plan in the actual engineering field, and improve the application scope and depth of the sequential test plan. It provides another fast and convenient test plan for the current test verification of testability indicators, and can improve the overall test efficiency. Description of the Drawings

[0077] Figure 1 It is a discrete analysis change diagram of 30,000 samples sampled in the embodiment of the present invention;

[0078] Figure 2 It is a discrete analysis change diagram of 20,000 samples sampled in the embodiment of the present invention;

[0079] Figure 3 It is the variation diagram of discrete analysis of sampling for 10,000 samples in the embodiment of the present invention;

[0080] Figure 4 It is the schematic flow diagram of the testability test verification method for the radar system of the present invention.

[0081] Figure 5 It is the sequential diagram of the censored sequential test plan in the embodiment of the present invention;

[0082] Figure 6 It is the acceptance / rejection schematic diagram of the censored sequential test in the embodiment of the present invention;

[0083] Figure 7 It is the schematic diagram that the censored sequential test in the embodiment of the present invention is accepted at (n0, 0);

[0084] Figure 8 It is the schematic diagram that the censored sequential test in the embodiment of the present invention is accepted at (n1, 1);

[0085] Figure 9 It is the schematic diagram that the censored sequential test in the embodiment of the present invention is accepted at (n2, 2);

[0086] Figure 10 It is the schematic diagram that the censored sequential test in the embodiment of the present invention is accepted at (n3, 3);

[0087] Figure 11 It is the schematic diagram that the censored sequential test in the embodiment of the present invention is accepted at (n4, 4);

[0088] Figure 12 It is the received result diagram of the detection rate of the censored sequential test in the embodiment of the present invention;

[0089] Figure 13 It is the received result diagram of the isolation rate of the censored sequential test in the embodiment of the present invention. Detailed implementation manners

[0090] Hereinafter, with reference to the attached Figure 1 - attached Figure 4 The implementation manners of the present invention will be described.

[0091] The testability test verification method for the radar system provided by the embodiment of the present invention, also called the large-sample small-sampling method, is intuitively understood as selecting a smaller sample size for sampling tests in the case of a larger sample space of the radar system test to complete the evaluation of the radar system indicators.

[0092] First, for the same number of fault modes, the evaluation discrete analysis under different sample sizes is carried out. The specific steps include:

[0093] Step 1: Conduct failure mode and effects analysis for the radar system. Starting from the failure modes at the bottom component layer from bottom to top, and ending at the product level corresponding to the agreed hierarchy. Take the failure modes of the lower layer as the causes of the upper layer modes, and the failure modes of the upper layer as the effects of the lower layer modes. A corresponding connection relationship needs to be established between the layers. For the analyzed failure modes, select the failure modes at the required level to design the test sample library.

[0094] The failure mode and effects analysis of the radar system is an inductive analysis method that analyzes all possible failure modes and all possible effects they may produce, and analyzes according to the severity of the effects produced by each failure mode and its occurrence probability. The present invention adopts a single-factor analysis method. On the premise of single-factor analysis, in line with the principle of full coverage of all hardware, through a bottom-up recursive process, the existing failure mode and effects analysis method can achieve the induction and summary of top-level failures, and realize the derivation and calculation of the failure rates of each top-level failure mode. The levels of its analysis include: device / component level, functional circuit level, shop replaceable unit (SRU) level, line replaceable unit / line replaceable module (LRU / LRM) level and radar subsystem.

[0095] First, determine the test level selected for the testability test. The selection principle for the testability test level of the radar system is: generally select the LRU / LRM level required for the field maintenance of the radar system. Then select all the failure modes at the test level. Note that it is necessary to include: the failure modes of each LRU level in the radar system, the failure modes of each LRM level in the radar system, the independent system-level failure modes in the radar system, and the radar system-level failure modes that are not transmitted from the LRU / LRM level failure modes.

[0096] Finally, form the sample space for the testability test according to the required screening principle.

[0097] The screening principle is generally:

[0098] 1) The failure modes corresponding to the functional circuits that are no longer used after the radar system is finalized.

[0099] 2) The failure modes corresponding to the functions not included in the current technical state of the radar system.

[0100] 3) The failure modes corresponding to the redundant unused pins and pins of the radar system.

[0101] 4) Delete the performance degradation failures that exceed the technical agreement of the radar system.

[0102] According to needs, the screening principle can be supplemented on this basis.

[0103] Step 21: Determine the test sample size for the radar system based on the test sample library selected in Step 1. First, calculate the preliminary test sample size according to Formula (1) and the total number M of failure modes in the test sample library determined in Step 1.

[0104]

[0105] where β (FD) is the risk of the user; q T1(FD) is the minimum acceptable value of the detection rate; F is a variable; is the combination number of taking F from n (FD) ;

[0106] Step 22: If the period permits, the test can continue with the samples determined in Step 21. If the period does not permit, determine the truncation value according to the large-sample small-sampling method. For example, if the existing period requirement cannot meet the complete implementation of the preliminary sample size selected in Step 2, for example, the test implementation work must be completed within one month, then the truncation value needs to be determined according to the large-sample small-sampling method. The specific selection method is as follows.

[0107] See Table 1 below:

[0108] 1) When the sample size is less than or equal to 10,000, and the range target value is within 2%, select the truncation value as 2000;

[0109] 2) When the sample size is greater than 10,000 and less than or equal to 20,000, when the range target value is within 2%, select the truncation value as 1000; when the range target value is within 1%, select the truncation value as 2000;

[0110] 3) When the sample size is greater than 20,000 and less than or equal to 30,000, when the range target value is within 2%, select the truncation value as 2000;

[0111] 4) If the requirement for the range can be relaxed, fewer samples can also be selected.

[0112] Table 1 Truncation Scheme for Radar System Testability Test

[0113]

[0114]

[0115] The "large sample, small sampling" method is obtained from two dimensions. One is mainly for large systems in radar systems, generally referring to large systems where the number of failure modes involved in testability tests is in the range of 0.6 million to 3 million: By keeping the number of failure modes unchanged and gradually reducing the initial sample size from the minimum value greater than the total number of failure modes, analyze the discrete analysis change, that is, the range change, to determine how to carry out large sample, small sampling. The other is mainly for relatively smaller systems in radar systems, generally referring to radar systems where the number of failure modes involved in testability tests is in the range of 1000 to 6000: By using the method of synchronous change of the total number of failure modes and the initial sample size, analyze the size of the initial sample of failures to determine how to carry out large sample, small sampling. Finally, a method for determining the truncation value of the testability test plan for radar systems, the "large sample, small sampling" method, is given. The derivation process of this method is as follows.

[0116] 1) Evaluation discrete analysis, that is, range analysis, with the same number of failure modes and different sample sizes:

[0117] Select sample spaces of 10,000, 20,000, and 30,000 failure modes respectively, and start step-by-step analysis with initial sample sizes of 11,030, 23,030, and 32,030 respectively; each time the sample size is reduced by 1000 step by step, and 6 extractions are made each time to analyze the size of its discrete analysis; finally, step down to a sample size of 1000. Among them, the degree of dispersion refers to the degree of difference between the various values of the variable observed randomly. In the present invention, the range is used as this index to measure the degree of dispersion, and the range is the difference between the maximum value and the minimum value of the observed variable.

[0118] Figures 1 to 3 Respectively show the discrete analysis distribution when the number of samples is from 800 to the minimum value greater than the total number of failure modes under 30,000, 20,000, and 10,000 failure modes. Specifically:

[0119] For samples with a total number of failure modes between 10,000 and 30,000, when using the truncation plan of 2000, the discrete analysis will not exceed 2%, and the convergence is better.

[0120] For samples with a total number of failure modes between 10,000 and 20,000, when using the truncation plan of 1000, the discrete analysis will not exceed 2%, and the convergence is good.

[0121] Based on the above analysis, for the case where the total number of failure modes exceeds 10,000, it is recommended to adopt a test plan with truncation at 2000, and the discrete analysis at this time will not be greater than 2%; when the requirement for discrete analysis in the project allows, a test plan with truncation at 1000 can be adopted, and the discrete analysis at this time will not be greater than 3%; when the total number of failure modes of all products in the project does not exceed 23,000, a test plan with truncation at 1000 can be adopted, and the discrete analysis is not greater than 2% at this time.

[0122] Combined with the above analysis results, the test plan for the above phased array radar can adopt sample quantitative truncation, and the truncation value plan. The specific truncation method is shown in Table 2.

[0123] Table 2 Evaluation of discrete analysis for phased array radar under different truncation values

[0124]

[0125] 2) Evaluation of discrete analysis when the failure mode and the preliminary sample size change synchronously

[0126] The previous dimension analyzed mainly for the case where the total number of failure modes is greater than 10,000. In this section, through another dimension of analysis, it is analyzed and determined how to determine the truncation number when the number of failure modes is not particularly large, for example, less than 10,000. The selected preliminary sample size should be able to reflect the overall change trend. Finally, the number of failure modes is selected as 6910, 6134, 5521, 4416, and 3134 as samples for analysis, and the selected preliminary sample sizes are truncation at 2000 and truncation at 1000 respectively to complete the correction of the above situation.

[0127] The specific results are shown in Table 3 and Table 4.

[0128] Table 3 Trend of change in sampling plan with truncation at 2000

[0129]

[0130]

[0131] Table 4 Trend of change in sampling plan with truncation at 1000

[0132]

[0133]

[0134] Through the analysis of Table 3 and Table 4, it can be obtained that:

[0135] For the case of using a preliminary sample size with truncation at 2000, the discrete analysis of the confidence lower limit is between 1 - 2%, as shown in Table 3 specifically;

[0136] For the case of truncation with an initial sample size of 1000, the discrete analysis of the lower confidence limit is between 2 - 3%, as shown in Table 4 specifically.

[0137] Based on the above analysis results, the test plan for the phased array radar can select the truncation plan according to the acceptable evaluation discrete analysis value. For products with 1000 - 10000 failure modes, when designing the plan, if the discrete analysis requirement is less than 2%, it is not recommended to adopt the test plan with truncation at 1000, but rather adopt the plan with truncation at 2000. For failure modes with more than 20000 failure modes, the truncation value can be selected as 2000, and the discrete analysis can be controlled within 2%. See Table 1 specifically.

[0138] Step 3. In addition, when adopting the truncated sequential plan, evaluate the determined truncation value, which specifically includes the following sub - steps:

[0139] Step 31: Develop a truncated sequential test plan:

[0140] According to the required detection rate value q 0(FD) in the testability index, the lowest acceptable value q 1(FD) , the producer's risk α and the user's risk β, calculate some relevant test plan design parameters using formulas (1) and (2) and then look up the standard. The specific calculation formulas are:

[0141]

[0142]

[0143] Where: h is the intercept of the vertical coordinate of the test plan graph; s is the slope of the acceptance and rejection lines of the test plan graph; n t is the number of truncated tests; c t is the number of truncated failures; q 0(FD) is the required value of the detection rate; q 1(FD) is the lowest acceptable value of the detection rate. Among them, n t and c t are obtained by looking up the standard GB5080.5 - 85 "Verification Test Plan for the Success Rate of Equipment Reliability Tests". The graphical representation is as Figure 5 shown.

[0144] Step 32: Truncate the truncated sequential test and conduct the test implementation;

[0145] When d ≤ sn s - h, it will fall into the Figure 5 acceptance region and finally land on a certain solid point, that is, accept, Figure 5 represented by Ac in s ; where d is the cumulative number of failures and n

[0146] When d ≥ sn s + h, it will fall into Figure 5 the rejection region, and finally land on a certain hollow point, that is, rejection, Figure 5 denoted by Re in

[0147] When sn s - h ≤ d ≤ sn s + h, it will land in Figure 5 the continued test area, that is, continue the test, Figure 5 denoted by Co in

[0148] After the test ends, it will specifically land on which grid point in the above figure, whether it is a solid or hollow grid point.

[0149] Step 33: Truncated sequential test evaluation method, point estimation. Assume that the product is at a certain grid point (n Figure 6 , F) in F and is either accepted or rejected. Calculate the point estimate value of the truncated sequential test according to formula (3).

[0150]

[0151] Where: n F is the total number of the last test samples for the detection rate at the end of the test, and for the isolation rate, it is the number of samples with successful detection, that is, Figure 6 the abscissa in Figure 6 ; F is the number of samples that have not been successfully detected or isolated at the grid point where it lands at the end of the test, that is, the ordinate in

[0152] Step 34: Confidence lower limit estimation. Assume that the product is at a certain grid point (n Figure 6 , F) in F and is either accepted or rejected. Calculate the confidence lower limit value R L of the truncated sequential test according to the confidence level c according to formula (4):

[0153]

[0154] When conducting a testability test using a truncated sequential scheme based on the binomial distribution, the final acceptance and rejection boundaries of the test are not smooth straight lines, but are composed of Figure 6 the grid points shown in Figure 6 All the points in

[0155] That is to say, when the test scheme is determined, all possible final test results based on the binomial distribution will only be Figure 6a certain point in will not go outside because the binomial distribution is a discrete quantity rather than a continuous quantity, and these possible test results do not completely fall on the boundary but are distributed into Figure 6 the shape formed by each point in. In the figure, solid dots represent all possible received results, and hollow dots represent all possible rejected results.

[0156] Regarding the calculation of in the confidence lower limit evaluation formula (4), is the probability of the product at (n i , i), where is the probability that the product is received at (n0, 0); p(①) is the probability that the product is received at (n1, 1); and so on is the probability of the product at (n i , i), until is the probability of the product at (n F , F). Here The calculation method of is illustrated by examples. The calculation methods of examples (n0, 0), (n1, 1), (n2, 2), (n3, 3), (n4, 4) are as follows:

[0157] 1. The probability calculation of (n0, 0) is as Figure 1 shown: If the product is received at (n0, 0), then there is only one possible case, that is, along the path passed by the arrow pointing from the origin of coordinates to the point (n0, 0) to the right in Figure 7 . The probability that the product is received at (n0, 0) is represented by , and the calculation formula is:

[0158]

[0159] Among them: is the combination number of taking 0 from n0; is the n0th power of the confidence lower limit; n0 is the sample size corresponding to 0 failures;

[0160] 2. The probability calculation of (n1, 1) is as Figure 8 shown: If the product is received at (n1, 1), then there is also only one possible case, along the path passed by the arrow that first points from the origin of coordinates to the right to (n0, 0), then from (n0, 0) up to (n0, 1), and then from (n0, 1) to (n1, 1) in Figure 8 . p(①) is the probability that the product is received at (n1, 1), and the specific calculation formula is:

[0161]

[0162] Among them: is the combination number of choosing 1 from n0; is the (n0 - 1)th power of the confidence lower limit; is the (n1 - n0)th power of the confidence lower limit; n1 is the sample size corresponding to 1 failure.

[0163] 3. Probability calculation of (n2, 2), as Figure 9 shown, if the product is received at (n2, 2), there are two possible cases for the results:

[0164] A. (0, 0) → (n0, 0) → (n0, 2) → (n2, 2)

[0165] B. (0, 0) → (n0, 0) → (n0, 1) → (n1, 1) → (n1, 2) → (n2, 2)

[0166] The probability that the product is received at (n2, 2) is denoted as p(②), and the specific calculation formula is:

[0167]

[0168] where: is the combination number of choosing 2 from n0; is the (n0 - 2)th power of the confidence lower limit; is the combination number of choosing 1 from n1 - n0; is the (n1 - n0 - 1)th power of the confidence lower limit; is the (n2 - n1)th power of the confidence lower limit; is the (n2 - n0)th power of the confidence lower limit; n2 is the sample size corresponding to 2 failures.

[0169] 4. Probability calculation of (n3, 3), as Figure 10 shown, if the product is received at (n3, 3), there are five possible cases, and the specific possible paths are respectively:

[0170] C. (0, 0) → (n0, 3) → (n3, 3)

[0171] D. (0, 0) → (n0, 2) → (n1, 3) → (n3, 3)

[0172] E. (0, 0) → (n0, 2) → (n1, 2) → (n2, 3) → (n3, 3)

[0173] F. (0, 0) → (n0, 1) → (n1, 2) → (n2, 3) → (n3, 3)

[0174] G. (0, 0) → (n0, 1) → (n1, 3) → (n3, 3)

[0175] The probability that the product is received at (n3, 3) is denoted by p(③), and the specific calculation formula is:

[0176]

[0177] Where: is the combination number of taking 3 from n0; is the (n0 - 3)th power of the lower confidence limit; is the (n3 - n0)th power of the lower confidence limit; is the (n3 - n1)th power of the lower confidence limit; is the combination number of taking 1 from n2 - n1; is the (n2 - n1 - 1)th power of the lower confidence limit; is the (n3 - n2)th power of the lower confidence limit; is the (n1 - n0 - 2)th power of the lower confidence limit; is the combination number of taking 2 from n1 - n0; n3 is the sample size corresponding to 3 failures.

[0178] 5. Probability calculation for (n4, 4), as Figure 11 shown, if the product is received at (n4, 4), there are 14 possible results, and the specific possible paths are respectively:

[0179] A. (0, 0) → (n0, 4) → (n4, 3)

[0180] B. (0, 0) → (n0, 3) → (n1, 4) → (n4, 4)

[0181] C. (0, 0) → (n0, 3) → (n1, 3) → (n2, 4) → (n4, 4)

[0182] D. (0, 0) → (n0, 3) → (n1, 3) → (n2, 3) → (n3, 4) → (n4, 4)

[0183] E. (0, 0) → (n0, 2) → (n1, 4) → (n4, 4)

[0184] F. (0, 0) → (n0, 2) → (n1, 3) → (n2, 3) → (n3, 4) → (n4, 4)

[0185] G. (0, 0) → (n0, 2) → (n1, 3) → (n2, 4) → (n4, 4)

[0186] H. (0, 0) → (n0, 2) → (n1, 2) → (n2, 4) → (n4, 4)

[0187] I. (0, 0) → (n0, 2) → (n1, 2) → (n2, 3) → (n3, 4) → (n4, 4)

[0188] J. (0, 0) → (n0, 1) → (n1, 4) → (n4, 4)

[0189] K. (0, 0) → (n0, 1) → (n1, 3) → (n2, 4) → (n4, 4)

[0190] L. (0, 0) → (n0, 1) → (n1, 3) → (n2, 3) → (n3, 4) → (n4, 4)

[0191] M. (0, 0) → (n0, 1) → (n1, 2) → (n2, 4) → (n4, 4)

[0192] N. (0, 0) → (n0, 1) → (n1, 2) → (n2, 3) → (n3, 4) → (n4, 4)

[0193] The probability that the product is received at (n4, 4) is denoted as p(④), and the specific calculation formula is:

[0194]

[0195] Where: is the combination number of choosing 4 from n0; is the (n0 - 4)th power of the lower confidence limit; is the (n4 - n0)th power of the lower confidence limit; is the (n4 - n1)th power of the lower confidence limit; is the combination number of choosing 0 from n1 - n0; is the (n4 - n2)th power of the lower confidence limit; is the combination number of choosing 0 from n2 - n0; is the (n2 - n0)th power of the lower confidence limit; is the combination number of choosing 1 from n3 - n2; is the (n3 - n2 - 1)th power of the lower confidence limit; is the (n4 - n3)th power of the lower confidence limit; is the combination number of choosing 1 from n2 - n1; is the combination number of choosing 2 from n2 - n1; n4 is the sample size corresponding to 4 failures.

[0196] Next, the calculation methods of all possible truncated lattice points will be introduced one by one according to the direction of the circular arrows in the above figure.

[0197] 1) Receiving point: If the product is finally received, it will fall on Figure 6 one of the solid lattice points. Introduce step by step in the counterclockwise direction: Define the above solid lattice points as where n0, n1, …, nt The calculation formula method is as follows:

[0198] a) Solve 0 = sn s - h, and obtain the result n s Round up to n0;

[0199] b) Solve 1 = sn s - h, and obtain the result n s Round up to n1;

[0200] c) Solve A = sn s - h, and obtain the result n s Round up to n A , where A is the result of rounding down (sn t - h);

[0201] d) (n t , t) is the first point upward along the solid line on the right side of the square in the test plan diagram, and t is the result of rounding up (sn t - h);

[0202] e) Then n t remains unchanged, and t increases until the last point n t is the censored test number; C t is the censored failure number.

[0203] 2) Rejection point: If the product is finally rejected, it will fall on one of the hollow grid points in the above figure. The rejection boundary is not smooth but presents a stepped shape as shown in the above figure, which is caused by the fact that the binomial distribution can only take integer values. Introduce each point step by step in the counterclockwise direction according to Figure 6 The first point starts from the next point of the acceptance point (n t , c t ). For the convenience of interpretation, the first point is renamed So the rejection points are successively: is the value obtained by rounding up the intercept h, Figure 6 Only the first - order step is drawn, m i represents the critical value when the step occurs, and the value range of i is to C t . If there are multiple - order steps, there can be multiple values, and the calculation formula for each value is:

[0204] The value obtained by rounding down;

[0205] The value obtained by rounding down;

[0206] The value of rounding down;

[0207] …。

[0208] Provide a specific embodiment, requiring that the discrete analysis be less than 2%, and reducing the test cycle. Then the design of this radar system solution can be completed by using the method proposed in the present invention, as follows.

[0209] Step 1: Conduct tests on all the failure modes at the required level in the failure mode analysis report of the radar system, and formulate the sample space for the testability test.

[0210] Step 21: Determine the test sample size of the radar system according to the sample space selected in Step 1. The total number of failure modes M of the sample space determined in Step 1 is 20628, q T1(FD) = 0.9, and the user risk β (FD) is required to be 0.2. Multiple groups of n (FD) and c (FD) are determined by formula (1):

[0211] wherein, the minimum value greater than M is n (FD) is 20639, and c (FD) is 2027.

[0212] Step 22: Due to the limitation of the implementation cycle of 1 month, early truncation is required. Refer to the following method:

[0213] 1) When the sample size is less than or equal to 10,000, when the range target value is within 2%, select the truncation value as 2000;

[0214] 2) When the sample size is greater than 10,000 and less than or equal to 20,000, when the range target value is within 2%, select the truncation value as 1000; when the range target value is within 1%, select the truncation value as 2000;

[0215] 3) When the sample size is greater than 20,000 and less than or equal to 30,000, when the range target value is within 2%, select the truncation value as 2000;

[0216] 4) If the requirement for the range can be relaxed, fewer samples can also be selected.

[0217] In order to control the dispersion to be less than 2%, according to Table 1, the test truncation value is selected as 2000. Therefore, the finally determined test sample size is 2000.

[0218] Step 3: As Figure 12 and Figure 13As shown, according to the truncated sequential test plan of this product, the product is rarely accepted and is often rejected. The evaluation methods in both cases are the same. Therefore, in this case, only the confidence requirement is specified, and the lower confidence limit of the acceptance situation is evaluated.

[0219] 1. False Discovery Rate (FDR) Evaluation

[0220] The truncated sequential test plan used to evaluate the detection rate this time is: s = 0.01215, h = 1.2466, n t = 323, c t = 4. All possible points in the case of acceptance are as Figure 12 shown. There are a total of four points, which are: (103, 0), (185, 1), (268, 2), (323, 3).

[0221] The evaluation results of the four points with acceptance and an 80% confidence interval are as shown in Table 1 below according to the evaluation method in formula (3).

[0222] Table 1

[0223]

[0224] 2. False Isolation Rate (FIR) Evaluation

[0225] The truncated sequential test plan used to evaluate the isolation rate this time is: s = 0.030435, h = 1.223454, n t = 128, c t = 4. All possible points in the case of acceptance of the isolation rate in this case are shown in the following figure. There are a total of four points. The values of the four points are: (41, 0), (74, 1), (106, 2), (128, 3).

[0226] The evaluation results obtained according to the evaluation method in formula (3) under the condition of acceptance and an 80% confidence interval at the four points are as shown in Table 2 below.

[0227] Table 2

[0228]

[0229]

[0230] The evaluation method of the isolation rate is the same as that of the detection rate. Evaluation is only required when the permutation and combination of the sample size results in acceptance.

[0231] The evaluation method of truncated sequential test data based on binomial distribution proposed in the present invention can effectively complete the index evaluation work.

[0232] The testability test and verification method for radar systems proposed by the present invention solves the problems of long implementation cycle and uncontrollable cost encountered in the current testability tests of radar systems, fills the blank of the special applicability research in the current testability test scheme design theory of radar systems, and forms a testability test scheme design and verification method with engineering applicability. It provides a theoretical basis for the subsequent testability tests of various types of radar products, and greatly promotes the in-depth popularization of the testability specialty in various complex subsystems.

[0233] The embodiments described above are only used to describe the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A testability test verification method for a radar system, characterized in that It includes the following steps: Step 1: Conduct a failure mode and effects analysis for the radar system to obtain the failure modes at all levels of the analyzed radar system, and select the failure modes at the required test level from the failure modes at all levels of the radar system to design a test sample library; Step 2: Based on the design method of the testability fixed number sampling plan for binomial distribution, combined with the large sample and small sampling plan, determine the final truncated sample size of the radar system testability test, and complete the design of the test plan; Step 21: Based on the number M of failure modes in the test sample library of the radar system selected in Step 1, determine multiple groups of fault criteria c according to the binomial distribution theory (FD) and the preliminary sample size n (FD) matched with C (FD) : Where: β (FD) is the user risk; q T1(FD) is the minimum acceptable value of the detection rate; F is a variable; is the combination number of taking F from n (FD) ; Among the multiple groups of fault criteria c (FD) and the preliminary sample size n (FD) matched with C (FD) select the minimum value greater than the number M of fault modes in the test sample library of the radar system to determine the preliminary test sample size for the radar system testability test; Step 22: Conduct tests according to the samples of the radar system determined in Step 21, and perform truncation according to the large sample and small sampling method for testing using the samples; the large sample and small sampling method conducts a step-by-step analysis of the preliminary test sample size of the radar system testability test, calculates the range results of the confidence lower limit when different truncated values are used at different sample sizes, and determines the truncated value that meets the range target value according to the change trend of the range results. Specifically: When the preliminary test sample size of the radar system testability test is less than or equal to 10,000, and when the range target value is within 2%, select the truncated value as 2000; When the preliminary test sample size of the radar system testability test is greater than 10,000 and less than or equal to 20,000, and when the range target value is within 2%, select the truncated value as 1000; when the preliminary test sample size of the radar system testability test is greater than 10,000 and less than or equal to 20,000, and when the range target value is within 1%, select the truncated value as 2000; or When the preliminary test sample size of the radar system testability test is greater than 20,000 and less than or equal to 30,000, and when the range target value is within 2%, select the truncated value as 2000; Step 3: It also includes using the binomial distribution success / failure type truncated sequential method to evaluate the results, specifically including the following sub-steps: Step 31: Develop a truncated sequential test plan for the determined truncated value to obtain a test plan diagram; Step 32: Conduct tests according to the test plan diagram obtained in Step 31 to obtain the final test results. Specifically: When d ≤ sn s - h, it is for reception; When d ≥ sn s + h, it is rejected; When sn s -h ≤ d ≤ sn s +h, continue the test; where: d is the cumulative number of failures; s is the slope of the acceptance and rejection lines in the test plan diagram; h is the vertical intercept of the test plan diagram; n s is the cumulative number of tests; Step 33: Conduct a truncated sequential test point estimation evaluation according to the final test results obtained in Step 32; Step 34: Evaluate the lower confidence limit of the truncated sequential test based on the final test results obtained in Step 32. For the lattice point (n F , F) in the test plan diagram obtained for the product in Step 31, perform truncation, and calculate the lower confidence limit R L of the detection rate according to the confidence level c Where: n F At the end of the test, for the detection rate, it is the total amount of the last test samples, and for the isolation rate, it is the number of samples with successful detection; F is the number of samples that have not been successfully detected and not successfully isolated at the end of the test; is the probability at the i-th point (n i , i) of the product; n i is the test sample size matched with i; The point estimation is specifically: Wherein: is the point estimate value.

2. The testability test verification method for a radar system according to claim 1, wherein The specific steps in Step 1 include the following steps: Step 11: Conduct a failure mode and effects analysis for the radar system using a single-factor analysis method to obtain the failure modes at all levels of the analyzed radar system. The levels include: device / component level, functional circuit level, SRU level, LRU / LRM level, and radar subsystem; Step 12: Select the failure modes at the required test level from the failure modes at all levels of the radar system obtained in Step 11; Step 13: Screen the failure modes selected in Step 12, and use the screened failure modes to form a testability test sample library; The specific screening method is: Screen out the failure modes corresponding to the functional circuits that are no longer used after the radar system is finalized; screen out the failure modes corresponding to the functions not included in the current technical state of the radar system; screen out the failure modes corresponding to the redundant unused pins and pins of the radar system; or, delete the performance degradation type failure modes that exceed the technical agreement of the radar system.

3. The testability test verification method for a radar system according to claim 2, wherein The specific method of single-factor analysis in step 11 is as follows: Starting from the failure mode of the bottommost component layer from bottom to top, with the product level corresponding to the agreed hierarchy as the end point; taking the failure mode of the lower layer as the cause of the failure mode of the upper layer, and the failure mode of the upper layer as the impact of the failure mode of the lower layer, a connection relationship is established between layers.

4. The testability test verification method for a radar system according to claim 1, wherein The non-satisfaction of the operating conditions for the testability test of the radar system in step 3 includes: The existing cycle requirements cannot meet the implementation of the preliminary test sample size of the radar system testability test selected in step 2.

5. The testability test verification method for a radar system according to claim 1, wherein The specific calculation method of the censored lattice points in step 34 is as follows: If the product is finally accepted, the acceptance points will fall into the grid points (n0, 0), (n1, 1), (n2, 2), (n3, 3), (n4, 4), (n5, 5), (n6, 6)...(n A , A), (n t , t), (n t+1 , t + 1)... Solve for 0 = sn s -h to obtain the result n s Round up to obtain n0; Solve 1 = sn s -h to obtain the result n s Round up to obtain n1; Solve for A = sn s - h, to obtain the result n s Round up to n A , where A is the result of rounding down (sn t - h); (n t , t) is the first point upward along the solid line on the right side of the square in the test plan diagram, and t is the result of rounding up (sn t -h); Then n t remains unchanged, t increases until the last point n t is the number of censored trials; C t is the number of censored failures; If the product is ultimately rejected, the rejection point will fall within For the receiving point The next point Where: m i is the critical value when a step occurs, and the value range of i is from to C t ; is the rounded-up value of the ordinate intercept h of the test plan diagram; Solve for (C t - 1) = (sn s + h), and obtain the result n s by rounding down to get Solve (C t -2) = (sn s +h), and obtain the result n s Round down to obtain Solve (C t - 3) = (sn s + h), to obtain the result n s Obtained by rounding down 6. The testability test verification method for a radar system according to claim 1, characterized in that The said When i is 0: Wherein: is the combination number of taking 0 from n0; is the n0-th power of the lower confidence limit; The said When i is 1: Wherein: is the combination number of taking 1 from n0; is the (n0 - 1)th power of the lower confidence limit; is the (n1 - n0)th power of the lower confidence limit; The said When i is 2: Where: is the combination number of choosing 2 from n0; is the (n0 - 2)th power of the lower confidence limit; is the combination number of choosing 1 from n1 - n0; is the (n1 - n0 - 1)th power of the lower confidence limit; is the (n2 - n1)th power of the lower confidence limit; is the (n2 - n0)th power of the lower confidence limit; The When i is 3: Wherein: is the combination number of taking 3 from n0; is the (n0 - 3)th power of the lower confidence limit; is the (n3 - n0)th power of the lower confidence limit; is the (n3 - n1)th power of the lower confidence limit; is the combination number of taking 1 from n2 - n1; is the (n2 - n1 - 1)th power of the lower confidence limit; is the (n3 - n2)th power of the lower confidence limit; is the (n1 - n0 - 2)th power of the lower confidence limit; is the combination number of taking 2 from n1 - n0.

7. The testability test verification method for a radar system according to claim 6, wherein The said When i is 4: where: is the combination number of choosing 4 from n0; is the (n0 - 4)th power of the lower confidence limit; is the (n4 - n0)th power of the lower confidence limit; is the (n4 - n1)th power of the lower confidence limit; is the combination number of choosing 0 from n1 - n0; is the (n4 - n2)th power of the lower confidence limit; is the combination number of choosing 0 from n2 - n0; is the (n2 - n0)th power of the lower confidence limit; is the combination number of choosing 1 from n3 - n2; is the (n3 - n2 - 1)th power of the lower confidence limit; is the (n4 - n3)th power of the lower confidence limit; is the combination number of choosing 1 from n2 - n1; is the combination number of choosing 2 from n2 - n1.

8. The testability test verification method for a radar system according to claim 1, characterized in that The specific design of the truncated sequential test plan in step 31 is as follows: according to the specified detection rate q 0(FD) , the lowest acceptable value q 1(FD) of the detection rate, the producer's risk α and the user's risk β, four parameters are determined to obtain the test plan diagram. The four parameters include the vertical intercept h of the test plan diagram, the slopes s of the acceptance and rejection lines of the test plan diagram, the truncated test number n t and the truncated failure number c t .

9. The testability test verification method for a radar system according to claim 8, characterized in that The slope s of the acceptance and rejection lines in the test plan diagram is specifically: The vertical intercept h of the test plan diagram is specifically:

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