CN105893696B - A kind of multistage reliability evaluation method that more products are gradually put into - Google Patents
A kind of multistage reliability evaluation method that more products are gradually put into Download PDFInfo
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Abstract
A kind of multistage reliability evaluation method that more products are gradually put into, steps are as follows: one: using the reliability growth test data of the 1st product, calculating the failure distribution function of the 1st product terminal stage；Two: according to the failure distribution function of the 1st product terminal stage, calculating the equivalent primary fault time that the 2nd product is inherited from the 1st product testing；Three: using the equivalent primary fault time of the 2nd product and the reliability growth test data of the 2nd product, calculating the failure distribution function of the 2nd product terminal stage；Four: repeating step 2 and three, successively calculate the failure distribution function of the 3rd product to i-th product terminal stage；Five: final reliability index calculates；The data that the present invention is obtained using the multistage reliability growth test that more products are gradually put into, reliability index of correlation can directly be calculated by having reached, and carry out the purpose of reliability assessment, calculated simply, be easy to use, have application value.
Description
Technical field
The present invention proposes a kind of multistage reliability evaluation method that more products are gradually put into, integrated use condition
Density function and pivot amount method carry out more multistage reliability evaluations, it can effectively solve more products gradually
Investment, every product persistently carry out the complicated propagation process of reliability growth on the basis of inheriting previous product maturity state
Reliability assessment problem belongs to and is suitable for the correlative technology fields such as the analysis of reliability growth data, reliability assessment.
Background technique
It is reliable to have become raising product for an important component of the reliability growth technology as Reliability Engineering
Property, test period is saved, test number (TN) is reduced and reduces the effective way of research fund.
Common reliability evaluation method has Duane model, AMSAA model etc..Duane model, AMSAA model ginseng
Several explicit physical meaning, form are succinct, convenient for carrying out the tracking and assessment of reliability growth process.But these models can only
The reliability evaluation launched simultaneously suitable for the reliability evaluation of separate unit product or more products.Currently, practical
Department limits according to needs, equipment time, appointed condition and research fund etc. is developed, it will usually in the multistage of a product
After reliability growth, a new product is researched and developed, the good technique state after product reliability increases before succession, then
Carry on multistage reliability growth；It repeats the above process, the multistage reliability growth that more products are gradually put into is presented
Process.For the reliability growth process of this kind of complexity, currently, still without corresponding reliability evaluation method.
For this purpose, the present invention proposes that a kind of more products gradually put into multistage reliability evaluation method, it is scientific and reasonable
The reliability level of ground evaluation corresponding product.
Summary of the invention
(1) purpose of the present invention: the present invention increases for the multistage reliability that in Practical Project, more products are gradually put into
Growth process, integrated use conditional density function and pivot amount method propose a kind of practical reliability evaluation method.This can
The test data obtained by property growth test is as follows:
1st fault time of the 1st product is t11, the 2nd fault time is t12..., n-th1Secondary fault time is2nd product is to be disposed in the long term test of the 1st product, failure zero on the basis of improving and optimizating and promoted
, the 1st fault time is t21, the 2nd fault time is t22..., n-th2Secondary fault time is…；I-th product
It is to be disposed on the basis of the long term test of (i-1)-th product, failure are zeroed and improve and optimizate promotion, the 1st event
Downtime is ti1, the 2nd fault time is ti2..., n-thiSecondary fault time isThe more products proposed are gradually put into
Multistage reliability evaluation method can effectively solve the problems, such as the reliability assessment of above-mentioned complicated reliability growth process.
(2) technical solution:
The multistage reliability evaluation method that more products of one kind of the invention are gradually put into, implementation step are as follows:
Step 1: the reliability growth test data of the 1st product: t are utilized11, t12...,Calculate the 1st product
The failure distribution function of terminal stage
Its calculation method is as follows:
Assuming that the likelihood function of parameter θ is L (θ), and θ ∈ Θ*, Θ*For Parameter Subspace, the distribution density of defined parameters θ
Function is as follows:
WhereinFor norming constant.
During actual reliability growth, usually according to testing, finding the problem, taking measures to be zeroed, continue test
Process carries out, and the reliability level that during which can reduce product failure, improve product, therefore, crash rate is monotone decreasing.In
It is, if the crash rate of the 1st product is λ1jIt gradually decreases:
It has been generally acknowledged that dead time interval obeys exponential distribution, then pivot amount is apparent from
2t11λ11~χ2,
So, λ11Distribution density function be
For λ12, pivot amount is 2 (t12-t11)λ12~χ2, and constrained: λ12≤λ11, then in given λ11Under conditions of,
λ12Conditional Distribution Density Functions be
So as to obtain λ12Distribution density be
For λ13, likelihood functionThen in given λ12Under conditions of, λ13Condition distribution it is close
Spending function is
WhereinTherefore, λ13Distribution density be
By λ11And λ12Distribution density function substitute into, can obtain
WhereinFor norming constant, it can thus be concluded that λ13Limit
It is distributed as
Similarly, it can obtainMarginal distribution functionThat is the invalid cost of the terminal stage of First product
FunctionParticularly,
Wherein:
Wherein:
Step 2: according to the failure distribution function of the 1st product terminal stageThe 2nd product is calculated from
The equivalent primary fault time that 1 product testing is inherited
Its calculation method is as follows:
Since the 2nd product is the carry out portion on the basis of long term test of the 1st product, failure zero optimization are promoted
Administration, therefore, the initial stage of the 2nd product inherits the state of the art of the 1st product terminal stage, i.e. the 2nd product
Initial stage failure distribution function F21(λ21) be the 1st product terminal stage failure distribution function
Remember the 2nd product in the primary fault timeUnder crash rate density function be
Distribution function is accordingly
Successively chooseM value: R1, R2..., Rm, then basisIt calculates
To correspondingThen, it utilizesIt can obtain
The then primary fault time of the 2nd productIt can be obtained with least-squares estimation
Step 3: the equivalent primary fault time of the 2nd product is utilizedWith the reliability growth test of the 2nd product
Data calculate the failure distribution function of the 2nd product terminal stage
Its calculation method is as follows:
According to the equivalent primary fault time of the 2nd productThe fault time obtained with the 2nd product: t21,
t22...,The equivalent reliability growth test data of available 2nd product:
Then, using the method for step 1, the failure distribution function of the 2nd product terminal stage is calculated
Step 4: repeating step 2 and three, successively calculates the invalid cost of the 3rd product to i-th product terminal stage
Function
Step 5: final reliability index calculates；
Utilize the terminal stage failure distribution function of i-th obtained productIt enablesIt can find outConfidence level be γ confidence upper limitIt enablesProduct failure rate can be found outPoint estimationLife of productPoint
EstimationIt further, is the typical mission of t (unit: hour), task for task time according to above formula
ReliabilityPoint estimationAnd at confidence level γ, Task Reliability confidence
Lower limit
By above step, the data that the multistage reliability growth test that more products can be used gradually to put into obtains,
Reliability assessment is carried out, reliability index of correlation can directly be calculated by having reached, and carry out the purpose of reliability assessment, solve test
The complicated reliability growth process that product is few, the stage is few is difficult to carry out reliability assessment with existing reliability evaluation model
Problem ensure that monotone decline of crash rate during reliability growth, meet engineering practice, calculate simple, side
Just engineers and technicians use, and have stronger application value.
(3) advantage:
The invention proposes the multistage reliability evaluation methods that more products of one kind are gradually put into, and advantage is such as
Under:
1. effectively being solved the invention proposes the multistage reliability evaluation method that more products of one kind are gradually put into
The reliability assessment problem of the above-mentioned complicated reliability growth process often occurred in practice.
2. method proposed by the invention calculates simplicity, easy to accomplish, engineers and technicians is facilitated to use, therefore had good
Good application value.
Detailed description of the invention
Fig. 1 is the method for the invention flow chart.
Symbol, code name are described as follows in figure:
tij: the jth time fault time for i-th product that achieved reliability growth test obtains；
ni: the number of faults occurred in the reliability growth test for i-th product that achieved reliability growth test obtains；
With (i-1)-th product carry out it is equivalent after the primary fault time；
With (i-1)-th product carry out it is equivalent after i-th product jth time fault time；
Seek invalid cost method: what is proposed in step 1 asks failure distribution function theoretical；
Equivalent method: excellent performance after what is proposed in step 2 increased using previous product reliability with next
The equivalent method of product.
Specific embodiment
The multistage reliability evaluation method that more products of one kind of the invention are gradually put into, flow chart such as Fig. 1 institute
Show.
Reliability growth test data instance is gradually put into more products of certain type ground system, the present invention is done further
It is described in detail.
Certain type ground system is carried out corresponding more products according to the strategy of test, test of failure, being zeroed, continue and is gradually thrown
Enter reliability test, it is as follows to obtain reliability test data:
First ground system tests 1120 hours altogether, breaks down altogether 2 times, ground system when each failure occurs
Accumulate test period successively are as follows: 180,285,1120.
Second ground system is dispose under the state of the art after failure is effectively zeroed in first ground system.
It tests 476 hours, breaks down 1 time altogether, be hardware fault.The accumulation test period of the system is 95 hours when failure occurs.
The multistage reliability evaluation method that more products of one kind of the invention are gradually put into, as shown in Figure 1, it is implemented
Steps are as follows:
Step 1: the fault data situation of first ground system is as follows:
0 <, 180 <, 285 < 1120 (test dwell time T),
T known to then11=180, t12=285, t13=1120, above-mentioned data are substituted into:
WhereinIt is calculated: C13=17563.4236, it may be assumed that
Step 2: since second ground system is to configure deployment on the basis of first ground system, it is assumed that the 2nd
Platform product is in the primary fault timeUnder crash rate density function beCorresponding distribution function
Are as follows:
Then successively choose F13(λ13) value { 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9 } (can be according to essence
Spend oneself selection institute's value number), utilize
It finds out It recycles
It can be obtained by least-squares estimation:
Therefore, second ground system obtained according to the reliability growth data of first ground system it is equivalent initial
Fault timeHour；
Step 3: the equivalent primary fault time of the 2nd ground system is utilizedWith the reliability of the 2nd ground system
Growth test data seek the failure distribution function of the 2nd ground system terminal stage
According to the equivalent primary fault time of the 2nd ground systemWhen the failure obtained with the 2nd ground system
Between: t21, t22...,The equivalent reliability growth test data of available 2nd ground system:
It willIt substitutes into
It obtains: C23=15468,
Step 4: according to above formula, F is enabled23(λ23)=0.8 obtains under confidence level γ=0.8, the mistake of single ground system
Efficiency confidence upper limitService life confidence lower limitHour.Enable F23(λ23)=0.5, can
Obtain the crash rate point estimation of ground systemThe point estimation in service lifeHour.
It is the typical mission of 10 hours, the point estimation of Task Reliability for task timeIt is setting
Under reliability γ=0.8, Task Reliability confidence lower limit
In conclusion The present invention gives a kind of multistage reliability evaluation methods that more products are gradually put into.
This method, first, in accordance with test products sequence, calculates the invalid cost of the 1st product terminal stage after obtaining test data
Function；2nd product is disposed based on the final state of the 1st product, using its equivalent nature, calculates the 2nd product
The equivalent primary fault time；Equivalent fault time data are converted by the reliability growth data that test obtains, utilize step
One method obtains the failure distribution function of second product terminal stage；Finally calculated respectively using gained failure distribution function
The point estimation of the crash rate of platform product, confidence upper limit, the reliability indexs such as point estimation, the confidence lower limit in service life complete reliability
Growth Evaluation work.
This method directly can not utilize existing model to carry out reliability evaluation for solving above-mentioned data cases
Difficulty, and ensure that monotone decreasing characteristic of crash rate during reliability growth, simplicity is calculated, it is easy to accomplish, it is convenient
Engineers and technicians use, and have good application value.
Claims (4)
1. a kind of multistage reliability evaluation method that more products are gradually put into, it is characterised in that: implementation step is such as
Under:
Step 1: the reliability growth test data of the 1st product are utilized:Calculate the 1st product most
The failure distribution function in whole stage
Step 2: according to the failure distribution function of the 1st product terminal stageThe 2nd product is calculated to produce from the 1st
The obtained equivalent primary fault time is inherited in product test
Step 3: the equivalent primary fault time of the 2nd product is utilizedWith the reliability growth test data of the 2nd product,
Calculate the failure distribution function of the 2nd product terminal stage
Step 4: repeating step 2 and three, successively calculates the failure distribution function of the 3rd product to i-th product terminal stage
Step 5: the point estimation of calculating task reliability and Reliability confidence lower limit；
Utilize the terminal stage failure distribution function of i-th obtained productIt enablesIt can find outConfidence level be γ confidence upper limitIt enablesProduct failure rate can be found outPoint estimationLife of productPoint
EstimationFurther, according to above formula, the typical mission for being t for task time, the unit of t: hour, times
Business reliabilityPoint estimationAnd at confidence level γ, Task Reliability is set
Believe lower limit
By above step, the data obtained using the multistage reliability growth test that more products are gradually put into, progress can
It is assessed by property, reliability index of correlation can directly be calculated by having reached, and carry out the purpose of reliability assessment, solve test products
Less, stage few complicated reliability growth process is difficult to carry out asking for reliability assessment with existing reliability evaluation model
Topic, ensure that monotone decline of crash rate during reliability growth, meets practical implementation situation.
2. the multistage reliability evaluation method that more products of one kind according to claim 1 are gradually put into, special
Sign is: it is described in step 1 " utilize the reliability growth test data of the 1st product:
Calculate the failure distribution function of the 1st product terminal stage", calculation method is as follows:
Assuming that the likelihood function of parameter θ is L (θ), and θ ∈ Θ*, Θ*For Parameter Subspace, the distribution density function of defined parameters θ
It is as follows:
Wherein C=∫θ∈Θ* L (θ) is norming constant；
During actual reliability growth, usually according to testing, finding the problem, taking measures to be zeroed, continue the process of test
It carries out, the reliability level that during which can reduce product failure, improve product, therefore, crash rate is monotone decreasing；Then, if
The crash rate of 1st product is λ1jIt gradually decreases:
It has been generally acknowledged that dead time interval obeys exponential distribution, then pivot amount is apparent from
2t11λ11~χ2,
So, λ11Distribution density function be
For λ12, pivot amount is 2 (t12-t11)λ12~χ2, and constrained: λ12≤λ11, then in given λ11Under conditions of, λ12's
Conditional Distribution Density Functions are
To obtain λ12Distribution density be
For λ13, likelihood functionThen in given λ12Under conditions of, λ13Condition distribution density letter
Number is
WhereinTherefore, λ13Distribution density be
By λ11And λ12Distribution density function substitute into, obtain
WhereinFor norming constant, λ is thus obtained13Invalid cost be
Similarly, it can obtainFailure distribution functionThat is the failure distribution function of the terminal stage of First productParticularly,
Wherein:
Wherein:
3. the multistage reliability evaluation method that more products of one kind according to claim 1 are gradually put into, special
Sign is: described in step 2 " according to the failure distribution function of the 1st product terminal stageCalculate the 2nd
The equivalent primary fault time that platform product is inherited from the 1st product testing", calculation method is as follows:
Since the 2nd product is disposed on the basis of the long term test of the 1st product, failure zero optimization are promoted,
Therefore, the initial stage of the 2nd product inherits the state of the art of the 1st product terminal stage, i.e., the initial rank of the 2nd product
Segment fault distribution function F21(λ21) be the 1st product terminal stage failure distribution function
Remember the 2nd product in the primary fault timeUnder crash rate density function be
Distribution function is accordingly
Successively chooseM value: R1, R2..., Rm, then basisIt is calculated corresponding
'sThen, it utilizes?
The then primary fault time of the 2nd productIt can be obtained with least-squares estimation
4. the multistage reliability evaluation method that more products of one kind according to claim 1 are gradually put into, special
Sign is: " utilizing the equivalent primary fault time of the 2nd product described in step 3With the reliability of the 2nd product
Growth test data calculate the failure distribution function of the 2nd product terminal stage", calculation method
It is as follows:
According to the equivalent primary fault time of the 2nd productThe fault time obtained with the 2nd product: It can obtain the equivalent reliability growth test data of the 2nd product:
Then, using the method for step 1, the failure distribution function of the 2nd product terminal stage is calculated
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| US6091157A (en) * | 1997-12-05 | 2000-07-18 | Advanced Micro Devices, Inc. | Method to improve internal package delamination and wire bond reliability using non-homogeneous molding compound pellets |
| CN101714182A (en) * | 2008-12-29 | 2010-05-26 | 北京航空航天大学 | Integration method of collaborating assembly design, process planning and simulation verification of complicated product |
| CN103218495A (en) * | 2013-04-23 | 2013-07-24 | 北京航空航天大学 | Design method for communication system reliability statistic test scheme on basis of competing failure |
| CN105373687A (en) * | 2014-08-18 | 2016-03-02 | 鲍珂 | Multistage experiment-based heavy vehicle power system reliability evaluation method |
-
2016
- 2016-04-21 CN CN201610252182.0A patent/CN105893696B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6091157A (en) * | 1997-12-05 | 2000-07-18 | Advanced Micro Devices, Inc. | Method to improve internal package delamination and wire bond reliability using non-homogeneous molding compound pellets |
| CN101714182A (en) * | 2008-12-29 | 2010-05-26 | 北京航空航天大学 | Integration method of collaborating assembly design, process planning and simulation verification of complicated product |
| CN103218495A (en) * | 2013-04-23 | 2013-07-24 | 北京航空航天大学 | Design method for communication system reliability statistic test scheme on basis of competing failure |
| CN105373687A (en) * | 2014-08-18 | 2016-03-02 | 鲍珂 | Multistage experiment-based heavy vehicle power system reliability evaluation method |
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