A method for designing life verification test of average life subject to type I minimum distribution

Abstract

This invention discloses a method for designing an average lifetime verification test that follows a Type I minimum distribution, comprising the following specific steps: Step 1: For products whose lifetime follows a Type I minimum distribution, determine the probability density function and cumulative distribution function of their lifetime; establish the probability function corresponding to the number of sample failures; Step 2: Establish the mapping relationship between the true average lifetime of the product and location parameters and scale parameters, and derive the correlation function between the probability function corresponding to the number of sample failures and the acceptance probability function corresponding to the true average lifetime when given a number of received failures; and establish the first constraint condition and the second constraint condition; Step 3: Preset the test conditions, calculate and output the total test duration, the number of received failures, and the number of rejected failures that meet the test conditions, and form a time-truncated test scheme. The method proposed in this invention is simple to calculate, the evaluation results are more stable, it is convenient for engineering technicians to master and use, and it is easy to apply and promote.

Description

Technical Field

[0001] This invention relates to the field of product life verification technology, and in particular to an average life verification test design method in which the lifespan follows a type I minimum distribution. Background Technology

[0002] Life verification testing is a testing technique that uses sampling statistical methods to verify whether the average lifespan of a product meets specified requirements under given risk conditions. It is a crucial link between design and verification in reliability engineering, and its results directly affect whether the product can be commercialized and delivered to users, playing a significant role in controlling production costs and ensuring safe operation. The Type I minimum distribution (also known as the Gombbel distribution) is an important distribution type in extreme value theory, mainly used to characterize engineering products with obvious "weakest link" characteristics, such as material strength, fatigue life of structural components, and lifespan of high-reliability electronic components. The failure of these products often depends on their weakest local component, and their lifespan pattern precisely conforms to the theoretical assumptions of the Type I minimum distribution. However, current design methods for average life verification tests mainly focus on the case where the lifespan distribution follows an exponential distribution. For the Type I minimum distribution, which also has a wide range of engineering applications, there is still a lack of systematic and operable verification test schemes.

[0003] Therefore, there is an urgent need to propose an average lifetime verification test design method that allows the lifetime to follow a type I minimum distribution in order to meet the needs of product verification tests. Summary of the Invention

[0004] The purpose of this invention is to provide a method for designing average lifetime verification tests in which the lifetime follows a type I minimum distribution, so as to meet the verification requirements of products.

[0005] The objective of this invention is achieved through the following technical solution: a method for designing an average lifetime verification test where the lifetime follows a Type I minimum distribution, comprising the following specific steps:

[0006] Step 1: For products whose lifetime follows a Type I minimum distribution, determine their lifetime probability density function and cumulative distribution function; and based on the test rules of time-truncated tests, establish the probability function corresponding to the number of sample failures under given total test time, location parameters, and scale parameters. Step 2: Based on the average lifetime calculation formula of the Type I minimum distribution, establish the mapping relationship between the true value of the product's average lifetime and the location and scale parameters, and derive the correlation function between the probability function corresponding to the number of sample failures when a given number of received failures is received and the acceptance probability function corresponding to the true value of the average lifetime; and based on the preset producer risk and user risk, establish the first constraint when the true value of the average lifetime is the upper limit of the test and the second constraint when the true value of the average lifetime is the lower limit of the test, respectively. Step 3: Preset test conditions. Test conditions include the manufacturer's risk requirement value, the user's risk requirement value, the upper limit of the average lifetime true value test, and the lower limit of the average lifetime true value test. Combined with the correlation function, the first constraint condition, and the second constraint condition obtained in Step 2, calculate and output the total test duration, the number of received faults, and the number of rejected faults that meet the test conditions, and form a timed truncated test plan.

[0007] Preferably, in step one, the probability function corresponding to the number of sample failures... for: ; Where T is the total duration of the experiment. The number of sample failures. For position parameters, For scale parameters; Let be the failure probability density function; the failure probability density function is: ; In the formula, Let be the probability density function that follows a type I minimum distribution; This is an indicator function; its value is 1 when the condition within the parentheses is met, and 0 otherwise. For the first The time of the failure, y is the time when the failure occurred. Total time of each failure.

[0008] As a preferred method, the Monte Carlo method is used to solve the probability function corresponding to the number of sample failures, so as to obtain the probability of the number of failures given the total test duration, location parameters, and scale parameters.

[0009] As a preferred method, in step one, when solving the probability function corresponding to the number of sample failures using the Monte Carlo method, the specific method is as follows: First, the multiple indefinite integrals of the acceptor probability function are transformed into definite integrals, as follows: ; In the formula, ; ; For the occurrence Total time of each failure; This is the total duration of the experiment; The mean time to failure. , for the first The cumulative distribution function at the time of the second failure Cumulative distribution function The inverse function; This is an indicator function; its value is [value] when the condition within the parentheses is met. Otherwise ; Then generate A set of random numbers, each set containing a set from a uniform distribution The random number drawn from the sample is denoted as the nth random number. , ; Next, for each set of random numbers, calculate the number of sample failures for each set of random numbers. The probability of time ; ; The final number of sample failures was calculated as follows: Approximate probability of the time: .

[0010] As a preferred option, the correlation function in step two is: ; This represents the true mean lifetime. True value of average lifetime The corresponding reception probability, To receive fault counts.

[0011] As a preferred option, in step two... The first constraint is: ; The second constraint is: ; in, For the risk of the producer, For the user's risk, and This indicates the lower limit of the truth test for mean lifetime. The corresponding position parameters and scale parameters; and Indicates the upper limit of average life inspection. The corresponding position parameters and scale parameters, To reject the number of faults, .

[0012] As a preferred method, the specific calculation methods for the total test duration, the number of reception failures, and the number of rejection failures in step three are as follows: N1: Set the number of reception failures The initial value is zero; N2: Substitute the user's risk requirement value and the currently set number of reception failures into the formula of the first constraint to calculate the total test duration; N3: Substitute the total test duration and the number of rejected failures obtained in step N2 into the formula of the second constraint to calculate the actual value of the producer's risk; N4: If the actual risk value of the producer is less than the required risk value of the producer, then the current solution meets the requirements, and the current total test duration, number of accepted failures, and number of rejected failures are output; otherwise, let Repeat steps N2-N4 until the requirements are met.

[0013] As a preferred option, when a sample fails during the test, a new sample is immediately replaced and the test continues until the total cumulative test time of all samples reaches the preset total test duration, at which point the test is stopped; based on the total number of sample failures counted at the end of the test, it is determined whether the average product lifespan meets the acceptance requirements.

[0014] Preferably, the product is any one of electrical connectors, structural components, or high-reliability electronic components whose lifespan follows a Type I minimum distribution.

[0015] The beneficial effects of this invention are: 1. This invention targets products whose lifetime distribution follows a Type I minimum distribution. Based on the requirements of timed truncation test, it establishes the product's acceptance probability function, derives the relationship between the true value of the product's average lifetime and the acceptance probability function, and then, based on the manufacturer's risk, the user's risk, and the upper and lower limits of the average lifetime inspection requirements, finally gives the test duration, number of accepted failures, and number of rejected failures for the product's average lifetime verification test, ensuring the efficient generation of the average lifetime verification test plan.

[0016] 2. The method proposed in this invention is simple to calculate, easy to implement, and the evaluation results are more stable, making it convenient for engineering technicians to master and use, and easy to apply and promote. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0019] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0020] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0021] like Figure 1 As shown, a method for designing an average lifetime verification test where the lifetime follows a Type I minimum distribution includes the following specific steps: Step 1: For products whose lifetime follows a Type I minimum distribution, determine their lifetime probability density function and cumulative distribution function; and based on the test rules of timed truncated tests, establish the probability function corresponding to the number of sample failures under given total test time, location parameters, and scale parameters.

[0022] In this step, when the product lifetime follows a Type I minimum distribution, the product lifetime is... probability density function and cumulative distribution function Represented as: ; In the formula, For position parameters, This is the scale parameter.

[0023] The rule for time-truncated testing is: samples must be tested within a given total test time, and when a sample fails, it must be immediately replaced with a new sample to continue testing, until the total test time for all samples reaches the specified test time. Average lifetime verification based on time-truncated testing determines whether the product's average lifetime is acceptable (i.e., whether the product's average lifetime is qualified) based on the number of sample failures at the end of the test. Therefore, it is necessary to determine the distribution function of the number of sample failures at the end of the test.

[0024] Assume the total trial time is Then the samples are tested sequentially and the following occurs. The probability of failure is: ; In the formula, For the first The time of the next failure. For the first The time of failure.

[0025] To give an analytical expression of the above formula, let ; In the formula, It indicates that something has happened. The time of the next failure Indicates the first The time to failure is then used to derive the failure probability density function from the formula: ; In the formula, Let be the probability density function that follows a type I minimum distribution; This is an indicator function; its value is 1 when the condition within the parentheses is met, and 0 otherwise. For the first The time of the failure, y is the time when the failure occurred. Total time of each failure .

[0026] Therefore, the samples were tested sequentially and the following occurred. The probability of a failure is equivalent to the probability of a given occurrence. Total time of each failure In the case of the first Total time of each failure The probability, i.e., given the total trial time Position parameters Scale parameters have The probability function of subsample failure for: ; cumulative distribution function Substituting into the above formula, we get: ; Where T is the total duration of the experiment. The number of sample failures. For position parameters, For scale parameters; This is the failure probability density function.

[0027] In particular, when When the time is greater than the total test time, it means that the lifetime of the first sample is greater than the total test time. Therefore, its probability number is: .

[0028] Furthermore, the probability function corresponding to the number of sample failures involves multiple integrals, making direct solution difficult. To address this issue, this invention employs the Monte Carlo method to solve the probability function corresponding to the number of sample failures, obtaining the probability of the number of failures given the total test duration, location parameters, and scale parameters. The specific process is as follows: First, transform the multiple indefinite integrals of the receiving probability function into definite integral form, that is: ; In the formula, ; ; For the occurrence Total time of each failure; This is the total duration of the experiment; The mean time to failure. , for the first The cumulative distribution function at the time of the second failure Cumulative distribution function The inverse function; This is an indicator function; its value is [value] when the condition within the parentheses is met. Otherwise ; Then generate A set of random numbers, each set containing a set from a uniform distribution The random number drawn from the sample is denoted as the nth random number. , ; Next, for each set of random numbers, calculate the number of sample failures for each set of random numbers. The probability of time ; ; The final number of sample failures was calculated as follows: Approximate probability of the time: .

[0029] Step 2: Based on the average lifetime calculation formula of the Type I minimum distribution, establish the mapping relationship between the true value of the product's average lifetime and the location parameters and scale parameters, and derive the correlation function between the probability function corresponding to the number of sample failures when a given number of received failures is received and the acceptance probability function corresponding to the true value of the average lifetime; and based on the preset producer risk and user risk, establish the first constraint condition when the true value of the average lifetime is the upper limit of the test and the second constraint condition when the true value of the average lifetime is the lower limit of the test.

[0030] In this step, the average lifetime formula for the Type I minimum distribution is: ; In the above formula, This represents the true mean lifetime. For position parameters; This is a scale parameter. Given a given number of receiver failures... True value of average lifespan With the probability of receiving The relationship between them is: ; In the formula, To receive the number of faults; Given a total test time Position parameters Scale parameters Below The probability of a sample failing.

[0031] in, When the true value of average lifespan To test the upper limit When the probability of receiving is: ; In the formula, Risk for the producer.

[0032] When the true value of average lifespan Lower limit of average test When the probability of receiving is: ; In the formula, This is a risk for the user.

[0033] Furthermore, based on the reception probability And are position parameters Scale parameters Number of received faults The functional relationship between them, i.e. Furthermore, based on the true value of average lifetime. With position parameters Scale parameters There exists a specific functional relationship between them, namely Therefore, given the producer's risk... User risks Upper limit of average life inspection Lower limit of average life inspection At that time, the total duration of the experiment and number of receiving faults The following two constraints must be met (i.e., the first constraint and the second constraint): First constraint: When the true value of mean lifetime is the lower limit of the test. At that time, the probability that the product is accepted is ,Right now: ; Second constraint: When the true value of the mean lifetime is the upper limit of the test. At that time, the probability of the product being rejected is ,Right now: ; Given that the formula for the second constraint is difficult to calculate in practice, the formula is adjusted and the number of rejected faults is used. Replace the number of receiver failures in the formula. The second constraint can then be transformed into the following formula: ; In the formulas for the first and second constraints mentioned above: For the risk of the producer, For the user's risk, and This indicates the lower limit of the truth test for mean lifetime. The corresponding position parameters and scale parameters; and Indicates the upper limit of average life inspection. The corresponding position parameters and scale parameters, To reject the number of faults, .

[0034] Based on the above formulas, the first constraint condition when the true mean lifetime is the upper limit of the test and the second constraint condition when the true mean lifetime is the lower limit of the test are established, which will provide a basis for the subsequent output of the test time. Number of received faults and the number of rejected faults Constraints were provided.

[0035] Step 3: Preset test conditions. Test conditions include the manufacturer's risk requirement value, the user's risk requirement value, the upper limit of the average lifetime true value test, and the lower limit of the average lifetime true value test. Combined with the correlation function, the first constraint condition, and the second constraint condition obtained in Step 2, calculate and output the total test duration, the number of received faults, and the number of rejected faults that meet the test conditions, and form a timed truncated test plan.

[0036] In this step, the specific calculation methods for the total test duration, the number of received failures, and the number of rejected failures are as follows: N1: Set the number of reception failures The initial value is zero, that is ; N2: Substitute the user's risk requirement and the currently set number of reception failures into the formula of the first constraint to calculate the total test duration. ; N3: The total test duration and the number of rejected faults calculated in step N2 ( Substitute these values ​​into the formula for the second constraint to calculate the actual value of the producer's risk. ; N4: If the actual value of the producer's risk If the value is less than the manufacturer's risk requirement, then the current solution meets the requirements, and the total test duration, number of accepted failures, and number of rejected failures are output; otherwise, let... Repeat steps N2-N4 until the requirements are met.

[0037] The products to which this invention applies are those whose lifespan follows a Type I minimum distribution, and may include any one of electrical connectors, structural components, and high-reliability electronic components.

[0038] The following is a specific implementation example to further illustrate the solution of the present invention.

[0039] Case 1: The lifespan of a certain type of electrical connector follows a type I minimum distribution. The goal is to verify the average lifespan of this connector and whether its upper limit is satisfied. (day), where the position parameter Scale parameters The corresponding lower limit of the test is (day), where the position parameter Scale parameters ; require the manufacturer to take risks User risks The specific steps are as follows: Step 1: Constructing the receive probability function.

[0040] When the product life follows a Type I minimum distribution, and its total test time is At that time, the samples were tested sequentially and the following occurred. The probability function for the second failure is: ; In the formula, The total test time, For position parameters, For scale parameters, Let the failure probability density function be expressed as: ; In the formula, Indicates the sample's expiration time. To follow a Type I minimum distribution and have a product lifetime of probability density function The probability density function is expressed as:

[0041] In the formula, For position parameters, This is the scale parameter.

[0042] Step 2: Constructing the relationship between the true mean lifetime and the reception probability function.

[0043] Given the number of receiver failures True value of average lifespan With the probability of receiving The relationship between them is: ; When the true value of mean lifetime is the upper limit of the test At (day) time, the probability of receiving is: ; When the true value of mean lifetime is the lower limit of the test At (day) time, the probability of receiving is: ; Step 3: Mean Life Validation Test Design: Given producer risk User risks Upper limit of average life inspection Lower limit of average life inspection At that time, according to the above formula, the total test duration for average life verification is... Number of received faults and the number of rejected faults Must meet: ; Therefore, based on the above constraints and the steps for generating the average lifetime verification test scheme, the average lifetime verification test schemes under different numbers of received failures and rejected failures are output, as shown in Table 1.

[0044] Table 1

[0045] This invention has the following advantages: 1. This invention targets products whose lifetime distribution follows a Type I minimum distribution. Based on the requirements of timed truncation test, it establishes the product's acceptance probability function, derives the relationship between the true value of the product's average lifetime and the acceptance probability function, and then, based on the manufacturer's risk, the user's risk, and the upper and lower limits of the average lifetime inspection requirements, finally gives the test duration, number of accepted failures, and number of rejected failures for the product's average lifetime verification test, ensuring the efficient generation of the average lifetime verification test plan.

[0046] 2. The method proposed in this invention is simple to calculate, easy to implement, and the evaluation results are more stable, making it convenient for engineering technicians to master and use, and easy to apply and promote.

[0047] This invention is not limited to the preferred embodiments described above. Anyone can derive other products in various forms under the guidance of this invention. However, regardless of any changes in shape or structure, any technical solution that is the same as or similar to this application falls within the protection scope of this invention.

Claims

1. A method for designing an average lifetime verification test where the lifetime follows a Type I minimum distribution, characterized in that, The specific steps include the following: Step 1: For products whose lifetime follows a Type I minimum distribution, determine their lifetime probability density function and cumulative distribution function; and based on the test rules of time-truncated tests, establish the probability function corresponding to the number of sample failures under given total test time, location parameters, and scale parameters. Step 2: Based on the average lifetime calculation formula of the Type I minimum distribution, establish the mapping relationship between the true value of the product's average lifetime and the location and scale parameters, and derive the correlation function between the probability function corresponding to the number of sample failures when a given number of received failures is received and the acceptance probability function corresponding to the true value of the average lifetime; and based on the preset producer risk and user risk, establish the first constraint when the true value of the average lifetime is the upper limit of the test and the second constraint when the true value of the average lifetime is the lower limit of the test, respectively. Step 3: Preset test conditions. Test conditions include the manufacturer's risk requirement value, the user's risk requirement value, the upper limit of the average lifetime true value test, and the lower limit of the average lifetime true value test. Combined with the correlation function, the first constraint condition, and the second constraint condition obtained in Step 2, calculate and output the total test duration, the number of received faults, and the number of rejected faults that meet the test conditions, and form a timed truncated test plan.

2. The method for designing an average lifetime verification test according to claim 1, characterized in that, In step one, the probability function corresponding to the number of sample failures for: ； Where T is the total duration of the experiment. The number of sample failures. For position parameters, For scale parameters; Let be the failure probability density function; the failure probability density function is: ； In the formula, Let be the probability density function that follows a type I minimum distribution; This is an indicator function; its value is 1 when the condition within the parentheses is met, and 0 otherwise. For the first The time of the failure, y is the time when the failure occurs. Total time of each failure.

3. The method for designing an average lifetime verification test according to claim 1, characterized in that, The Monte Carlo method is used to solve the probability function corresponding to the number of sample failures, so as to obtain the probability of the number of failures given the total test duration, location parameters, and scale parameters.

4. The method for designing an average lifetime verification test according to claim 3, characterized in that, In step one, when solving the probability function corresponding to the number of sample failures using the Monte Carlo method, the specific method is as follows: First, the multiple indefinite integrals of the acceptor probability function are transformed into definite integrals, as follows: ； In the formula, ; ; For the occurrence Total time of each failure; This is the total duration of the experiment; The mean time to failure. , for the first The cumulative distribution function at the time of the second failure Cumulative distribution function The inverse function; This is an indicator function; its value is [value] when the condition within the parentheses is met. Otherwise ; Then generate A set of random numbers, each set containing a set from a uniform distribution The random number drawn from the sample is denoted as the nth random number. , ; Next, for each set of random numbers, calculate the number of sample failures for each set of random numbers. The probability of time ; ； The final number of sample failures was calculated as follows: Approximate probability of the time: 。 5. The method for designing an average lifetime verification test according to claim 1, characterized in that, The correlation function in step two: ； This represents the true mean lifetime. True value of average lifetime The corresponding reception probability, To receive fault counts.

6. The method for designing an average lifetime verification test according to claim 5, characterized in that, In step two, The first constraint is: ； The second constraint is: ； in, For the risk of the producer, For the user's risk, and This represents the lower limit of the truth test for mean lifetime. The corresponding position parameters and scale parameters; and Indicates the upper limit of average life inspection. The corresponding position parameters and scale parameters, To reject the number of faults, .

7. The method for designing an average lifetime verification test according to claim 6, characterized in that, In step three, the specific calculation methods for the total test duration, the number of reception failures, and the number of rejection failures are as follows: N1: Set the number of reception failures The initial value is zero; N2: Substitute the user's risk requirement value and the currently set number of reception failures into the formula of the first constraint to calculate the total test duration; N3: Substitute the total test duration and the number of rejected failures obtained in step N2 into the formula of the second constraint to calculate the actual value of the producer's risk; N4: If the actual risk value of the producer is less than the required risk value of the producer, then the current solution meets the requirements, and the current total test duration, number of accepted failures, and number of rejected failures are output; otherwise, let Repeat steps N2-N4 until the requirements are met.

8. The method for designing an average lifetime verification test according to claim 1, characterized in that, During the test, when a sample fails, it is immediately replaced with a new sample and the test continues until the total cumulative test time of all samples reaches the preset total test duration, at which point the test is stopped; based on the total number of sample failures counted at the end of the test, it is determined whether the average lifespan of the product meets the acceptance requirements.

9. The method for designing an average lifetime verification test according to claim 1, characterized in that, The product is any one of electrical connectors, structural components, or high-reliability electronic components whose lifespan follows a Type I minimum distribution.

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