Reliability evaluation method for conversion from success-failure test to metering test

Abstract

The invention provides a reliability evaluation method for conversion from a success-failure test to a metering test, and the method comprises the steps: 1, building a reliability series model of a common spaceflight product according to the characteristic that the spaceflight product is composed of a plurality of mutually independent key subsystems which are connected in series; 2, realizing reliability evaluation of each subsystem by adopting a normal distribution tolerance limit method according to the measured small sample measurement data of the subsystems; 3, based on a confidence limit theory of a sum-difference-product quotient, according to reliability evaluation results of completely different subsystems, realizing aerospace product complete machine reliability evaluation under high confidence; and 4, establishing a reliability evaluation method for the whole spaceflight product under the condition that the subsystems are completely the same. According to the invention, by measuring the performance parameter test data of each key subsystem, the traditional success and failure test of the spaceflight product is converted into the small sample metering test, so that a large amount of test cost and time are saved, and the small sample reliability evaluation of the whole spaceflight product can be realized under the high reliability index requirement.

Description

Technical Field

[0001] The present invention relates to a reliability assessment method for converting a success-failure test into a metrological test, and aims to conduct a whole-machine reliability assessment on aerospace products that can only undergo success-failure tests based on metrological data and reliability assessment results of key subsystems of aerospace products under high reliability index requirements, thereby saving a large amount of test costs and significantly improving the whole-machine reliability assessment accuracy in small sample conditions, and belongs to the field of reliability engineering. Background Art

[0002] With the development of deep space exploration technologies such as space stations and manned lunar landings, the reliability requirements for aerospace products are getting higher and higher. In order to quantitatively verify whether the reliability indicators of aerospace products have reached the specified values, reliability identification tests need to be carried out. However, aerospace products are expensive and have limited production batches, so only small sample tests can be carried out. Especially for aerospace products that can only undergo success-failure type tests, if their reliability is verified according to traditional success-failure counting tests, thousands of tests are required. Such high test costs are difficult for engineering to accept.

[0003] In order to reduce the number of tests, save test costs, and achieve the purpose of verifying reliability, it is usually recommended that aerospace products adopt metrological test solutions. Compared with counting tests that only record the number of successes and failures, metrological tests obtain metrological information on product performance, and a single set of products obtains more reliability information, so the required sample size is much smaller. On the other hand, the reliability of many aerospace products is mainly determined by key subsystems. If any subsystem fails, the entire machine will not operate normally. Therefore, aerospace products can usually be regarded as a series system composed of key subsystems, so that the reliability of the entire machine can be evaluated through the test data of key subsystems. At present, the method commonly used in engineering to evaluate the reliability of series systems by subsystem test data is based on the maximum likelihood theory, so the error is large in the case of small samples.

[0004] In view of the above problems, the present invention proposes a reliability assessment method for converting a success-failure type test into a metrological type test. The method converts the reliability test of aerospace products from a success-failure type test into a metrological test with richer information by measuring the metrological data of key subsystems. Then, the reliability of the entire aerospace product is evaluated based on the metrological data of the subsystems, and a one-sided lower confidence limit of the reliability under high confidence is given, thereby realizing the reliability assessment of a small sample of aerospace products and solving the above problems. Summary of the invention

[0005] Purpose: In view of the fact that aerospace products can only undergo success-failure tests, while their subsystems can undergo metrological tests, a reliability assessment method for converting success-failure tests into metrological tests was established. The reliability assessment of the entire aerospace product can be achieved based on the small sample metrological data of the key subsystems, saving a lot of test costs while ensuring the assessment accuracy.

[0006] Technical solution: The present invention first establishes a reliability series model for aerospace products, and then transforms the success or failure test of the aerospace product into a metrological test of the subsystem by measuring the metrological data of the key subsystems, and evaluates the reliability of each subsystem. On this basis, based on the confidence limit theory of sum-difference-product-quotient, the reliability unilateral confidence lower limit of the aerospace product is statistically inferred according to the reliability evaluation results of the subsystem.

[0007] The present invention proposes a reliability evaluation method for converting a success-failure test into a quantitative test, and the specific steps are as follows:

[0008] Step 1: Considering the characteristics of aerospace products that are composed of several independent key subsystems connected in series, a reliability series model of general aerospace products is established;

[0009] Step 2: Based on the measured small sample measurement data of the subsystem, the normal distribution tolerance limit method is used to realize the reliability evaluation of each subsystem;

[0010] Step 3: Based on the confidence limit theory of sum-difference-product-quotient, the reliability evaluation of aerospace products under high confidence is realized according to the reliability evaluation results of completely different subsystems;

[0011] Step 4: For the situation where all subsystems are exactly the same, establish a reliability assessment method for the entire aerospace product.

[0012] Among them, in step 1, "according to the characteristics of aerospace products consisting of several independent key subsystems in series, a reliability series model of general aerospace products is established", the method is as follows:

[0013] Assume that a certain aerospace product consists of m completely different and independent key subsystems connected in series, and the reliability of the ninth subsystem is R i , then the reliability R of the aerospace product is:

[0014]

[0015] For the case where the above-mentioned aerospace product series model includes several identical and independent subsystems, the identical and independent subsystems can be regarded as a key subsystem. For example, if there are m identical and independent subsystems * The reliability of each identical subsystem is R *, they can be regarded as a key subsystem, and the reliability of this subsystem is

[0016] In engineering practice, it is impossible to directly use formula (1) to calculate the reliability of aerospace products. i The true value of is unknown, and its one-sided confidence lower limit R with a confidence level of γ can only be obtained through statistical inference of the corresponding reliability test data. Li ,satisfy:

[0017] P(R i ≥R Li ) = γi = 1, 2, ..., m (2)

[0018] Among them, in step 2, "according to the measured small sample measurement data of the subsystem, the reliability assessment of each subsystem is realized by using the normal distribution tolerance limit method", the method is as follows:

[0019] If the test data of subsystem performance parameters obtained after the test pass the normal distribution test, it can be considered that the reliability characteristic quantities of the subsystem all obey the normal distribution. In this case, the normal distribution tolerance method can be used to evaluate the reliability of the key subsystem in combination with the tolerance of the characteristic quantity. The specific process is as follows:

[0020] Assume that the performance parameter test data of each subsystem is X i (i=1,2,…,m) all obey the normal distribution, and the allowable limit of its characteristic quantity is X i <x iU or X i >x iL , where x iU is the upper limit of the performance parameters required by the product technical indicators, x iL is the lower limit that the performance parameter needs to meet, and the reliability of the subsystem can be expressed as:

[0021]

[0022] or:

[0023]

[0024] In the formula, μ i , σ i are the mean and standard deviation of the performance parameters of the ith subsystem, respectively, and Φ(·) is the standard normal distribution function.

[0025] If a certain aerospace product conducts n reliability tests on the whole machine, after each test, the whole machine is disassembled and the performance parameter test data x of n groups of key subsystems are obtained by actual measurement. i =(x i1 , xi2 , …, x in ), i = 1, 2, ..., m. Based on these measured data, the sample mean of each subsystem can be calculated separately and the sample standard deviation s i :

[0026]

[0027]

[0028] Then, the sample mean, sample standard deviation and characteristic tolerance are combined to construct the statistic ψ according to the following formula i for:

[0029]

[0030] When the confidence level is given as γ, the one-sided confidence lower limit of the reliability of each subsystem is R Li Solving the following equation yields:

[0031]

[0032] In the formula, is the R of the standard normal distribution Li Quantile, The degrees of freedom are v = n-1, and the noncentrality parameter is The distribution function of the noncentral t distribution.

[0033] The one-sided confidence lower limit R of the reliability of the subsystem in equation (8) is Li It can be obtained by looking up the numerical table of non-central t distribution or solving it by dichotomy. At this time, the reliability one-sided confidence lower limit R of each subsystem with confidence γ Li It can be expressed as:

[0034]

[0035] In the formula, yes The non-central parameters are calculated by formula (8) Find the inverse function.

[0036] At this point, the reliability assessment of key subsystems has been achieved based on the measured small sample metrology data of the subsystems.

[0037] Among them, in step 3, "based on the confidence limit theory of sum-difference product quotient, the reliability evaluation of aerospace products under high confidence is realized according to the reliability evaluation results of completely different subsystems", and its practice is as follows:

[0038] Assume that the confidence level of each subsystem is γ and the lower limit of the reliability is R Li(i=1, 2, ..., m), which can be obtained according to the subsystem reliability evaluation method described in step 2.

[0039] For the case where the subsystems of aerospace products are completely different and independent of each other, based on the confidence limit theory of sum-difference-product-quotient, we first set the reliability unilateral confidence lower limit R of each subsystem with confidence level γ as Li (i=1, 2, ..., m) is substituted into the whole machine reliability series model described in step 1, and the calculated result is used as the initial approximate value of the one-sided confidence lower limit of the system reliability R under a given confidence level γ, that is:

[0040]

[0041] Let γ * Represents R L The actual confidence level of . It can be calculated numerically by the following formula:

[0042]

[0043] Where:

[0044]

[0045]

[0046] In actual calculation, first select M according to the accuracy requirement (such as 10 4 , 10 5 , 10 6 etc.), and substitute into formula (13) to obtain Then, the corresponding Finally, the confidence γ is obtained by formula (11): * In particular, when Φ in equation (12) -1 When the value * in {*} is greater than 1, let the corresponding

[0047] Further, the value of γ in formula (10) is adjusted by dichotomy to γ ** , so that the γ calculated by formula (11) * =γ, the one-sided confidence lower limit of the reliability of aerospace products with a confidence level of γ can be obtained as:

[0048]

[0049] In the formula, The confidence level of the reliability of subsystem i is γ ** The one-sided lower confidence limit of is given by formula (9).

[0050] At this point, reliability assessment of the entire aerospace product with high confidence has been achieved for completely different situations of the subsystems.

[0051] Among them, in step 4, "for the situation where all subsystems are exactly the same, establish a reliability assessment method for the entire aerospace product", the method is as follows:

[0052] For the case where the subsystems of aerospace products are completely identical and independent of each other, assuming that the reliabilities of the m subsystems are completely identical and equal to the reliability R1 of subsystem 1, the reliability of the entire aerospace product is:

[0053]

[0054] At this time, the reliability unilateral confidence lower limit R of the aerospace product with a confidence level of γ L，γ Calculated by the following formula:

[0055]

[0056] satisfy:

[0057]

[0058] At this point, for situations where the subsystems are exactly the same, reliability assessment of the entire aerospace product has been achieved with a high degree of confidence.

[0059] The advantages and beneficial effects of the present invention are as follows: the present invention transforms the traditional success-failure test of aerospace products into a small-sample metrological test by measuring the performance parameter test data of each key subsystem, which not only saves a lot of test costs and time, but also can realize small-sample reliability evaluation of aerospace product complete machines under high reliability index requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0061] It should be noted that the aerospace product in the present invention generally has multiple key subsystems. If any key subsystem fails, the aerospace product cannot operate normally. Therefore, the aerospace product can be regarded as a series system composed of several key subsystems. In addition, the aerospace product can only carry out success and failure counting tests, while its key subsystems have reliability characteristic quantities that are easy to measure and obey the normal distribution law.

[0062] The present invention proposes a reliability evaluation method for converting a success-failure test into a metrology test. The landing buffer mechanism of a certain spacecraft is taken as an example, and the present invention is further described in detail in combination with actual engineering applications. The specific steps are as follows:

[0063] Among them, in step 1, "according to the characteristics of aerospace products consisting of several independent key subsystems in series, a reliability series model of general aerospace products is established", the method is as follows:

[0064] The landing buffer mechanism of a spacecraft is composed of key subsystems such as the main buffer, auxiliary buffer I, and auxiliary buffer II. If any of the main buffer, auxiliary buffer I, and auxiliary buffer II does not work effectively, the landing buffer mechanism can be considered to have lost its buffering function. Therefore, during the mission phase of the lander's free fall, the landing buffer mechanism can be regarded as a series system consisting of the main buffer, auxiliary buffer I, and auxiliary buffer II.

[0065] Then the reliability model of a single landing buffer mechanism is:

[0066] R=R1×R2×R3 (18)

[0067] Where: R, R1, R2, R3 are the buffer reliability of a single landing buffer mechanism, main buffer, auxiliary buffer I and auxiliary buffer II respectively.

[0068] A lander is equipped with 4 sets of identical landing buffer mechanisms. At the moment of landing, the 4 landing buffer mechanisms work together to perform combined buffering and energy absorption. Since any set of landing buffer mechanisms loses its buffering capacity, it is considered that the system buffering fails. Therefore, in this mission phase, the 4 landing buffer mechanisms can be regarded as a series system. The buffering reliability R of the landing buffer system is * for:

[0069]

[0070] In engineering practice, it is impossible to directly use equations (18) and (19) to calculate the reliability of the landing buffer mechanism and the landing buffer system. This is because the reliability R of the main buffer, auxiliary buffer I and auxiliary buffer II is i The true value of (i=1, 2, 3) is unknown, and its one-sided confidence lower limit R with a confidence level of γ can only be inferred through the corresponding reliability test data statistics. Li (i=1,2,3), satisfying:

[0071] P(R i ≥R Li )=γi=1,2,3 (20)

[0072] Among them, in step 2, "according to the measured small sample measurement data of the subsystem, the reliability assessment of each subsystem is realized by using the normal distribution tolerance limit method", the method is as follows:

[0073] The buffer stroke of the main and auxiliary buffers of the landing buffer mechanism is not only easy to measure, but also can directly reflect the comprehensive buffer performance of the landing buffer mechanism, so the buffer stroke is selected as the reliability characteristic quantity of each subsystem. To this end, the landing buffer mechanism was tested for buffer reliability three times. After each test, the whole machine was disassembled and three groups of effective buffer stroke test data were obtained by actual measurement, which are summarized in Table 1.

[0074] Table 1 Buffer reliability test results of a landing buffer mechanism (mm)

[0075]

[0076] In addition, based on the analysis results of previous test data and engineering experience, it is determined that the buffer strokes of the main and auxiliary buffers obey the normal distribution law, and the corresponding maximum buffer design stroke is: X1<x 1U , X2<x 2U and X3<x 2U , where x 1U =423mm, and x 2U =149mm, the maximum buffer design stroke of auxiliary buffer I and auxiliary buffer II is the same.

[0077] Then, the sample mean and standard deviation of the buffer stroke in Table 1 can be calculated according to formula (5) and formula (6), respectively. The results are shown in Table 2.

[0078] Table 2 Sample mean and standard deviation of buffer stroke of each subsystem (mm)

[0079]

[0080] Substitute the sample mean and standard deviation of each subsystem in Table 2 and the corresponding upper limit of characteristic quantity into formula (7) to calculate ψ i (i=1, 2, 3), that is:

[0081]

[0082] The calculation results are:

[0083]

[0084] At this time, according to formula (9), the reliability one-sided confidence lower limits of the main buffer, auxiliary buffer I and auxiliary buffer II with a confidence level of γ = 0.9 are obtained respectively:

[0085]

[0086]

[0087]

[0088] Among them, in step 3, "based on the confidence limit theory of sum-difference product quotient, the reliability evaluation of aerospace products under high confidence is realized according to the reliability evaluation results of completely different subsystems", and its practice is as follows:

[0089] The reliability one-sided confidence lower limit R with confidence level γ = 0.9 for the main buffer, auxiliary buffer I and auxiliary buffer II Li (i=1, 2, 3) are multiplied to calculate the initial approximate lower limit of the reliability R of the landing cushion mechanism:

[0090]

[0091] Further, according to formula (11), we can obtain R L The confidence level γ * for:

[0092]

[0093] Where, the numerical precision M = 10 5 .

[0094] Then, the value of γ in equation (26) is adjusted to γ ​​by the dichotomy method. ** =0.9311, so that γ calculated by equation (27) * =0.9, and then the reliability one-sided confidence lower limit of the landing cushion mechanism confidence γ = 0.9 is obtained as:

[0095]

[0096] Among them, in step 4, "for the situation where all subsystems are exactly the same, establish a reliability assessment method for the entire aerospace product", the method is as follows:

[0097] In engineering practice, four sets of landing buffer mechanisms are usually used in combination to form a landing buffer system. The failure of any one of the landing buffer mechanisms will cause the entire combination to lose its buffering function. In this case, the landing buffer system can be regarded as a series system consisting of four identical landing buffer mechanisms, and its reliability is:

[0098] R * =R 4 (29)

[0099] From formula (16), we can know that the reliability R of the landing cushion system corresponding to the confidence level γ = 0.9 is * The one-sided lower confidence limit for is:

[0100]

[0101] At this point, under the requirements of high reliability indicators, a small sample reliability evaluation of the landing cushion mechanism and the landing cushion system has been achieved.

Claims

1. A reliability evaluation method for converting a success-failure test into a quantitative test, characterized in that: The specific steps are as follows: Step 1: Establish a reliability series model for aerospace products based on the series structure of several independent key subsystems of aerospace products; Step 2: Based on the measured small sample measurement data of the subsystem, the normal distribution tolerance limit method is used to realize the reliability evaluation of each subsystem; Step 3: Based on the confidence limit theory of sum-difference-product-quotient, and according to the reliability evaluation results of completely different subsystems, the reliability evaluation of the aerospace product can be achieved with high confidence. Step 4: For the situation where all subsystems are exactly the same, establish a reliability assessment method for the entire aerospace product.

2. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 1, characterized in that: In step 1, suppose a certain aerospace product is composed of m completely different and independent key subsystems connected in series, and the reliability of the i-th subsystem is R i , then the reliability R of the aerospace product is: For the case where the above-mentioned aerospace product series model includes several identical and independent subsystems, the identical and independent subsystems are regarded as a key subsystem; if there are m identical and independent subsystems * The reliability of each identical subsystem is R * , they are considered as a key subsystem, and the reliability of this subsystem is 3. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 2, characterized in that: In step 1, it is impossible to directly use formula (1) to calculate the reliability of the aerospace product; because the reliability of the subsystem R i The true value of is unknown, and its one-sided confidence lower limit R with a confidence level of γ can only be obtained through statistical inference of the corresponding reliability test data. Li ,satisfy: P(R i ≥R Li )=γ i=1,2,...,m (2)。 4. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 1 or 2, characterized in that: In step 2, if the test data of the subsystem performance parameters obtained after the test pass the normal distribution test, it is considered that the reliability characteristic quantities of the subsystem all obey the normal distribution. In view of this situation, the reliability of the key subsystem is evaluated by the normal distribution tolerance method in combination with the tolerance limit of the characteristic quantity. The specific process is as follows: Assume that the performance parameter test data of each subsystem is X i (i=1,2,…,m) all obey the normal distribution, and the allowable limit of its characteristic quantity is X i <x iU or X i >x iL ; where x iU is the upper limit of the performance parameters required by the product technical indicators, x iL is the lower limit that the performance parameter needs to meet, and the reliability of the subsystem is expressed as: or: In the formula, μ i ,σ i are the mean and standard deviation of the performance parameters of the ith subsystem, respectively, and Φ(·) is the standard normal distribution function.

5. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 4, characterized in that: In step 2, if a certain aerospace product conducts n reliability tests on the whole machine, after each test, the whole machine is disassembled and the performance parameter test data x of n groups of key subsystems are obtained by actual measurement. i =(x i1 ,x i2 ,…,x in ),i=1,2,…,m; calculate the sample mean of each subsystem based on these measured data and the sample standard deviation s i : Then, the sample mean, sample standard deviation and characteristic tolerance are combined to construct the statistic ψ according to the following formula i for: When the confidence level is given as γ, the one-sided confidence lower limit of the reliability of each subsystem is R Li Solving the following equation yields: In the formula, is the R of the standard normal distribution Li Quantile, The degrees of freedom are ν = n-1, and the noncentrality parameter is The distribution function of the noncentral t distribution.

6. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 5, characterized in that: In step 2, the one-sided confidence lower limit R of the reliability of the subsystem in equation (8) is Li By looking up the numerical table of non-central t distribution or solving it by dichotomy, the reliability one-sided confidence lower limit R of each subsystem with confidence γ is obtained. Li It is expressed as: In the formula, yes The non-central parameters are calculated by formula (8) The inverse function obtained by inversion; At this point, the reliability assessment of key subsystems has been achieved based on the measured small sample metrology data of the subsystems.

7. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 1 or 6, characterized in that: In step 3, let the confidence level of each subsystem be γ and the one-sided confidence lower limit of the reliability be R Li (i=1,2,…,m), for the case where the subsystems of aerospace products are completely different and independent of each other, based on the confidence limit theory of sum-difference-product-quotient, firstly, the reliability unilateral confidence lower limit R of each subsystem with confidence level γ is Li (i=1,2,…,m) is substituted into the whole machine reliability series model, and the calculated result is used as the initial approximate value of the one-sided confidence lower limit of the system reliability R under a given confidence level γ, that is: Let γ * Represents R L The actual confidence level is calculated by the following formula: Where:

8. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 7, characterized in that: In step 3, when actually calculating, first select M according to the accuracy requirement (e.g. 10 4 , 10 5 , 10 6 ), and substitute into formula (13) to obtain Then, the corresponding Finally, the confidence γ is obtained by formula (11): * ; When Φ in formula (12) -1 When the value * in {*} is greater than 1, let the corresponding 9. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 7, characterized in that: In step 3, the value of γ in equation (10) is further adjusted by dichotomy to γ ** , so that the γ calculated by formula (11) * =γ, that is, the one-sided confidence lower limit of the reliability of aerospace products with a confidence level of γ is obtained as: In the formula, The confidence level of the reliability of subsystem i is γ ** The one-sided lower confidence limit of ; At this point, reliability assessment of the entire aerospace product with high confidence has been achieved for completely different situations of the subsystems.

10. The reliability evaluation method for converting a success-failure test to a quantitative test according to claim 1, characterized in that: In step 4, for the case where the subsystems of aerospace products are completely identical and independent of each other, assuming that the reliabilities of the m subsystems are completely identical and equal to the reliability R1 of subsystem 1, the reliability of the entire aerospace product is: At this time, the reliability unilateral confidence lower limit R of the aerospace product with a confidence level of γ L,γ Calculated by the following formula: satisfy: At this point, for situations where the subsystems are exactly the same, reliability assessment of the entire aerospace product has been achieved with a high degree of confidence.

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