CN107301285B - Non-electronic product sequential verification test method based on residual life prediction - Google Patents

Abstract

The invention discloses a non-electronic product sequential verification test method based on residual life prediction, which comprises the steps of firstly, establishing a wiener degradation model of a product by utilizing monitoring data of a test product, and estimating parameters of the degradation model; secondly, obtaining a probability density function f of the residual life T of the sample under test by using a residual life prediction method based on a wiener process_T|X(τ)(t | X (τ)) and the cumulative distribution function F_T|X(τ)(T | X (tau)) and calculating to obtain an expected value E (T | X (tau)) of the residual service life, and taking the total service life value E (T | X (tau)) + tau of the product as new fault data to make a judgment in advance; because the judgment is made in advance, a certain risk is increased for the producer and the consumer, so that the initially determined risk values of the producer and the consumer (the risk alpha of the producer and the risk beta of the consumer) are changed, and in order to keep the total risk value borne by the producer and the consumer unchanged, the initially determined risk values of the producer and the consumer are respectively adjusted to alpha 'and beta'; and finally, substituting all fault data containing the new fault data, corresponding alpha 'and beta' values and the like into a receiving and rejecting equation, and further making a judgment.

Description

Non-electronic product sequential verification test method based on residual life prediction

The technical field is as follows:

the invention relates to a non-electronic product sequential verification test method based on residual life prediction.

Background art:

the probability ratio sequential sampling test schemes provided by GJB 899-899A-2009 standard and MIL-STD-781D standard of the US army are all based on the assumption that the product failure time follows exponential distribution, and the assumption is true for most electronic products. However, most non-electronic products do not comply with exponential distribution, but rather comply or approximately comply with Weibull distribution, so that a probability ratio sequential test scheme of Weibull distribution is given in the handbook of engineering for reliability and maintenance (the following book). However, since the testing time required for long-life non-electronic products is long, reducing the verification testing time is a focus of current attention. The accelerated life test can reduce the test time, but the accelerated life test has high requirements on test equipment, and the research on the aspect of the current accelerated life model is not perfect. Therefore, a large amount of monitoring information generated in the product test process is fully utilized, the idea of residual life prediction is adopted, and the prediction of the fault time of the product is an effective way for reducing the test time. Practice shows that in many occasions, the state and the behavior of a product are non-monotonous, and a degradation model based on the wiener process can well describe the non-monotonous degradation process, so that the residual life prediction based on the wiener process is widely researched and applied.

At present, no literature exists for combining the residual life prediction based on the wiener process with a probability ratio sequential test scheme of Weibull distribution so as to achieve the purpose of shortening the test time of long-life non-electronic products.

The invention content is as follows:

the invention provides a non-electronic product sequential verification test method based on residual life prediction for solving the problems in the prior art, which can solve the problem that the test time of a long-life product is too long because residual life information hidden in product monitoring data is not utilized in a non-electronic product sequential verification test scheme given by reliability and maintainability engineering handbook (the following book).

The technical scheme adopted by the invention is as follows: a non-electronic product sequential verification test method based on residual life prediction comprises the following steps:

firstly, according to the performance degradation data monitored by the finished test sample and the ongoing test sample, establishing a wiener degradation model of a product and estimating model parameters, and according to a residual life prediction method based on the wiener process, obtaining a probability density function f of the residual life T of the ongoing test sample_T|X(τ)(t | X (τ)) and the cumulative distribution function F_T|X(τ)(t|X(τ))；

Next, the expected remaining life values are calculated as:

the total lifetime value of the sample was obtained:

t_n＝E(T|X(τ))+τ (2)

and calculating the risk values brought to the producer and the user by making a judgment in advance as follows:

R_{risk_product}＝1-F_T|X(τ)(E(T|X(τ))|X(τ)) (3)

R_{risk_customer}＝F_T|X(τ)(E(T|X(τ))|X(τ)) (4)

then, in order to ensure that the respective total risks of the producer and the consumer are not changed, the producer risk and the consumer risk substituted into the decision formula are respectively adjusted to be:

finally, the n-1 sample fault data t of the completed test is processed_i(i-1, 2 …, n-1), and the expected total lifetime t of the sample under test_nThe shape parameter m is estimated by plotting E (T | X (τ)) + τ on weibull probability paper, and a dimensionless value is calculated according to equation (7):

according to the receiving equation (8) and the rejection equation (9), K under n sample faults is obtained through calculation respectively_aAnd K_nValue of

Wherein:

θ₀an MFBF upper check limit for the mean fault interval of the product;

θ₁the MFBF check lower limit is the mean failure interval of the product;

d is the discrimination ratio, i.e. d ═ θ₀/θ₁；

If K < K_nMaking a rejection decision; if K > K_aMaking a reception decision; otherwise, continuing the test.

The invention has the following beneficial effects: the invention replaces the traditional Weibull distribution probability ratio sequential test scheme, adopts a residual life prediction method, and makes a receiving or rejecting judgment by controlling the total risk of a production party and a use party, thereby saving the test time.

Description of the drawings:

fig. 1 is a schematic diagram of a non-electronic product sequential verification test method based on residual life prediction.

The specific implementation mode is as follows:

the invention will be further described with reference to the accompanying drawings.

The invention discloses a non-electronic product sequential verification test method based on residual life prediction, which comprises the following steps:

firstly, according to the performance degradation data monitored by the finished test sample and the ongoing test sample, establishing a wiener degradation model of the product and estimating model parameters (drift parameter lambda and diffusion parameter sigma), and according to a residual life prediction method based on the wiener process, obtaining a probability density function f of the residual life T of the ongoing test sample_T|X(τ)(tX (τ)) and the cumulative distribution function F_T|X(τ)(t|X(τ))；

Next, the expected remaining life values are calculated as:

the total lifetime value of the sample was obtained:

t_n＝E(T|X(τ))+τ (2)

and calculating the risk values brought to the producer and the user by making a judgment in advance as follows:

R_{risk_product}＝1-F_T|X(τ)(E(T|X(τ))|X(τ)) (3)

R_{risk_customer}＝F_T|X(τ)(E(T|X(τ))|X(τ)) (4)

then, in order to ensure that the respective total risks of the producer and the consumer are not changed, the producer risk and the consumer risk substituted into the decision formula are respectively adjusted to be:

finally, the n-1 sample fault data t of the completed test is processed_i(i-1, 2 …, n-1), and the expected total lifetime t of the sample under test_nThe shape parameter m is estimated by plotting E (T | X (τ)) + τ on weibull probability paper. And (4) calculating according to the formula (7) to obtain a dimensionless value:

according to the receiving equation (8) and the rejection equation (9), K under n sample faults is obtained through calculation respectively_aAnd K_nThe value is obtained.

Wherein:

θ₀an MFBF upper check limit for the mean fault interval of the product;

θ₁the MFBF check lower limit is the mean failure interval of the product;

d is the discrimination ratio, i.e. d ═ θ₀/θ₁。

If K < K_nMaking a rejection decision; if K > K_aMaking a reception decision; otherwise, continuing the test.

The following describes a non-electronic product sequential verification test method based on residual life prediction according to the present invention with specific embodiments:

1) parameter estimation of wiener process

Assuming that n-1 sample tests have been completed, the nth sample test is currently being performed, with each sample i (i ═ 1, 2 …, n) at an initial time t_i0The amount of deterioration of the properties of (A) is X (t)_i0) 0; at the moment of time

The measured sample property degradation amounts are respectively

Note Δ x_ij＝X(t_ij)-X(t_i(j-1)) Is the sample i at time (t)_i(j-1),t_ij) The amount of degradation of performance between, Δ x is known from the nature of the wiener process_ijObey a normal distribution:

Δx_ij～N(λΔt_ij,σ²Δt_ij)

where Δ t_ij＝t_ij-t_i(j-1)，i＝1，2··，n，j＝1，2…，m_i。

Establishing a likelihood function using the monitored performance degradation data:

the parameters λ and σ can be directly obtained from the formula (10)²The maximum likelihood estimate of (a) is:

2) residual life prediction for nth sample

Suppose that at time τ, the amount of degradation X (τ) of the nth sample is X_rThus, the remaining life T can be expressed as:

T＝inf{t|X(t+τ)≥L，X(τ)＝x_r,t≥0} (13)

because the increment of the wiener process is independent of each other and has homogeneous Markov property, the method can be obtained by the formula (13):

therefore, the probability density function and the cumulative distribution function of the remaining lifetime T are:

the expected remaining life values are:

thus, the total lifetime values for the nth sample are:

t_n＝E(T|X(τ))+τ (18)

3) producer user risk calculation

From the risk perspective, it can be seen that by predicting the remaining life of the sample, a decision is made in advance or a certain risk is created that the sample may not reach the desired value of remaining life E (tx), which is equivalent to an increased risk to the user. As can be seen from equation (16), the risk values brought to the producer and the consumer by making a decision in advance are:

R_{risk_product}＝1-F_T|X(τ)(E(T|X(τ))|X(τ)) (19)

R_{risk_customer}＝F_T|X(τ)(E(T|X(τ))|X(τ)) (20)

the total risk incurred by the user is:

β_all＝β·(1+R_{risk_customer}) (21)

the corresponding risk of the producer is:

α_all＝α·(1+R_{risk_product}) (22)

in order to ensure that the total risk of the producer and the consumer is constant, i.e. the same as required in the contract, the producer risk and the consumer risk for the decision are adjusted to:

4) receive and reject decisions

N-1 sample fault data t of completed test_i(i-1, 2 …, n-1), and the expected total lifetime t of the nth sample_nThe shape parameter m is estimated by plotting E (T | X (τ)) + τ on weibull probability paper.

A dimensionless value is calculated according to equation (25):

according to the receiving equation (26) and the rejection equation (27), K under n sample faults is obtained through calculation respectively_aAnd K_nThe value is obtained.

Wherein:

θ₀an MFBF upper check limit for the mean fault interval of the product;

θ₁the MFBF check lower limit is the mean failure interval of the product;

d is the discrimination ratio, i.e. d ═ θ₀/θ₁。

If K < K_nMaking a rejection decision; if K > K_aMaking a reception decision; otherwise, continuing the test.

The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (1)

1. A non-electronic product sequential verification test method based on residual life prediction is characterized in that: the method comprises the following steps:

firstly, according to the performance degradation data monitored by the finished test sample and the ongoing test sample, establishing a wiener degradation model of a product and estimating model parameters, and according to a residual life prediction method based on the wiener process, obtaining a probability density function f of the residual life T of the ongoing test sample_T|X(τ)(t | X (τ)) and the cumulative distribution function F_T|X(τ)(t|X(τ))；

Next, the expected remaining life values are calculated as:

the total lifetime value of the sample was obtained:

t_n＝E(T|X(τ))+τ (2)

t is the remaining life value from the current time point;

and calculating the risk values brought to the producer and the user by making a judgment in advance as follows:

R_{risk_product}＝1-F_T|X(τ)(E(T|X(τ))|X(τ)) (3)

R_{risk_customer}＝F_T|X(τ)(E(T|X(τ))|X(τ)) (4)

then, in order to ensure that the respective total risks of the producer and the consumer are not changed, the producer risk and the consumer risk substituted into the decision formula are respectively adjusted to be:

finally, the n-1 sample fault data t of the completed test is processed_i(i-1, 2 …, n-1), and the expected total lifetime t of the sample under test_nThe shape parameter m is estimated by plotting E (T | X (τ)) + τ on weibull probability paper, and a dimensionless value is calculated according to equation (7):

according to the receiving equation (8) and the rejection equation (9), respectively calculating to obtain the fault conditions of the n samplesK_aAnd K_nValue of

Wherein:

θ₀an MFBF upper check limit for the mean fault interval of the product;

θ₁the MFBF check lower limit is the mean failure interval of the product;

d is the discrimination ratio, i.e. d ═ θ₀/θ₁；

If K < K_nMaking a rejection decision; if K > K_aMaking a reception decision; otherwise, continuing the test.

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