CN109376407B - Reliability evaluation method for carrier-based aircraft catapult - Google Patents
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Abstract
The invention provides a reliability evaluation method of a disposable martial arts equipment, which provides a calculation method of a point estimation value of reliability, a single-side confidence lower limit value of reliability, a lower limit value and an upper limit value of a double-side confidence interval of reliability, and the obtained point estimation value, the single-side confidence lower limit value, the lower limit value and the upper limit value of the double-side confidence interval can comprehensively evaluate the reliability of the disposable martial arts equipment, thereby solving the problems that the reliability of the disposable martial arts equipment such as a carrier-based aircraft catapult cannot be accurately modeled, the physical significance is not matched and the like, being capable of establishing a complete reliability evaluation model of the disposable martial arts equipment and improving the accuracy of an evaluation result.
Description
Technical Field
The invention belongs to the technical field of carrier-based aircraft catapult reliability engineering, and particularly relates to a reliability evaluation method for carrier-based aircraft catapult.
Background
Aiming at the weapon equipment used in time, the prior solution is to ignore the phenomenon of discretization of fault probability distribution caused by the discretization of the equipment in the use process, and still calculate the reliability of the weapon equipment used in time according to the index distribution hypothesis-based method given in GJB 899A-2009 reliability identification and acceptance test and other standards and documents.
An exponential distribution is a continuous probability distribution. The failure time of electronic products (such as computers for ships, communication equipment for ships and the like) which normally work continuously is subjected to exponential distribution, and the failure time of large complex repairable equipment (such as a ship power system, a power system and the like) can be any time (such as 101.032 hours, 1000.43 hours and the like) on an equipment accumulated working time axis. However, for the weapon equipment such as the carrier-based aircraft catapult, the warship and the like which are used according to times, the time scale of occurrence of faults is a positive integer (such as 100 times, 400 times, 10000 times and the like) in terms of times. Thus, the reliability of the present engineering in evaluating the on-demand use of the armed forces using an exponential distribution based approach suffers from three disadvantages: firstly, the theory is incomplete, and the exponential distribution is a continuous variable distribution function, so that discontinuous fault occurrence frequency variables of the weapon equipment used according to times cannot be accurately described; the physical meaning is not matched, and the probability meaning contained in the index distribution is not matched with the probability event of the fault of the equipment of the device for using the armed device in time; thirdly, the calculation result is inaccurate, and the evaluation result given by the method based on the index distribution assumption is an approximate result because of the fact that the calculation result is not perfect in theory and the physical meaning is not matched.
Disclosure of Invention
In order to solve the problems, the invention provides a reliability evaluation method of a carrier-based aircraft catapult, which can establish a complete reliability evaluation model of the carrier-based aircraft catapult and improve the accuracy of an evaluation result.
A reliability evaluation method of a carrier-based aircraft catapult comprises the following steps:
obtaining a point estimate of reliability
wherein ,
for the probability of failure of the carrier-based aircraft catapult when used n times,/for the carrier-based aircraft catapult>
The maximum likelihood estimation value of the probability V that the carrier-based aircraft catapult is not failed is used for a single time;
acquiring a single-side confidence lower limit value R of reliability Single, L (n)：
wherein ,VSingle, L A single-side confidence lower limit of the probability V of no fault for single use of the carrier-based aircraft catapult;
lower limit value R of double-side confidence interval for obtaining reliability Double, L (n) and the upper limit value R Double U (n)：
wherein ,VDouble, L A lower limit of a double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult Double U The upper limit of the double-side confidence interval of the probability V that the carrier-based aircraft catapult is used for a single time without faults;
point estimation based on reliability
Single side confidence lower limit value R for reliability Single, L (n) lower limit value R of double confidence interval of reliability Double, L (n) and the upper limit value R Double U (n) evaluating whether the reliability meets the product reliability development requirements.
Further, the carrier-based aircraft catapult uses the maximum likelihood estimated value of the probability V without faults once
The acquisition mode of (a) is as follows:
constructing a maximum likelihood function L (V):
L(V)＝V (N-Z) W Z
wherein N is the total number of effective reliability tests performed by the carrier-based aircraft catapult, Z is the accumulated failure number of the carrier-based aircraft catapult in the N reliability tests, V is the probability of failure of the carrier-based aircraft catapult in single use, and W is the probability of failure of the carrier-based aircraft catapult in single use;
obtaining the derivative L' (V) of the maximum likelihood function L (V):
L′(V)＝V (N-Z-1) (1-V) Z-1 [(N-Z)(1-V)-ZV]
let L' (V) =0, then there is:
(N-Z)(1-V)-Z×V＝0
solving the above method to obtain the maximum likelihood estimated value of the probability V that the carrier-based aircraft catapult is not faulty when being used once
The method comprises the following steps:
further, the single-side confidence lower limit V of the probability V of failure of the carrier-based aircraft catapult in single use Single, L The acquisition mode of (a) is as follows:
assuming that the confidence coefficient is gamma, obtaining a unilateral confidence lower limit V based on a binomial distribution confidence lower limit calculation method Single, L The following relation is satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
solving the above by adopting a numerical traversal method, wherein when the confidence coefficient is gamma, the carrier-based aircraft catapult is not generated when being used onceSingle-sided confidence lower limit V for probability V of failure Single, L 。
Further, the carrier-based aircraft catapult uses the lower limit V of the double-sided confidence interval of the probability V of no failure in a single use Double, L And upper limit V Double U The acquisition mode of (a) is as follows:
assuming that the confidence coefficient is gamma, obtaining the lower limit V of the double-side confidence interval based on the binomial distribution confidence interval calculation method Double, L And upper limit V Double U The following relations are satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
solving the upper part by adopting a numerical traversal method to obtain the lower limit V of the double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult when the confidence coefficient is gamma Double, L And upper limit V Double U 。
The beneficial effects are that:
the invention provides a reliability evaluation method of a carrier-based aircraft catapult, which provides a calculation method of a point estimation value, a single-side confidence lower limit value, a double-side confidence interval lower limit value and an upper limit value of the reliability, and the obtained point estimation value, the single-side confidence lower limit value, the double-side confidence interval lower limit value and the upper limit value can comprehensively evaluate the reliability of the carrier-based aircraft catapult, thereby solving the problems that the reliability of the carrier-based aircraft catapult such as the carrier-based aircraft catapult cannot be accurately modeled, the physical significance is not matched and the like, and being capable of establishing a complete reliability evaluation model of the carrier-based aircraft catapult and improving the accuracy of an evaluation result.
Drawings
FIG. 1 is a flow chart of a reliability evaluation method of a carrier-based aircraft catapult provided by the invention;
fig. 2 is a schematic diagram of a functional relationship between the number of times of use and reliability of the carrier-based aircraft catapult provided by the invention.
Detailed Description
In order to enable those skilled in the art to better understand the present application, the following description will make clear and complete descriptions of the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application.
Example 1
Referring to fig. 1, the figure is a flowchart of a reliability evaluation method of a carrier-based aircraft catapult provided in this embodiment. A reliability evaluation method of a carrier-based aircraft catapult comprises the following steps:
s1: obtaining a point estimate of reliability
wherein ,
for the probability of failure of the carrier-based aircraft catapult when used n times,/for the carrier-based aircraft catapult>
And (5) using the probability V of no fault for the carrier-based aircraft catapult for a single time.
Further, the carrier-based aircraft catapult uses the maximum likelihood estimated value of the probability V without faults once
The acquisition mode of (a) is as follows:
s101: constructing a maximum likelihood function L (V):
L(V)＝V (N-Z) W Z (2)
wherein N is the total number of effective reliability tests performed by the carrier-based aircraft catapult, Z is the number of faults accumulated by the carrier-based aircraft catapult in the N reliability tests, V is the probability of failure caused by single use of the carrier-based aircraft catapult, and W is the probability of failure caused by single use of the carrier-based aircraft catapult, wherein w=1-V.
The number of effective reliability tests F that the carrier-based aircraft catapult has been subjected to on the Z-th fault Z Detailed description will be made. Assume that a certain on-board aircraft catapult used in time carries out effective reliability tests for N times, and Z (Z is less than or equal to N) faults occur in the period. See table 1, which is a table of the number of effective reliability tests that have been performed by the carrier-based aircraft catapult each time a fault occurs.
TABLE 1
| Failure of | Failure 1 st time | Failure of 2 nd time | … | Failure of the Z th time |
| Number of tests | F 1 | F 2 | … | F Z |
wherein ,{F1 ,F 2 ,…,F Z N or less.
According to Table 1, the 1 st to Z th failure occurrence events are counted as approximateRate event A 1 ,A 2 ,…,A Z The number of continuous tests without failure before each failure occurred can be obtained as shown in table 2.
TABLE 2
Based on geometric distribution, each probability event A is established 1 ,A 2 ,…,A Z Is a probabilistic model of (a).
Probability event A corresponding to the occurrence of the 1 st failure 1 The occurrence probability is as follows:
wherein, P (·) represents a function for solving probability of occurrence of probability event, V is probability of failure of single use of the carrier-based aircraft catapult, W is probability of failure of single use of the carrier-based aircraft catapult, and obviously w=1-V.
Similarly, for the ith (1.ltoreq.i.ltoreq.Z) th fault event A i The occurrence probability is as follows:
f if the effective reliability test is cut off after the Z-th fault occurs Z =n. If the reliability test continues after the occurrence of the Z-th fault, i.e. F Z <N, the equipment continuously performs fault-free test N-F after the Z-th fault Z Next, the event is denoted as A o The occurrence probability is as follows:
so far, each probability event A is obtained 1 ,A 2 ,…,A Z Is a probabilistic model of (a).
In the case where the validity reliability test is completed after the occurrence of the Z-th failure (F Z =n), the maximum likelihood function is:
wherein ,P(Ai ) S is the probability corresponding to the ith fault event of the carrier-based aircraft catapult i The number of continuous tests without faults before the ith fault occurs.
For the case where the test is continued after the occurrence of the Z-th failure for the effective reliability test (F Z <N), the maximum likelihood function is:
wherein ,P(Ao ) For the continuous fault-free test N-F of the carrier-based aircraft catapult after the Z-th fault Z Probability of times F Z The number of effective reliability tests which are carried out on the carrier-based aircraft catapult for the occurrence of the Z-th fault is S i The number of continuous tests without faults before the ith fault occurs.
Thus, whether the reliability test is cut off after the Z-th fault occurs or the test is continued, the form of the maximum likelihood function is as follows:
L(V)＝V (N-Z) W Z (8)
s102: obtaining the derivative L' (V) of the maximum likelihood function L (V):
L′(V)＝V (N-Z-1) (1-V) Z-1 [(N-Z)(1-V)-ZV] (9)
let L' (V) =0, then there is:
(N-Z)(1-V)-Z×V＝0 (10)
the specific process of deriving the maximum likelihood function L (V) is as follows:
v in the above (N-Z-1) and (1-V)Z-1 Obviously, not 0, so L' (V) =0 is equivalent to:
(N-Z)(1-V)-Z×V＝0 (12)
s103: solving the above method to obtain the maximum likelihood estimated value of the probability V that the carrier-based aircraft catapult is not faulty when being used once
The method comprises the following steps:
s2: acquiring a single-side confidence lower limit value R of reliability Single, L (n)：
wherein ,VSingle, L And a single-side confidence lower limit of the probability V that the carrier-based aircraft catapult is single-use and does not generate faults.
Further, the single-side confidence lower limit V of the probability V of failure of the carrier-based aircraft catapult in single use Single, L The acquisition mode of (a) is as follows:
s201: assuming that the confidence coefficient is gamma, obtaining a unilateral confidence lower limit V based on a binomial distribution confidence lower limit calculation method Single, L The following relation is satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
s202: collectingSolving the above by using a numerical traversal method to obtain a single-side confidence lower limit V of the probability V of failure of single use of the carrier-based aircraft catapult when the confidence coefficient is gamma Single, L 。
S3: lower limit value R of double-side confidence interval for obtaining reliability Double, L (n) and the upper limit value R Double U (n)：
wherein ,VDouble, L A lower limit of a double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult Double U And (3) the upper limit of the double-side confidence interval of the probability V that the carrier-based aircraft catapult is used singly and does not generate faults.
Further, the carrier-based aircraft catapult uses the lower limit V of the double-sided confidence interval of the probability V of no failure in a single use Double, L And upper limit V Double U The acquisition mode of (a) is as follows:
s301: assuming that the confidence coefficient is gamma, obtaining the lower limit V of the double-side confidence interval based on the binomial distribution confidence interval calculation method Double, L And upper limit V Double U The following relations are satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
s302: solving the upper part by adopting a numerical traversal method to obtain the lower limit V of the double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult when the confidence coefficient is gamma Double, L And upper limit V Double U 。
S4: point estimation based on reliability
Single side confidence lower limit value R for reliability Single, L (n) lower limit value R of double confidence interval of reliability Double, L (n) and the upper limit value R Double U (n) evaluating whether the reliability meets the product reliability development requirements.
Example two
Based on the above embodiments, the present embodiment evaluates the reliability of a catapult of a carrier-based aircraft of a certain aircraft carrier (example needs, non-real data).
Step one, analyzing and processing reliability test data
(1) Assume that a certain carrier-based aircraft catapult performs a reliability test n=2000 times altogether, during which time a fault z=5 times occurs (example needs, non-real data).
(2) The total number of tests corresponding to the 1 st to 5 th failures are shown in table 3:
TABLE 3 Table 3
According to the table, the 1 st to 5 th fault occurrence events are counted as probability event A 1 ,A 2 ,…,A 5 And the number of continuous tests without failure before each failure occurred was counted as shown in table 4:
TABLE 4 Table 4
Step two, establishing a probability model of fault occurrence event
(1) Assuming that the probability of failure of the equipment single test task is V, the probability of failure is W, and obviously w=1 to V.
(2) Then, the 1 st failure occurrence corresponds to probability event A 1 The occurrence probability is as follows:
probability event A corresponding to occurrence of the 2 nd fault 2 The occurrence probability is as follows:
probability event A corresponding to occurrence of 3 rd fault 3 The occurrence probability is as follows:
probability event A corresponding to occurrence of the 4 th fault 4 The occurrence probability is as follows:
probability event A corresponding to the 5 th fault occurrence 5 The occurrence probability is as follows:
the corresponding probability event A of 4 times of fault-free tests is continued after the 5 th fault o The occurrence probability is as follows:
step three, constructing a maximum likelihood function
Step four, solving likelihood function
(1) Obtaining an equivalent formula (N-Z) (1-V) -Z multiplied by V=0 according to L' (V) =0, and solving the maximum likelihood estimation of the probability V that the ejector is not failed in single use as follows:
(2) according to the formula
Solving a single-sided confidence lower limit (confidence of 80%) for the probability that the ejector is not failed for single use. Substituting the test data into a formula to obtain:
solving the equation by using a numerical traversal method to obtain a single-side confidence lower limit V when the confidence coefficient is 0.8 Single, L The estimation is:
V single, L ＝0.99664180 (27)
(3) According to the formula
Solving double-sided confidence intervals (confidence of 80%) for the probability that the ejector is single-use and fails. Substituting the test data into a formula to obtain:
solving the equation by using a traversal method to obtain a double-side confidence interval [ V ] when the confidence coefficient is 80% L ,V U ]The estimation is:
step five, reliability parameter estimation
(1) Reliability point estimation
The reliability point of the catapult used n times (n is larger than or equal to 1) in succession in the combat mission is estimated as (confidence 80%):
reliability point estimation in the range of n being 1,2, … and 3000
The trend of the change with the number n of continuous use is shown in fig. 2. The reliability corresponding to the number n of partial typical continuous use is shown in table 5:
TABLE 5
(2) Reliability single-sided confidence lower limit estimation
The reliability single-side confidence lower limit of the catapult used for n times (n is more than or equal to 1) in the combat task is estimated as follows (the confidence is 80%):
within the range of n being 1,2, … and 3000, reliability single-side confidence lower limit is estimated to be R Single, L (n) the trend of change with the number of continuous use n is shown in FIG. 2. The reliability corresponding to the number n of partial typical continuous use is shown in table 6:
TABLE 6
(3) Reliability double-sided confidence interval estimation
Reliability double-sided confidence interval estimation of catapult used n times (n is greater than or equal to 1) in combat mission is as follows (confidence 80%):
taken at nReliability double confidence interval estimation [ R ] within the range of 1,2, …,3000 Double, L (n),R Double U (n)]The trend of the continuous use times n is shown in fig. 2, the reliability function in fig. 2 is a discrete function of the continuous use times n, and n is a positive integer. The reliability corresponding to the number n of partial typical continuous use is shown in table 7:
TABLE 7
Therefore, the reliability test data of the carrier-based aircraft catapult are analyzed, the effectiveness of the data is determined, and the data such as the accumulated test times, the total fault times and the number of times of tests of the carrier-based aircraft catapult are mastered. Then, based on geometric distribution, namely a memoryless discrete random variable probability distribution, which has basically the same characteristics in a discrete random variable space and an exponential distribution in a continuous random variable space, a probability model of the occurrence of the failure of the carrier-based aircraft catapult is established. And secondly, establishing a maximum likelihood function based on a geometric distribution model according to probability event basis of fault occurrence. And finally, obtaining the reliability evaluation result of the carrier-based aircraft catapult by solving the maximum likelihood function.
Of course, the present invention is capable of other various embodiments and its several details are capable of modification and variation in light of the present invention by one skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (4)
1. The reliability evaluation method of the carrier-based aircraft catapult is characterized by comprising the following steps of:
obtaining a point estimate of reliability
wherein ,
for the probability of failure of the carrier-based aircraft catapult when used n times,/for the carrier-based aircraft catapult>
The maximum likelihood estimation value of the probability V that the carrier-based aircraft catapult is not failed is used for a single time;
acquiring a single-side confidence lower limit value R of reliability Single, L (n)：
wherein ,VSingle, L A single-side confidence lower limit of the probability V of no fault for single use of the carrier-based aircraft catapult;
lower limit value R of double-side confidence interval for obtaining reliability Double, L (n) and the upper limit value R Double U (n)：
wherein ,VDouble, L A lower limit of a double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult Double U The upper limit of the double-side confidence interval of the probability V that the carrier-based aircraft catapult is used for a single time without faults;
point estimation based on reliability
Single side confidence lower limit value R for reliability Single, L (n) lower limit value R of double confidence interval of reliability Double, L (n) and the upper limit value R Double U (n) evaluate reliability isWhether the product reliability development requirement is met.
2. The method for evaluating the reliability of a carrier-based aircraft ejector according to claim 1, wherein the carrier-based aircraft ejector is single-use and does not have a maximum likelihood estimation value of a failure probability V
The acquisition mode of (a) is as follows:
constructing a maximum likelihood function L (V):
L(V)＝V (N-Z) W Z
wherein N is the total number of effective reliability tests performed by the carrier-based aircraft catapult, Z is the accumulated failure number of the carrier-based aircraft catapult in the N effective reliability tests, V is the probability of failure of the carrier-based aircraft catapult in single use, and W is the probability of failure of the carrier-based aircraft catapult in single use;
obtaining the derivative L' (V) of the maximum likelihood function L (V):
L′(V)＝V (N-Z-1) (1-V) Z-1 [(N-Z)(1-V)-ZV]
let L' (V) =0, then there is:
(N-Z)(1-V)-Z×V＝0
solving the above method to obtain the maximum likelihood estimated value of the probability V that the carrier-based aircraft catapult is not faulty when being used once
The method comprises the following steps:
3. the method for evaluating the reliability of a carrier-based aircraft ejector according to claim 2, wherein the carrier-based aircraft ejector is single-use and does not have a single-side confidence lower limit V of the probability V of failure Single, L The acquisition mode of (a) is as follows:
assuming that the confidence coefficient is gamma, obtaining a unilateral confidence lower limit V based on a binomial distribution confidence lower limit calculation method Single, L The following relation is satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
solving the upper part by adopting a numerical traversal method to obtain a single-side confidence lower limit V of the probability V of failure when the confidence coefficient is gamma, wherein the single-use failure of the carrier-based aircraft catapult is realized by using the single-side confidence lower limit V Single, L 。
4. The method for evaluating the reliability of a carrier-based aircraft ejector according to claim 2, wherein the carrier-based aircraft ejector is single-use without failure and has a lower limit V of a double-sided confidence interval of probability V Double, L And upper limit V Double U The acquisition mode of (a) is as follows:
assuming that the confidence coefficient is gamma, obtaining the lower limit V of the double-side confidence interval based on the binomial distribution confidence interval calculation method Double, L And upper limit V Double U The following relations are satisfied:
wherein ,
representing the number of combinations of k failures occurring randomly in N effective reliability tests;
solving the upper part by adopting a numerical traversal method to obtain the lower limit V of the double-side confidence interval of the probability V of single-use failure of the carrier-based aircraft catapult when the confidence coefficient is gamma Double, L And upper limit V Double U 。
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