CN113704988A - Method for rapidly judging service life of chemical safety related equipment under small sample - Google Patents

Method for rapidly judging service life of chemical safety related equipment under small sample Download PDF

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CN113704988A
CN113704988A CN202110963162.5A CN202110963162A CN113704988A CN 113704988 A CN113704988 A CN 113704988A CN 202110963162 A CN202110963162 A CN 202110963162A CN 113704988 A CN113704988 A CN 113704988A
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王海清
毛奇
刘荫
刘美晨
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China University of Petroleum East China
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Abstract

The invention discloses a method for quickly judging the service life of chemical safety related equipment under a small sample, which is suitable for the field of petrochemical safety and comprises the following steps: (1) according to field device failure time xi(i 1.. n), rapidly judging whether the failure data distribution type is exponential distribution or not under a small sample by using an Anderson-Darling test method, if the assumption is rejected, deducing the failure rate variation trend, and if the assumption is accepted, continuously collecting the failure time of the equipment
Figure DDA0003222835660000011
(2) Combining with OREDA database, and obtaining acceptable failure rate by Bayesian estimation
Figure DDA0003222835660000012
And judge
Figure DDA0003222835660000013
Whether the equipment failure rate is greater than
Figure DDA0003222835660000014
(3) And judging whether the service life of the equipment exceeds the allowable service life (useful) or not, and preparing for preventive maintenance. The judging method of the invention realizes the purpose of deducing the service life of the equipment under the failure data of the small sample, and avoids serious safety accidents.

Description

Method for rapidly judging service life of chemical safety related equipment under small sample
Technical Field
The invention relates to the technical field of petroleum, petrochemical and chemical safety, in particular to a method for quickly judging the service life of chemical safety related equipment under a small sample.
Background
Safety-related equipment is widely applied to process industries and other industrial departments for ensuring the safety of production processes, detecting dangerous events in the production processes and preventing the events from developing into accidents. Safety Integrity Level (SIL) is one of the key indicators measuring safety functions of safety-related devices, and is determined by calculating the average demand-time failure probability (PFDavg) of an interlock loop. In IEC61508-6, the failure rate of safety-related equipment is assumed to be constant when calculating PFDavg, but it is assumed to be true if the in-service time of the safety-related equipment is within the allowable service life (Useful life). In IEC61508-2, when the service life of the safety-related device exceeds the allowable service life, the failure rate of the safety-related device will increase rapidly, which leads to meaningless calculation results of PFDavg under the assumption of the original constant failure rate, and is likely to cause a large calculation error and serious production safety accidents, so that the actual service life of the safety-related device needs to be determined in time.
Because the reliability of the safety-related equipment is high, field failure data samples are few, and the service life range of the safety-related equipment needs to be judged quickly under the condition of small samples, the judgment method in GB/T5080.6 can reject the assumption of constant failure rate only by using larger failure sample data, which means that when the method is used for obtaining the conclusion that the service life of the safety-related equipment exceeds the service life of the safety-related equipment, the safety-related equipment has faults for many times. In order to guarantee the safe production of a factory, a quick judgment method is needed to be capable of deducing the service life range of safety-related equipment under small sample data.
Therefore, the invention provides a method for quickly judging the service life of chemical safety related equipment under a small sample, and the distribution type of failure data and the change trend of failure rate are judged through an Anderson-Darling test method and a statistic U calculation method; based on Bayesian estimation and combined with failure data collected by enterprises, the service life range of safety-related equipment is rapidly deduced. The method needs small sample data, is fast and accurate, and provides a theoretical basis for timely preventive maintenance of safety-related equipment in a factory.
Disclosure of Invention
The invention aims to provide a method for rapidly judging the service life of chemical safety related equipment (hereinafter referred to as equipment) under a small sample aiming at the defects of the existing method, on one hand, whether the data distribution type is exponential distribution or not can be rapidly judged under the condition of small sample failure data, and if the data distribution type does not accord with the assumption of exponential distribution, the change trend of failure rate can be deduced; on the other hand, the allowable service life range of the equipment can be deduced according to the failure time of the field equipment, and since the data supplier generally does not provide the data and is closely related to the external environment and the management level of factory production, the significance of mastering the service life of the equipment to the preventive maintenance of the equipment is realized.
In order to achieve the above purpose of the present invention, the following technical solutions are adopted: (1) collecting field device failure time xi(i 1.. n), rapidly judging whether the failure data distribution type is exponential distribution under a small sample by using an Anderson-Darling test method, wherein the data needing to be calculated comprises the following steps: equipment failure rate lambda, probability integral transformation function Fn(xi) Discrete distance of
Figure BDA0003222835640000017
A critical value CV; if the hypothesis is rejected, deducing the failure rate variation trend according to whether the statistic U is greater than 0, and if the hypothesis is accepted, continuously collecting the failure time of the equipment
Figure BDA0003222835640000011
(2) Combining foreign databases and field device failure time xiUsing Bayesian estimation to derive energyAcceptable equipment failure rate
Figure BDA0003222835640000012
The risk of the producer alpha, the risk of the consumer beta and the failure rate
Figure BDA0003222835640000013
Judgment of
Figure BDA0003222835640000018
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure BDA0003222835640000014
(3) And (3) judging the allowable service life of the equipment on the basis of the step (2), and preparing for preventive maintenance.
Further, the specific step of rapidly judging whether the data distribution type is exponential distribution or not in step (1) is as follows:
p1, assuming that the distribution type of the equipment failure data is exponential distribution, estimating the equipment failure rate lambda by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure BDA0003222835640000015
in the formula: l (λ) is the maximum likelihood function, λ is the equipment failure rate, xiA device failure time (i 1.. n);
the partial derivative is calculated for lambda, and the following can be obtained:
Figure BDA0003222835640000016
let the above equation equal 0, we obtain:
Figure BDA0003222835640000021
p2 calculating discrete distance
Figure BDA0003222835640000022
Comparing it with a threshold value (CV) if
Figure BDA0003222835640000023
If the value is greater than the critical value, rejecting the assumption of exponential distribution, otherwise accepting the assumption at a significant level alpha, in the actual engineering, after discretization
Figure BDA0003222835640000024
Can be expressed as:
Figure BDA0003222835640000025
in the formula, Fn(xi) The distribution function based on exponential distribution is expressed as:
Figure BDA0003222835640000026
the CV value can be obtained by:
s1, generating equipment failure data based on exponential distribution by using a random generator, and calculating failure rate lambda by applying maximum likelihood estimation;
s2, calculating probability integral transformation function Fn (x)i)；
S3, calculating discrete distance
Figure BDA0003222835640000027
Repeating the steps S1-S3 according to the given number of Monte Carlo simulation times
Figure BDA0003222835640000028
And (5) arranging from small to large to obtain an Anderson-Darling distance vector AD, and acquiring the CV value from the distance vector according to the significance level. Taking 10000 Monte Carlo simulations as an example, the calculated distance vector AD length is 10000, the vector elements are arranged from small to large, the critical value corresponding to the significance level of 0.05 is 9500 th elements of the AD vector, and the vector is subjected to 10000 simulations, when the significance level is 0.05, the regression equation for CV can be expressed as:
Figure BDA0003222835640000029
wherein n is the number of equipment failures.
Furthermore, the specific method for judging the failure rate variation trend in the step (1) is as follows:
q1, if collecting time xrEqual to the last time of failure x of the device, the statistic U is:
Figure BDA00032228356400000210
in the formula: x is the number ofiThe time of failure of the equipment is x, and the time of the last failure of the equipment is x;
if the collection time xrIf the time is greater than the last failure time x of the equipment, the statistic U is as follows:
Figure BDA00032228356400000211
q2, if U >0, the failure rate gradually increases, which indicates that the last failure time of the equipment exceeds the service life of the equipment, and the equipment is in the aging period at the moment, if U <0, the failure rate gradually decreases, the last failure time of the equipment does not exceed the service life of the equipment, and the equipment is in the early failure period.
Further, combining the foreign database and the field device failure time x in the step (2)iObtaining acceptable device failure rate using Bayesian estimation
Figure BDA00032228356400000212
The method comprises the following specific steps:
n1, to fully utilize the failure time of the equipment collected by the enterprise, since the average value of the failure rate of the equipment in the service life stage is provided in the OREDA database, the information is taken as the settingThe failure rate lambda can be obtained by synthesizing the prior information of the failure rate and the collected equipment failure timemBayesian estimation of
Figure BDA00032228356400000213
Comprises the following steps:
Figure BDA00032228356400000214
wherein r is the number of equipment failures, alpha0、β0The lambda is a prior distribution parameter, and T is the accumulated running time of the equipment;
n2, OREDA database under the same classification number, if lambdameanNot equal to n/τ, the prior distribution parameter can be expressed as:
Figure BDA00032228356400000215
if λmeanThe a priori distribution parameters can be expressed as:
Figure BDA0003222835640000031
[λmean]means not exceeding λmeanMaximum integer of (a) (-)meanAnd SD can be obtained from the OREDA database.
Furthermore, the risk of the producer alpha, the risk of the consumer beta and the failure rate are determined in the step (2)
Figure BDA0003222835640000032
Judgment of
Figure BDA0003222835640000033
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure BDA0003222835640000034
The method comprises the following specific steps:
m1, defining the original hypothesis and the alternative hypothesis as follows:
primitive assumptions
Figure BDA0003222835640000035
Alternative assumptions
Figure BDA0003222835640000036
Because of the randomness of the test, the test risk is inevitable, and the scheme is that
Figure BDA0003222835640000037
Then, the original hypothesis is accepted with a probability not lower than 1-alpha, and
Figure BDA0003222835640000038
then rejecting the original hypothesis with a probability not higher than β;
m2, setting
Figure BDA0003222835640000039
For the failure time of the subsequently collected equipment, take
Figure BDA00032228356400000310
Let the prior distribution parameter of parameter lambda be Fπ(λ), the SPRT method is to make a likelihood ratio, where the likelihood ratio is transformed into a likelihood function at Θ1，Θ2Posterior weighted ratio of above, when the prior distribution of λ is Ga (α)π,βπ) From the nature of the conjugated distribution, the posterior distribution is Ga (. alpha.)1,β1) Wherein:
Figure BDA00032228356400000311
Figure BDA00032228356400000312
wherein, E (x)i)、Var(xi) The mathematical expectation and variance, respectively, of the prior downtime of the device. Due to the simulation informationIs a major source of pre-test information and therefore the time to failure of a device can be obtained using monte carlo simulations.
The posterior weighted ratio is:
Figure BDA00032228356400000313
let y be 2 beta1λ, one can obtain:
Figure BDA00032228356400000314
wherein,
Figure BDA00032228356400000315
expressed as a degree of freedom of 2 alpha1Chi of2Distributed random variables less than
Figure BDA00032228356400000316
The probability of (c). With the above formula, the routine A, B is introduced to give the following test rules:
when S isnStopping collecting failure data when the failure rate is less than or equal to A, and receiving H0；
When S isnStopping collecting failure data when B is greater than or equal to B, and receiving H1；
When A is<Sn<And B, continuously collecting failure data without making a decision.
According to the same considerations as a.wald, take:
Figure BDA00032228356400000317
wherein, pi0、π1The expression of (a) is:
Figure BDA00032228356400000318
wherein alpha isπ0、απ1The expression of (a) is:
Figure BDA0003222835640000041
in the formula, α represents risk of the producer, and β represents risk of the consumer.
Furthermore, the service life of the equipment is deduced in the step (3) and preventive maintenance is carried out, and the deduction method comprises the following steps:
when receiving H0At the moment, the in-service time of the equipment is in the service life range;
when receiving H1And in time, the service life of the equipment exceeds the allowable service life range, and the service life range can be judged according to the collected last failure time.
Compared with the prior art, the beneficial effects of the paper are as follows:
1. the method can quickly judge whether the data distribution type is exponential distribution or not under the condition of small sample failure data, and can also deduce the change trend of failure rate if the data distribution type does not conform to the assumption of exponential distribution;
2. the allowable service life range of the equipment can be deduced according to the failure time of the field equipment, and the data has important significance for preventive maintenance of the equipment and avoidance of serious safety production accidents.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a Monte Carlo simulation algorithm.
Detailed Description
The test method in GB5080.6 has high requirements on the length of the sample, and can obtain ideal test effect under the condition of large sample; the accuracy of the KS inspection algorithm is yet to be further improved where the distribution parameters are unknown and need to be estimated from the sample, and these drawbacks limit the application of the conventional distribution inspection algorithm to the identification of the distribution type of the failure data. The Anderson-Darling goodness-of-fit test can realize the identification of the failure data distribution type under the condition of a small sample, and the detection performance of the Anderson-Darling goodness-of-fit test is superior to that of the KS hypothesis test under the same detection condition. Based on the above analysis, the present embodiment will determine the distribution type of failure data using the Anderson-Darling test.
At present, failure data collection work in China is not systematically carried out, so that failure data collected by enterprises are not fully utilized, and in the embodiment, according to Bayesian theorem, foreign database information is used as prior information of equipment failure rate, and the prior information and the failure data collected by the enterprises are integrated to obtain Bayesian estimation of the failure rate so as to obtain the failure rate more consistent with actual equipment failure rate of the enterprises.
The present invention will be further explained with reference to the drawings and specific examples so as to enable those skilled in the art to better understand the present invention and to practice the present invention, but the examples are not intended to limit the present invention. The invention discloses a method for quickly judging the service life of chemical safety related equipment under a small sample, and the flow of the method refers to FIG. 1, and the method specifically comprises the following steps:
(1) collecting field device failure time xi(i 1.. n), rapidly judging whether the failure data distribution type is exponential distribution under a small sample by using an Anderson-Darling test method, wherein the data needing to be calculated comprises the following steps: equipment failure rate lambda, probability integral transformation function Fn(xi) Discrete distance of
Figure BDA0003222835640000042
A critical value CV; if the hypothesis is rejected, deducing the failure rate variation trend according to whether the statistic U is greater than 0, and if the hypothesis is accepted, continuously collecting the failure time of the equipment
Figure BDA0003222835640000043
Further, the method comprises the following specific steps:
p1, assuming that the distribution type of the equipment failure data is exponential distribution, estimating the equipment failure rate lambda by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure BDA0003222835640000044
in the formula: l (λ) is the maximum likelihood function, λ is the equipment failure rate, xiA device failure time (i 1.. n);
the partial derivative is calculated for lambda, and the following can be obtained:
Figure BDA0003222835640000045
let the above equation equal 0, we obtain:
Figure BDA0003222835640000046
p2 calculating discrete distance
Figure BDA0003222835640000047
Comparing it with a threshold value (CV) if
Figure BDA0003222835640000048
If the value is greater than the critical value, rejecting the assumption of exponential distribution, otherwise accepting the assumption at a significant level alpha, in the actual engineering, after discretization
Figure BDA0003222835640000051
Can be expressed as:
Figure BDA0003222835640000052
in the formula, Fn(xi) The distribution function based on exponential distribution is expressed as:
Figure BDA0003222835640000053
the CV value can be obtained by:
s1, generating equipment failure data based on exponential distribution by using a random generator, and calculating failure rate lambda by applying maximum likelihood estimation;
s2, calculating probability integral transformation function Fn (x)i)；
S3, calculating discrete distance
Figure BDA0003222835640000054
Repeating the steps S1-S3 according to the given number of Monte Carlo simulation times
Figure BDA0003222835640000055
And (5) arranging from small to large to obtain an Anderson-Darling distance vector AD, and acquiring the CV value from the distance vector according to the significance level. Taking 10000 monte carlo simulations as an example, the calculated distance vector AD length is 10000, the vector elements are arranged from small to large, the critical value corresponding to the significance level of 0.05 is 9500 th elements of the AD vector, and after 10000 simulations, when the significance level is 0.05, the regression equation of CV can be expressed as:
Figure BDA0003222835640000056
wherein n is the number of equipment failures.
Further, the method for determining the failure rate variation trend in step (1) can be summarized as calculating the statistical quantity U:
q1 failure data collection time x in this caserEqual to the last time the device failed x, the statistic U can be expressed as:
Figure BDA0003222835640000057
in the formula: x is the number ofiAnd x is the time of the failure of the equipment, and x is the time of the last failure of the equipment.
Q2, if U >0, the failure rate gradually increases, which indicates that the last failure time of the equipment exceeds the service life of the equipment, and the equipment is in the aging period at the moment, if U <0, the failure rate gradually decreases, the last failure time of the equipment does not exceed the service life of the equipment, and the equipment is in the early failure period.
(2) Combining foreign databases and field device failure time xiObtaining acceptable device failure rate using Bayesian estimation
Figure BDA0003222835640000058
The risk of the producer alpha, the risk of the consumer beta and the failure rate
Figure BDA0003222835640000059
Judgment of
Figure BDA00032228356400000510
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure BDA00032228356400000511
Further, combining foreign databases and field device failure time xiObtaining acceptable device failure rate using Bayesian estimation
Figure BDA00032228356400000512
The method comprises the following specific steps:
n1, in order to fully utilize the device failure time collected by the enterprise, since the OREDA database provides the average value of the device failure rate in the service life stage, the information is used as the prior information of the device failure rate, and the prior information and the collected device failure time are integrated to obtain the failure rate lambdamBayesian estimation of
Figure BDA00032228356400000513
Comprises the following steps:
Figure BDA00032228356400000514
wherein r is the number of equipment failures, alpha0、β0And f, calculating a prior distribution parameter and T is the accumulated running time of the equipment.
N2, in this case, λmeanThe a priori distribution parameters can be expressed as:
Figure BDA00032228356400000515
[λmean]means not exceeding λmeanMaximum integer of (a) (-)meanAnd SD can be obtained from the OREDA database.
Furthermore, the risk of the producer alpha, the risk of the consumer beta and the failure rate are determined in the step (2)
Figure BDA00032228356400000516
Judgment of
Figure BDA00032228356400000517
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure BDA00032228356400000518
The method comprises the following specific steps:
m1, defining the original hypothesis and the alternative hypothesis as follows:
primitive assumptions
Figure BDA00032228356400000519
Alternative assumptions
Figure BDA00032228356400000520
Because of the randomness of the test, the test risk is inevitable, and the scheme is that
Figure BDA00032228356400000521
Then, the original hypothesis is accepted with a probability not lower than 1-alpha, and
Figure BDA00032228356400000522
then, the original hypothesis is rejected with a probability not higher than β.
M2, setting
Figure BDA0003222835640000061
For subsequent collectionTime of failure of arriving equipment, take
Figure BDA0003222835640000062
Let the prior distribution parameter of parameter lambda be Fπ(λ), the SPRT method is to make a likelihood ratio, where the likelihood ratio is transformed into a likelihood function at Θ1，Θ2Posterior weighted ratio of above, when the prior distribution of λ is Ga (α)π,βπ) From the nature of the conjugated distribution, the posterior distribution is Ga (. alpha.)1,β1) Wherein:
Figure BDA0003222835640000063
Figure BDA0003222835640000064
wherein, E (x)i)、Var(xi) The mathematical expectation and variance, respectively, of the prior downtime of the device. Because simulation information is a major source of pre-test information, the pre-test downtime of a device can be obtained using Monte Carlo simulations. The flow of the monte carlo simulation algorithm is shown in fig. 2, and it should be emphasized that the failure data generated by monte carlo simulation is used as the test data, which does not affect the effectiveness of the computational analysis.
The posterior weighted ratio is:
Figure BDA0003222835640000065
let y be 2 beta1λ, one can obtain:
Figure BDA0003222835640000066
wherein,
Figure BDA0003222835640000067
expressed as a degree of freedom of 2 alpha1Chi of2Distributed random variables less than
Figure BDA0003222835640000068
The probability of (c). With the above formula, the routine A, B is introduced to give the following test rules:
when S isnStopping collecting failure data when the failure rate is less than or equal to A, and receiving H0；
When S isnStopping collecting failure data when B is greater than or equal to B, and receiving H1；
When A is<Sn<And B, continuously collecting failure data without making a decision.
According to the same considerations as a.wald, take:
Figure BDA0003222835640000069
wherein, pi0、π1The expression of (a) is:
Figure BDA00032228356400000610
wherein alpha isπ0、απ1The expression of (a) is:
Figure BDA00032228356400000611
in the formula, α represents risk of the producer, and β represents risk of the consumer. The production side risk α is a probability that the product is actually qualified and determined as being unqualified, and the use side risk β is a probability that the product is actually unqualified and determined as being qualified.
(3) And (3) judging the allowable service life of the equipment on the basis of the step (2), and preparing for preventive maintenance.
Furthermore, the service life of the equipment is deduced in the step (3) and preventive maintenance is carried out, and the deduction method comprises the following steps:
when receiving H0At the moment, the equipment is in use in the in-service timeThe service life is within the range;
when receiving H1And in time, the service life of the equipment exceeds the allowable service life range, and the service life range can be judged according to the collected last failure time.
The following is a specific safety-related device: the emergency relief valve is an example, and the service life determination method of the present invention will be described in further detail.
The emergency relief valve is important overpressure protection equipment in the field of petrochemical safety, and the relief protection objects of the emergency relief valve relate to a hydrogenation reactor, a hot high-pressure separator and a cold high-pressure separator. The device is simultaneously provided with 0.7MPa/min and 2.1MPa/min emergency pressure relief systems for adjusting pressure and ensuring safe operation. When the temperature rise is less than 10 ℃/min, a pressure relief system of 0.7MPa/min is used for reducing the pressure, and if the temperature rise is more than 10 ℃/min or the reaction temperature reaches 453 ℃, the pressure relief system of 2.1MPa/min is started. The failure time of the emergency pressure release valves of a certain residue hydrocracking device 2 in northern China, which has the same type and working condition but has different external environment and plant management levels, is collected, the failure modes are all the failure times which cannot be opened, and the failure time of each pressure release valve group is shown in table 1.
TABLE 1 residual oil hydrocracking unit Emergency relief valve failure time
Figure BDA0003222835640000071
According to the method for judging the service life of the emergency relief valve, firstly, the failure time distribution types of two groups of equipment are assumed to be exponential distribution, and the failure rate lambda of the equipment obtained in the steps P1 and P2 is as follows: lambda [ alpha ]1*＝1.95×10-5/h、λ2*＝2.15×10-5At significance level of 0.05, a discrete distance of failure times of the two sets of equipment can be obtained
Figure BDA0003222835640000072
Comprises the following steps:
Figure BDA0003222835640000073
critical value CV ═0.8100。
By
Figure BDA0003222835640000074
It can be seen that the type of the distribution of the time to failure of device 1 accepts the original assumption, i.e. the exponential distribution, the type of the distribution of the time to failure of device 2 rejects the assumption of the exponential distribution. From step Q1, a statistical quantity U of the failure times of the plant 2 is determined: u shape2＝1.0236>0, namely the failure rate of the equipment 2 gradually increases, the service life of the equipment is prolonged beyond the service life of the equipment, and the service life of the equipment is less than 82171 h.
At this point, the equipment 2 needs to be replaced or a strict preventive maintenance schedule is made, and the failure times of the equipment 1 continue to be collected in order to further infer the useful life of the equipment 1, as shown in table 2.
TABLE 2 failure time of Emergency relief valve of device 1
Figure BDA0003222835640000075
Determining the failure rate lambda of the device 1 during the subsequent operating time1Whether or not to increase gradually, i.e. λ1Whether or not it is greater than lambda1*. Lambda of the device in OREDAmeanIs 7.52 multiplied by 10-6H and under the same class, λmeanN/τ, failure rate λ, obtained from steps N1, N2mBayesian estimation of
Figure BDA0003222835640000076
Comprises the following steps: 2.15X 10-5/h。
With the equipment failure rate λ in Table 11*＝1.95×10-5And/h is prior information, and 20 groups of equipment failure data are generated by using Monte Carlo simulation, wherein each group comprises 10 equipment failure times. The failure data simulated by the Monte Carlo is used as test data, the effectiveness of statistical analysis is not influenced, and a more objective analysis result can be provided compared with actual engineering collected data. The prior distribution parameter α is obtained from step M2π＝8.5960，βπ442689.20, the prior distribution of failure rates λ is Ga (8.5960, 442689.20), a posteriori scoreThe cloth is Ga (12.5960,911090.20).
From step M2, Sn25.8307, a is 0.0568, B is 4.6034, α is 0.1, β is 0.1. Obviously, Sn>B, accepting hypothesis H1When the failure rate of the equipment is greater than
Figure BDA0003222835640000077
The service life of the pressure release valve exceeds the service life of the pressure release valve, and the service life of the pressure release valve is less than 122830 h.
GB/T5080.6 also provides a method for verifying the effectiveness of the constant failure rate of the equipment, and the calculated χ can be obtained by substituting 14 equipment failure times of the equipment 1 in the embodiment2When the test statistic is 16.2469 and the significance level is 0.05, according to the chi-square test critical value table: chi shape2 0.025<χ2<χ2 0.975And thus the type of the distribution of the time to failure of the device 1 conforms to the assumption of an exponential distribution, thereby drawing an erroneous conclusion that the service life of the device 1 exceeds 122830 h. The method needs a larger sample to ensure the accuracy of the judgment result, but the reliability of safety related equipment is high, and the collected failure data is less, so that larger risk study and judgment errors can be caused.
Because the service life of the equipment is related to the management level of a factory floor, a manufacturer generally cannot provide the data, the judging method can judge the range of the service life of the equipment under a small sample, can also deduce the change trend of the failure rate of the equipment, and provides reasonable basis for making a preventive maintenance plan for the factory floor.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A method for rapidly judging the service life of chemical safety related equipment under a small sample is characterized by comprising the following steps:
(1) collecting field safety-related devices (hereinafter referred to as devices for short)) Time to failure xi(i 1.. n), rapidly judging whether the failure data distribution type is exponential distribution or not under a small sample by using an Anderson-Darling test method, if the assumption is rejected, deducing the failure rate variation trend according to the statistic U, and if the assumption is accepted, continuously collecting the failure time of the equipment
Figure FDA0003222835630000011
(2) Combining foreign databases and field device failure time xiObtaining acceptable device failure rate using Bayesian estimation
Figure FDA0003222835630000012
The risk of the producer alpha, the risk of the consumer beta and the failure rate
Figure FDA0003222835630000013
Judgment of
Figure FDA0003222835630000014
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure FDA0003222835630000015
(3) And judging the allowable service life of the equipment on the basis of the step two, and preparing for preventive maintenance.
2. The method for rapidly determining the service life of chemical safety-related equipment under the small sample according to claim 1, wherein the specific steps of rapidly determining whether the distribution type of the failure data is exponential distribution under the small sample by using an Anderson-Darling test method in the step (1) are as follows:
p1, assuming that the distribution type of the equipment failure data is exponential distribution, estimating the equipment failure rate lambda by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure FDA0003222835630000016
in the formula: l (λ) is the maximum likelihood function, λ is the equipment failure rate, xiA device failure time (i 1.. n);
the partial derivative is calculated for lambda, and the following can be obtained:
Figure FDA0003222835630000017
let the above equation equal 0, we obtain:
Figure FDA0003222835630000018
p2 calculating discrete distance
Figure FDA0003222835630000019
Comparing it with a threshold value (CV) if
Figure FDA00032228356300000110
If the value is greater than the critical value, rejecting the assumption of exponential distribution, otherwise accepting the assumption at a significant level alpha, in the actual engineering, after discretization
Figure FDA00032228356300000111
Can be expressed as:
Figure FDA00032228356300000112
in the formula, Fn(xi) The distribution function based on exponential distribution is expressed as:
Figure FDA00032228356300000113
the CV value can be obtained by:
s1, generating equipment failure data based on exponential distribution by using a random generator, and calculating failure rate lambda by applying maximum likelihood estimation;
s2, calculating probability integral transformation function Fn (x)i)；
S3, calculating discrete distance
Figure FDA00032228356300000114
Repeating the steps S1-S3 according to the given number of Monte Carlo simulation times
Figure FDA00032228356300000115
Arranging from small to large to obtain an Anderson-Darling distance vector AD, obtaining a CV value from the distance vector according to a significance level alpha, calculating the length of the obtained distance vector AD to be 10000 by taking 10000 Monte Carlo simulations as an example, arranging vector elements from small to large, wherein a critical value corresponding to the significance level of 0.05 is 9500 th elements of the AD vector, and after 10000 simulations, when the significance level is 0.05, a regression equation of CV can be expressed as:
Figure FDA00032228356300000116
wherein n is the number of equipment failures.
3. The method for rapidly determining the service life of the chemical safety related equipment under the condition of the small sample as claimed in claim 1, wherein the specific method for determining the failure rate variation trend in the step (1) is as follows:
q1, if collecting time xrEqual to the last time of failure x of the device, the statistic U is:
Figure FDA00032228356300000117
in the formula: x is the number ofiThe time of failure of the equipment is x, and the time of the last failure of the equipment is x;
if the collection time xrIf the time is greater than the last failure time x of the equipment, the statistic U is as follows:
Figure FDA0003222835630000021
q2, if U >0, the failure rate gradually increases, which indicates that the last failure time of the equipment exceeds the service life of the equipment, and the equipment is in the aging period at the moment, if U <0, the failure rate gradually decreases, the last failure time of the equipment does not exceed the service life of the equipment, and the equipment is in the early failure period.
4. The method for rapidly determining the service life of the chemical safety-related equipment under the condition of small sample according to claim 1, wherein the foreign database and the field equipment failure time x are combined in the step (2)iObtaining acceptable device failure rate using Bayesian estimation
Figure FDA0003222835630000022
The method comprises the following specific steps:
n1, in order to fully utilize the device failure time collected by the enterprise, since the OREDA database provides the average value of the device failure rate in the service life stage, the information is used as the prior information of the device failure rate, and the prior information and the collected device failure time are integrated to obtain the failure rate lambdamBayesian estimation of
Figure FDA0003222835630000023
Comprises the following steps:
Figure FDA0003222835630000024
wherein r is the number of equipment failures, alpha0、β0The lambda is a prior distribution parameter, and T is the accumulated running time of the equipment;
n2, same classification in OREDA databaseUnder number, if λmeanNot equal to n/τ, the prior distribution parameter can be expressed as:
Figure FDA0003222835630000025
if λmeanThe a priori distribution parameters can be expressed as:
Figure FDA0003222835630000026
[λmean]means not exceeding λmeanMaximum integer of (a) (-)meanAnd SD can be obtained from the OREDA database.
5. The method for rapidly determining the service life of chemical safety-related equipment under small sample according to claim 1, wherein the production party risk α, the user party risk β and the failure rate in the step (2) are determined by
Figure FDA0003222835630000027
Judgment of
Figure FDA0003222835630000028
Whether the failure rate lambda of the equipment is greater than the failure rate lambda of the equipment in the period
Figure FDA0003222835630000029
The method comprises the following specific steps:
m1, defining the original hypothesis and the alternative hypothesis as follows:
primitive assumptions
Figure FDA00032228356300000210
Alternative assumptions
Figure FDA00032228356300000211
Because of the randomness of the test, the test risk is inevitable, and the schemeIn that
Figure FDA00032228356300000212
Then, the original hypothesis is accepted with a probability not lower than 1-alpha, and
Figure FDA00032228356300000213
then rejecting the original hypothesis with a probability not higher than β;
m2, setting
Figure FDA00032228356300000214
For the failure time of the subsequently collected equipment, take
Figure FDA00032228356300000215
Let the prior distribution parameter of parameter lambda be Fπ(λ), the SPRT method is to make a likelihood ratio, where the likelihood ratio is transformed into a likelihood function at Θ1，Θ2Posterior weighted ratio of above, when the prior distribution of λ is Ga (α)π,βπ) From the nature of the conjugated distribution, the posterior distribution is Ga (. alpha.)1,β1) Wherein:
Figure FDA00032228356300000216
Figure FDA00032228356300000217
wherein, E (x)i)、Var(xi) The mathematical expectation and variance of the prior downtime of the equipment, respectively, since the simulation information is a main source of the prior information, the prior downtime of the equipment can be obtained using monte carlo simulation;
the posterior weighted ratio is:
Figure FDA0003222835630000031
let y be 2 beta1λ, one can obtain:
Figure FDA0003222835630000032
wherein,
Figure FDA0003222835630000033
expressed as a degree of freedom of 2 alpha1Chi of2Distributed random variables less than
Figure FDA0003222835630000034
With the above formula, the routine A, B is introduced to give the following test rules:
when S isnStopping collecting failure data when the failure rate is less than or equal to A, and receiving H0；
When S isnStopping collecting failure data when B is greater than or equal to B, and receiving H1；
When A is<Sn<When B, failure data continues to be collected, and no decision is made;
according to the same considerations as a.wald, take:
Figure FDA0003222835630000035
wherein, pi0、π1The expression of (a) is:
Figure FDA0003222835630000036
wherein alpha isπ0、απ1The expression of (a) is:
Figure FDA0003222835630000037
in the formula, α represents risk of the producer, and β represents risk of the consumer.
6. The method for rapidly determining the service life of the chemical safety-related equipment under the condition of the small sample as claimed in claim 1, wherein the method for determining the allowable service life of the equipment based on the step two in the step (3) comprises the following steps:
when receiving H0At the moment, the in-service time of the equipment is in the service life range;
when receiving H1And in time, the service life of the equipment exceeds the allowable service life range, and the service life range can be judged according to the collected last failure time.
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