CN115114776A - Method and device for converting Weibull type invalid data into success-failure type reliable data - Google Patents
Method and device for converting Weibull type invalid data into success-failure type reliable data Download PDFInfo
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Abstract
The application relates to a method and a device for converting Weibull invalid data into failure-type reliability data, wherein the method comprises the following steps: acquiring test time data of Weibull type invalid data, calculating maximum likelihood estimation of Weibull shape parameters and maximum likelihood estimation of Weibull scale parameters, and acquiring maximum likelihood estimation of reliability of a preset task moment; generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, calculating the simulation sample of the reliability at the preset task time, and solving the variance of the maximum likelihood estimation of the reliability at the task time; and calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time. The method and the device can equivalently convert the Weibull test time data containing failure data into success-or-failure data.
Description
Technical Field
The application relates to the technical field of reliability assessment, in particular to a method and a device for converting Weibull type invalid data into failure type reliability data.
Background
The reliability refers to the capability of the product to complete the specified functions under the specified conditions and within the specified time, is the inherent attribute of the product, and is an important index for measuring the quality of the product. The reliability of the product is accurately evaluated, and the reliability management of the product can be supported.
The types of the components of the product are very many, and from the viewpoint of reliability data, the types of the components can be classified into a success-or-failure type, an exponential type, a weibull type, and the like. The success-fail component refers to a component which does not work after working once, the index component refers to a component whose service life follows an index distribution, and the weibull component refers to a component whose service life follows a weibull distribution. For example, a missile consists of a fuze, which is a success-or-failure type component, an altimeter, which is an exponential type component, and a hydraulic assembly, which is a weibull type component. The types of components are different and the form of reliability data collected is also different. The success-failure type component collects success-failure type data comprising test times and test success times, and the exponential type component and the Weibull type component collect test time class data.
With the development of modern science and technology, the reliability of products is high, and more parts forming the products are provided, so that the reliability evaluation difficulty of complex products is high. For the reliability evaluation of complex products composed of various components, a commonly used idea at present is to convert data of different types of components into success-or-failure data by using a Modified Maximum Likelihood (MML) method, and then evaluate the reliability of the products by using the success-or-failure data of all the components.
In the existing research, there is a method for converting exponential data into success-or-failure data, however, the probability density function of the weibull distribution is:
wherein t is the lifetime, m is the shape parameter, and η is the scale parameter.
Due to the complexity of the weibull distribution, methods for converting weibull type data into success-or-failure type data are lacked in the existing research.
Disclosure of Invention
Therefore, in order to solve the above technical problems, there is a need to provide a device for a method for converting weibull type failure data into success/failure type reliability data, which can equivalently convert the failure data into success/failure type data when the weibull type test time data contains the failure data, thereby supporting complex reliability evaluation of products based on MML.
The method for converting Weibull invalid data into success-failure reliable data comprises the following steps:
acquiring test time data of Weibull type invalid data, calculating maximum likelihood estimation of Weibull shape parameters and maximum likelihood estimation of Weibull scale parameters, and acquiring maximum likelihood estimation of reliability of a preset task moment;
generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, and calculating a simulation sample of the reliability at the preset task time according to the Weibull simulation sample;
solving the variance of the maximum likelihood estimation of the reliability at the task time according to the Weibull simulation sample and the simulation sample of the reliability at the preset task time;
and calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
In one embodiment, obtaining test time data of Weibull type failure data, calculating maximum likelihood estimation of Weibull shape parameters and maximum likelihood estimation of Weibull scale parameters, and obtaining maximum likelihood estimation of reliability at a preset task time comprises:
acquiring test time data of a Weibull type with failure data, and calculating the maximum likelihood estimation of the Weibull shape parameters according to a monotonic function;
calculating the maximum likelihood estimation of the Weibull scale parameters according to the maximum likelihood estimation of the Weibull shape parameters;
and calculating the maximum likelihood estimation of the reliability of the preset task time according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters.
In one embodiment, obtaining trial time data for weibull-type failure data, calculating a maximum likelihood estimate of weibull shape parameters from a monotonic function, comprises:
wherein g (m) is a monotonic function for m, m is a shape parameter, and Weibull type data of the part is represented by (t) i ,δ i ) Wherein t is i For test time, delta i 1 represents t i To failure time, δ i 0 stands for t i The truncation time is i-1, …, n is the sample data size,
indicating that there is stale data.
In one embodiment, calculating the maximum likelihood estimate for the weibull scale parameters from the maximum likelihood estimate for the weibull shape parameters comprises:
in the formula (I), the compound is shown in the specification,
is a maximum likelihood estimate of the shape parameter m,
is a maximum likelihood estimate of the scale parameter η.
In one embodiment, calculating the maximum likelihood estimate of the reliability at the preset task time based on the maximum likelihood estimate of the weibull shape parameter and the maximum likelihood estimate of the weibull scale parameter comprises:
in the formula (I), the compound is shown in the specification,
is the maximum likelihood estimation of the reliability of the preset task time, and tau is the task time.
In one embodiment, generating the Weibull simulation samples from the maximum likelihood estimates for the Weibull shape parameters and the maximum likelihood estimates for the Weibull scale parameters comprises:
j＝1,…,r
in the formula (I), the compound is shown in the specification,
is a Weibull simulation sample, p j To obey to [0,1]The random number of (1).
In one embodiment, calculating the simulation sample of the reliability at the preset task time according to the weibull simulation sample comprises:
in the formula, R b (τ) is at preset task timeSimulation samples of reliability.
In one embodiment, solving for the variance of the maximum likelihood estimate of the reliability at the task time based on the weibull simulation samples and the simulation samples of the reliability at the preset task time comprises:
k＝1,…,B
in the formula (I), the compound is shown in the specification,
is the variance of the maximum likelihood estimate of the reliability at the task time, and B is the number of iterations.
In one embodiment, the calculating the success/failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time includes:
in the formula, (N, F) is success/failure type reliability data.
An apparatus for converting weibull-type stale data into stale reliability data, comprising:
the acquisition module is used for acquiring test time data of Weibull type invalid data, calculating the maximum likelihood estimation of Weibull shape parameters and the maximum likelihood estimation of Weibull scale parameters, and obtaining the maximum likelihood estimation of the reliability of a preset task time;
the computing module is used for generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, and computing the simulation sample with the reliability at the preset task time according to the Weibull simulation sample;
the solving module is used for solving the variance of the maximum likelihood estimation of the reliability at the task time according to the Weibull simulation sample and the simulation sample of the reliability at the preset task time;
and the output module is used for calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
According to the method and the device for converting the Weibull type invalid data into the success-failure type reliability data, when the Weibull type test time data contains the invalid data, the Weibull type test time data can be equivalently converted into the success-failure type data, so that the reliability evaluation of complex products based on MML is supported.
Drawings
FIG. 1 is a schematic flow chart illustrating a method for converting Weibull-type stale data to stale reliability data in one embodiment;
FIG. 2 is a block diagram of an apparatus for converting Weibull-type stale data into fail-safe data according to one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
As shown in fig. 1, the method for converting weibull-type failure data into success-failure-type reliability data provided by the present application, in one embodiment, includes the following steps:
step 102: acquiring test time data of Weibull type invalid data, calculating maximum likelihood estimation of Weibull shape parameters and maximum likelihood estimation of Weibull scale parameters, and acquiring maximum likelihood estimation of reliability of a preset task time.
Specifically, the method comprises the following steps:
acquiring test time data of a Weibull type with failure data, and calculating the maximum likelihood estimation of the Weibull shape parameters according to a monotonic function:
wherein g (m) is a monotonic function with respect to m, m is a shape parameter,
is a maximum likelihood estimate of the shape parameters, the Weibull type data of the memory element is (t) i ,δ i ) Wherein t is i For test time, delta i 1 represents t i To failure time, δ i 0 stands for t i The truncation time is i-1, …, n is the sample data size,
indicating that there is stale data.
It should be noted that the dichotomy in the prior art can be specifically utilized to solve
Calculating the maximum likelihood estimation of the Weibull scale parameters according to the maximum likelihood estimation of the Weibull shape parameters:
in the formula (I), the compound is shown in the specification,
is a maximum likelihood estimate of the shape parameter m,
is a maximum likelihood estimate of the scale parameter η.
Calculating the maximum likelihood estimation of the reliability of the preset task time according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters:
in the formula (I), the compound is shown in the specification,
is the maximum likelihood estimation of the reliability of the preset task time, and tau is the task time.
Note that the task time is preset according to actual problems.
Step 104: generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, and calculating the simulation sample with the reliability at the preset task time according to the Weibull simulation sample.
Specifically, the method comprises the following steps:
generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters:
j＝1,…,r
in the formula (I), the compound is shown in the specification,
is a Weibull simulation sample, p j Subject to [0,1]The random number in (1) is selected,the method can be obtained by using a common pseudo-random number generation algorithm, and r represents the simulation sample data size.
According to the Weibull simulation sample, calculating a simulation sample of the reliability of a preset task moment:
in the formula, R b (τ) is a simulated sample of the reliability at the preset task time.
Step 106: and solving the variance of the maximum likelihood estimation of the reliability at the task time according to the Weibull simulation sample and the simulation sample of the reliability at the preset task time.
Specifically, the method comprises the following steps: repeated generation of Weibull simulation samples
And simulation sample R of reliability of preset task time b (τ) B times (one complete iteration is: regenerating the random number p) j And according to p j Generating
Then according to
Obtaining R b (τ); b times of total iteration), wherein B is the iteration time, generally satisfies the condition that B is more than or equal to 1000, and can obtain B simulation samples with tau reliability
Maximum likelihood of reliability of task time is obtainedThe estimated variance:
k＝1,…,B
in the formula (I), the compound is shown in the specification,
is the variance of the maximum likelihood estimate of the reliability at the task time, and B is the number of iterations.
Step 108: and calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
Specifically, the method comprises the following steps:
in the formula, (N, F) is success/failure type reliability data, N represents the converted success/failure type test times, and F represents the converted failure type test times.
According to the method for converting the Weibull type invalid data into the success-or-failure type reliability data, when the Weibull type test time data contains the invalid data, the Weibull type test time data can be equivalently converted into the success-or-failure type data, the blank that the equivalent conversion data in the existing research is the success-or-failure type reliability data is filled, and therefore reliability evaluation of complex products based on MML is supported after data conversion is completed.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In a specific example, assuming a reliability life test was performed on 10 samples of a product hydraulic module, the 10 test time data collected was 23.8019,27.6021,32.2401,41.8375,45.5750,51.0492,62.8420,96.9323,108.0440,119.2424, where 41.8375,62.8420,119.2424 are failure data in hours.
According to the technical scheme provided by the invention, the task time is set to be 10 hours, and Weibull type test data is converted into success-or-failure type data.
Firstly, according to the maximum likelihood estimation of reliability calculated by Weibull type invalid data, the maximum likelihood estimation value of distribution parameter m is calculated
And find out
Solving maximum likelihood estimation value of distribution parameter eta
And find out
The reliability point estimate at which τ 10 is solved for is
Solving the variance of the maximum likelihood estimation of the reliability, setting B to 5000, repeatedly calculating the Weibull simulation sample and the simulation sample of the reliability of the preset task time for B times to obtain
Has a variance of
And finally, solving the equivalent converted success-failure type reliability data, wherein the converted success-failure type reliability data is obtained by taking N as 122.5671 and F as 0.1260.
As shown in fig. 2, the present application further provides a weibull-type apparatus for converting stale data to fail-safe reliability data, comprising, in one embodiment: an obtaining module 202, a calculating module 204, a solving module 206 and an output module 208, specifically:
the obtaining module 202 is configured to obtain test time data of the weibull type invalid data, calculate a maximum likelihood estimate of a weibull shape parameter and a maximum likelihood estimate of a weibull scale parameter, and obtain a maximum likelihood estimate of reliability at a preset task time;
the calculation module 204 is configured to generate a weibull simulation sample according to the maximum likelihood estimation of the weibull shape parameter and the maximum likelihood estimation of the weibull scale parameter, and calculate a simulation sample of the reliability at a preset task time according to the weibull simulation sample;
a solving module 206, configured to solve a variance of the maximum likelihood estimation of the reliability at the task time according to the weibull simulation sample and the simulation sample of the reliability at the preset task time;
and the output module 208 is configured to calculate to obtain success/failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
For the specific limitations of the apparatus for converting the weibull type failure data into the success/failure type reliability data, reference may be made to the limitations of the above method for converting the weibull type failure data into the success/failure type reliability data, and details thereof are not repeated herein. The various modules in the above-described apparatus may be implemented in whole or in part by software, hardware, and combinations thereof. The modules can be embedded in a hardware form or independent of a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. The method for converting Weibull type invalid data into success-failure type reliable data is characterized by comprising the following steps of:
acquiring test time data of Weibull type invalid data, calculating the maximum likelihood estimation of Weibull shape parameters and the maximum likelihood estimation of Weibull scale parameters, and acquiring the maximum likelihood estimation of the reliability of a preset task time;
generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, and calculating a simulation sample of the reliability at the preset task time according to the Weibull simulation sample;
solving the variance of the maximum likelihood estimation of the reliability at the task time according to the Weibull simulation sample and the simulation sample of the reliability at the preset task time;
and calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
2. The method of claim 1, wherein obtaining trial time data of Weibull-type failed data, calculating maximum likelihood estimates of Weibull shape parameters and maximum likelihood estimates of Weibull scale parameters, and obtaining maximum likelihood estimates of reliability at a predetermined mission time comprises:
acquiring test time data of Weibull type invalid data, and calculating maximum likelihood estimation of Weibull shape parameters according to a monotonic function;
calculating the maximum likelihood estimation of the Weibull scale parameters according to the maximum likelihood estimation of the Weibull shape parameters;
and calculating the maximum likelihood estimation of the reliability of the preset task time according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters.
3. The method of claim 1 or 2, wherein obtaining trial time data for weibull-type failure data, and calculating a maximum likelihood estimate of weibull shape parameters from a monotonic function comprises:
wherein g (m) is a monotonic function for m, m is a shape parameter, and Weibull type data of the part is represented by (t) i ,δ i ) Wherein t is i For test time, delta i 1 represents t i To failure time, δ i 0 stands for t i The truncation time is 1, …, n, n is the number of samplesAccording to the amount of the data,
indicating that there is stale data.
4. The method of claim 3, wherein computing the maximum likelihood estimate for the Weibull scale parameters from the maximum likelihood estimate for the Weibull shape parameters comprises:
in the formula (I), the compound is shown in the specification,
is a maximum likelihood estimate of the shape parameter m,
is a maximum likelihood estimate of the scale parameter η.
5. The method of claim 4, wherein computing the maximum likelihood estimate of the reliability at the preset task time based on the maximum likelihood estimate of the Weibull shape parameter and the maximum likelihood estimate of the Weibull scale parameter comprises:
in the formula (I), the compound is shown in the specification,
is the maximum likelihood estimation of the reliability of the preset task time, and tau is the task time.
6. The method of claim 5, wherein generating the Weibull simulation samples from the maximum likelihood estimates for the Weibull shape parameters and the maximum likelihood estimates for the Weibull scale parameters comprises:
j＝1,…,r
in the formula (I), the compound is shown in the specification,
is a Weibull simulation sample, p j To obey to [0,1]The random number of (1).
7. The method of claim 6, wherein calculating the Weibull simulation samples based on the reliability at the predetermined task time comprises:
in the formula, R b (τ) is a simulated sample of the reliability at the preset task time.
8. The method of claim 7, wherein solving for the variance of the maximum likelihood estimate of the reliability at the task time based on the weibull simulated samples and the simulated samples of the reliability at the preset task time comprises:
in the formula (I), the compound is shown in the specification,
is the variance of the maximum likelihood estimate of the reliability at the task time, and B is the number of iterations.
9. The method of claim 8, wherein calculating success-or-failure reliability data according to the maximum likelihood estimate of the reliability at the preset task time and the variance of the maximum likelihood estimate of the reliability at the task time comprises:
in the formula, (N, F) is success/failure type reliability data.
10. A weibull-type apparatus for converting stale data to stale reliability data, comprising:
the acquisition module is used for acquiring test time data of Weibull type invalid data, calculating the maximum likelihood estimation of Weibull shape parameters and the maximum likelihood estimation of Weibull scale parameters, and obtaining the maximum likelihood estimation of the reliability of a preset task time;
the computing module is used for generating a Weibull simulation sample according to the maximum likelihood estimation of the Weibull shape parameters and the maximum likelihood estimation of the Weibull scale parameters, and computing the simulation sample with the reliability at the preset task time according to the Weibull simulation sample;
the solving module is used for solving the variance of the maximum likelihood estimation of the reliability at the task time according to the Weibull simulation sample and the simulation sample of the reliability at the preset task time;
and the output module is used for calculating to obtain success-failure type reliability data according to the maximum likelihood estimation of the reliability at the preset task time and the variance of the maximum likelihood estimation of the reliability at the task time.
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