CN110334319B - Launching flight reliability evaluation method - Google Patents
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Abstract
The invention discloses a method for evaluating the reliability of launching flight, which comprises the following steps: applying a safety factor to the shelf life to be verified to obtain the shelf life to be verified of the product under the tightening condition; determining the product launching flight reliability under the tightening condition, determining the relation between the product launching flight reliability and the sample amount, and determining the sample amount required by reliability evaluation according to the set confidence coefficient, the variation coefficient and the launching flight reliability index requirement of the product. By introducing the distribution characteristic of the storage life of the product and adopting the method for evaluating the launching flight reliability under the tightening condition based on the safety coefficient, the invention can verify the extremely high launching flight reliability of the missile whole-level product after storage by using extremely few test times, thereby saving test samples and expenses.
Description
Technical Field
The invention relates to the technical field of life test and evaluation, in particular to a method for evaluating reliability of launching flight.
Background
The missile weapon has the characteristics of long-term storage and one-time use, so that the storage period of the missile and the launching flight reliability in the storage period are both very important tactical indexes in design and design. The missile whole-level product storage period research generally adopts a technical scheme of 'storage acceleration test + storage period verification test', and after the storage period verification test of the whole-level product, the reliability of launching and flying after storage needs to be evaluated. At present, the reliability of launching and flying after the product is stored mainly adopts a success-failure type launching and flying reliability evaluation method based on binomial distribution. However, in the existing transmission flight reliability evaluation method, when the transmission flight reliability index to be evaluated is high, the required sample size is large. The reliability index requirement R of the launching flight after the storage of the whole-machine-grade productLFor example, the confidence γ is 0.85 and 0.95, in the case of no fault, at least 37 samples are required, but it is difficult to meet the requirement of such a large number of samples in engineering. Therefore, the technical research for evaluating the launching flight reliability in the storage period of the missile is suitable for the situation requirements of short development period, low expenditure and high reliability requirement of the current model.
Disclosure of Invention
In view of this, the invention provides a method for evaluating reliability of launch flight, which only needs a small number of samples and meets the situation requirements of short development period, low expenditure and high reliability requirement.
The invention provides a method for evaluating the reliability of launching flight, which comprises the following steps:
applying a safety factor to the storage life to be verified to obtain the storage life ky of the product to be verified under the tightened condition, wherein k represents the safety factor, and Y represents the storage life of the product to be verified;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
determining the number of samples required by reliability evaluation according to the relationship between the product launching flight reliability and the sample size and the set confidence coefficient, the variation coefficient and the launching flight reliability index requirement of the product
Wherein the determining the relationship between the product launch flight reliability and the sample size comprises:
the following relation 1 is obtained according to the condition that the product has no failure:
obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein R isL(Y) represents the launching flight reliability index requirement of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Representing the inverse operation of a function phi, wherein the function phi represents a standard normal distribution function;
and deducing the relation between the product launching flight reliability and the sample size according to the relation 1 and the relation 2:
further, when the product storage life follows a normal distribution, the determining the product launching flight reliability under the tightening condition comprises: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; σ represents the variance of the product shelf life distribution.
Furthermore, the value range of the safety coefficient k is 1.2-2.
Further, the safety factor k is 1.5.
As another embodiment of the invention, a method for evaluating the reliability of a launch flight comprises the following steps
The method comprises the following steps:
applying a safety factor to the storage life to be verified to obtain the storage life ky of the product to be verified under the tightened condition, wherein k represents the safety factor, and Y represents the storage life of the product to be verified;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
according to the relationship between the product launching flight reliability and the sample size, the launching flight reliability is evaluated according to the set confidence coefficient, the variation coefficient and the given sample size
Wherein the determining the relationship between the product launch flight reliability and the sample size comprises:
the following relation 1 is obtained according to the condition that the product has no failure:
obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein R isL(Y) represents the launch flight reliability of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Representing the inverse operation of a function phi, wherein the function phi represents a standard normal distribution function;
and deducing the relation between the product launching flight reliability and the sample size according to the relation 1 and the relation 2:
further, the determining the launching flight reliability of the product under the tightening condition comprises: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; σ represents the variance of the product shelf life distribution.
Furthermore, the value range of the safety coefficient k is 1.2-2.
Further, the safety factor k is 1.5.
From the above, the launching flight reliability evaluation method provided by the invention can verify the extremely high launching flight reliability of the missile complete machine-level product after storage by introducing the storage life distribution characteristics of the product and adopting the launching flight reliability evaluation method under the tightening condition based on the safety coefficient with extremely few test times, thereby saving test samples and expenses.
In addition, under the conditions of given confidence coefficient, lower limit index of launching flight reliability after storage, safety coefficient and variation coefficient, the scheme can directly give the sample amount required by the test, and provides basis for the test design, and the number of the test samples obtained by the scheme is ideal for the aerospace field, so that the problem of reliability evaluation of small samples can be solved, and the method has extremely high theoretical and application values for the evaluation of launching flight reliability after storage of missiles or other types of equipment.
Drawings
FIG. 1 is a flow chart of a transmit flight reliability assessment method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a transmit flight reliability assessment method according to another embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Based on the above purpose, the method for evaluating the reliability of launching flight provided by the invention, as shown in fig. 1, comprises the following steps:
applying a safety factor to the shelf life to be verified to obtain the shelf life to be verified of the product under the tightening condition;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
and determining the number of samples required by reliability evaluation according to the relationship between the product launching flight reliability and the sample size and the set confidence coefficient, the variation coefficient and the launching flight reliability index requirement of the product.
In the embodiment of the invention, the shelf life to be verified of the product under the tightening condition is kY, wherein k represents a safety factor; y denotes the shelf life of the product to be verified.
When the storage life of the product is subjected to normal distribution, the step of determining the launching flight reliability of the product under the tightening condition comprises the following steps: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; σ represents the variance of the product shelf life distribution; the function Φ represents a standard normal distribution function.
In the embodiment of the invention, the value range of the safety coefficient k can be 1.2-2. In particular, the safety factor k may be 1.5.
In an embodiment of the present invention, the step of determining the relationship between the product launch flight reliability and the sample size comprises:
firstly, according to the condition that the product has no failure, a binomial distribution launching flight reliability evaluation method is utilized to obtain the following relation 1:
secondly, obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein Y represents the shelf life of the product to be verified; rL(Y) represents the launching flight reliability index requirement of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Represents the inverse operation of the function phi, where the function phi represents the standard normal distribution function.
How to obtain the above relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-or-failure type verification is described below.
Specifically, the following formula (1) can be obtained by calculating the formula of the product launching flight reliability under the tightening condition:
kY＝uL-Φ-1[RL(k，Y)]·σ (1)；
the reliability of the product launch flight under the non-tightening condition can be referred to the following formula (2):
operating on the above equation (2) can result in: u ═ YL-Φ-1[RL(Y)]·σ；
At this time, let RL(k,Y)＝RL(n, f, γ), the above relation 1 is obtained:
finally, the relationship between the determined product launching flight reliability and the sample size can be obtained by derivation according to the relation 1 and the relation 2:
therefore, when the confidence coefficient, the variation coefficient and the emission flight reliability index requirement of the product are given, the number of samples required by reliability evaluation can be determined according to the relation between the emission flight reliability of the product and the sample size.
For example, table 1 below shows a scheme table of the test sample amount obtained from the relational expression of the product launch flight reliability and the sample amount when the variation (coefficient of variation) is a known number, that is, when c is 0.1 and the confidence γ is 0.8:
TABLE 1
As can be seen from the above Table 1, when the launch flight reliability index of the product requires a certain time, the greater the safety factor k, the smaller the required sample size. And when the safety factor k is 1, the required sample amount is equal to the sample amount required by adopting the success-failure type transmitting flight reliability assessment method based on the binomial distribution. Therefore, the method can effectively reduce the sample amount required by the test during the test design, thereby saving the test sample and the expenditure.
As another embodiment of the present invention, as shown in fig. 2, a method for evaluating reliability of a launch flight includes the following steps:
applying a safety factor to the shelf life to be verified to obtain the shelf life to be verified of the product under the tightening condition;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
and according to the relationship between the product launching flight reliability and the sample size, evaluating the launching flight reliability according to the set confidence coefficient, the variation coefficient and the given sample size.
In the embodiment of the invention, the shelf life to be verified of the product under the tightening condition is kY, wherein k represents a safety factor; y denotes the shelf life of the product to be verified.
When the storage life of the product is subjected to normal distribution, the step of determining the launching flight reliability of the product under the tightening condition comprises the following steps: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; σ represents the variance of the product shelf life distribution; the function Φ represents a standard normal distribution function.
In the embodiment of the invention, the value range of the safety coefficient k can be 1.2-2. In particular, the safety factor k may be 1.5.
In an embodiment of the present invention, the step of determining the relationship between the product launch flight reliability and the sample size comprises:
firstly, according to the condition that the product has no failure, a binomial distribution launching flight reliability evaluation method is utilized to obtain the following relation 1:
secondly, obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein Y represents the shelf life of the product to be verified; rL(Y) represents the launching flight reliability index requirement of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Represents the inverse operation of the function phi, where the function phi represents the standard normal distribution function.
And finally, deriving the relation between the determined product launching flight reliability and the sample size according to the relation 1 and the relation 2:
according to the relation, under the condition of no fault, the variation coefficient c of the known product is obtained, the safety coefficient k and the confidence coefficient gamma are given, and the single-side confidence lower limit evaluation result of the launching flight reliability of the product is obtained through n times of tests.
The evaluation results of the single confidence lower limit of the post-storage launch flight reliability of the product when the confidence γ is 0.8 and c is 0.1 are shown in table 2 below:
TABLE 2
As can be seen from table 2 above, under the condition of a certain sample size, the higher the safety factor is, the higher the estimated launch flight reliability is, and the higher the validity of the estimated result is.
According to the scheme, by introducing the storage life distribution characteristics of the product and adopting the launching flight reliability evaluation method under the tightening condition based on the safety coefficient, the extremely high launching flight reliability of the missile whole-level product after storage can be verified by using extremely few test times, so that test samples and expenses are saved.
Under the conditions of given confidence coefficient, lower limit index of launching flight reliability after storage, safety coefficient and variation coefficient, the scheme can directly give the sample amount required by the test, provides basis for the test design, and the number of the test samples obtained by the scheme is ideal for the aerospace field, can solve the problem of reliability evaluation of small samples, and has extremely high theoretical and application value for the launching flight reliability evaluation of missiles or other types of equipment after storage.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (8)
1. A method for evaluating the reliability of a launch flight is characterized by comprising the following steps:
applying a safety factor to the storage life to be verified to obtain the storage life ky of the product to be verified under the tightened condition, wherein k represents the safety factor, and Y represents the storage life of the product to be verified;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
determining the number of samples required by reliability evaluation according to the relationship between the product launching flight reliability and the sample size and the set confidence coefficient, the variation coefficient and the launching flight reliability index requirement of the product,
wherein the determining the relationship between the product launch flight reliability and the sample size comprises:
the following relation 1 is obtained according to the condition that the product has no failure:
obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein R isL(Y) represents the launching flight reliability index requirement of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Representing the inverse operation of a function phi, wherein the function phi represents a standard normal distribution function;
and deducing the relation between the product launching flight reliability and the sample size according to the relation 1 and the relation 2:
2. the method of claim 1,
the step of determining the launching flight reliability of the product under the tightening condition comprises the following steps: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; sigma tableThe variance of the product shelf life distribution is shown.
3. The method according to claim 1, wherein the safety factor k is in a range of 1.2-2.
4. The method of claim 3, wherein the safety factor k is 1.5.
5. A method for evaluating the reliability of a launch flight is characterized by comprising the following steps:
applying a safety factor to the storage life to be verified to obtain the storage life ky of the product to be verified under the tightened condition, wherein k represents the safety factor, and Y represents the storage life of the product to be verified;
determining the launching flight reliability of the product under the tightening condition according to the storage period to be verified of the product under the tightening condition, the expected lower limit of the actual storage life of the product and the variance of the storage life distribution of the product;
determining the launching flight reliability of the product under the non-failure condition according to a success-failure type launching flight reliability evaluation method of the binomial distribution;
determining the relation between the product launching flight reliability and the sample size according to the conditions that the product launching flight reliability obtained under the tightening condition is equal to the product launching flight reliability obtained by the success-failure type launching flight reliability evaluation method and the product does not fail;
according to the relationship between the product launching flight reliability and the sample size, the launching flight reliability is evaluated according to the set confidence coefficient, the variation coefficient and the given sample size,
wherein the determining the relationship between the product launch flight reliability and the sample size comprises:
the following relation 1 is obtained according to the condition that the product has no failure:
obtaining the following relation 2 according to the condition that the product launching flight reliability under the tightening condition is equal to the product launching flight reliability under the success-failure type verification:
wherein R isL(Y) represents the launch flight reliability of the product after Y years of storage; rL(n, f, gamma) represents the launching flight reliability of the product under success-failure type verification; n is the sample size; f represents the number of failed tests in n tests; gamma is the confidence coefficient; c represents a variation coefficient; function phi-1Representing the inverse operation of a function phi, wherein the function phi represents a standard normal distribution function;
and deducing the relation between the product launching flight reliability and the sample size according to the relation 1 and the relation 2:
6. the method of claim 5, wherein said determining product launch flight reliability under tightened conditions comprises: determining the product launch flight reliability according to the following equation:
wherein R isL(k, Y) represents the launch flight reliability of the product after Y years of storage under stressed conditions; u shapeLRepresents a desired lower limit for the actual shelf life of the product; σ represents the variance of the product shelf life distribution.
7. The method according to claim 5, wherein the safety factor k is in a range of 1.2-2.
8. The method of claim 5, wherein the safety factor k is 1.5.
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