A trapezoidal cyclic stress accelerated life test method

Abstract

The application discloses a trapezoidal cyclic stress accelerated life test method, which comprises the following steps: obtaining test data of a trapezoidal cyclic stress accelerated life test of a product; selecting a life distribution model and an acceleration model according to the characteristics of the trapezoidal cyclic stress accelerated life test of the product; establishing a maximum likelihood estimation model of the trapezoidal cyclic stress accelerated life test of the product based on the test data, and estimating the parameters of the life distribution model and the acceleration model; and calculating the reliability parameters of the product under a service stress based on the estimation results of the parameters of the life distribution model and the acceleration model. The application can be applied to the field of product life prediction, and the accelerated life test is carried out by using cyclic stress as an acceleration stress, so that the cyclic stress loading mode in the service process of the product can be simulated, the test data are more effective, the prediction result is more accurate, the test efficiency is higher compared with the traditional constant stress and step stress accelerated life test method, and the test time and the test cost can be greatly shortened.

Description

Technical Field

[0001] This invention relates to the field of product life prediction technology, specifically a trapezoidal cyclic stress accelerated life test method. Background Technology

[0002] As product reliability requirements become increasingly stringent, traditional life testing methods struggle to achieve reliability assessment and prediction within a feasible timeframe. Accelerated life testing employs harsher environmental and operating conditions to expedite the product failure process. By modeling and analyzing data obtained under accelerated stress, it enables the assessment and prediction of product lifespan and reliability under normal operating conditions. Due to its high testing efficiency, accelerated life testing is increasingly widely used in reliability engineering, becoming a viable approach for product lifespan and reliability prediction.

[0003] However, products are generally subjected to cyclic stress during service. For example, wheel bearings of automobiles bear cyclic loads during driving; aerospace products are subjected to temperature cyclic stress due to alternating sunlight and shadow areas; and equipment is subjected to temperature stress due to day-night and seasonal cyclic changes during field service. It is obviously not reasonable to use basic accelerated life test methods such as constant stress, step stress, or sequential stress to conduct life and reliability assessments of these products.

[0004] Using cyclic stress as accelerated stress for accelerated life testing of such products offers several advantages. First, it simulates the cyclic stress loading experienced during product service, resulting in more effective test data and more accurate predictions. Second, by adjusting the cyclic stress profile elements, it increases test efficiency, significantly reduces testing costs, and shortens test time. Cyclic stress accelerated life testing has become a more accurate and efficient solution for predicting the lifespan and reliability of such products.

[0005] Trapezoidal cyclic stress profiles are relatively easy to implement in engineering, making accelerated life testing (CLT) with trapezoidal cyclic stress relatively feasible. However, no research on CLT methods has been reported to date. If CLT is used to predict the lifespan of long-life, high-reliability products, modeling and analysis problems will inevitably arise. How to describe the trapezoidal cyclic stress profile, how to establish a product cumulative damage model, cumulative failure distribution function, and cumulative failure distribution density function, and how to determine the likelihood function and solve its extrema are pressing problems in the field of reliability engineering. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides a trapezoidal cyclic stress accelerated life test method, which can be applied to the life prediction of long-life, high-reliability products that will be subjected to cyclic stress during service.

[0007] To achieve the above objectives, the present invention provides a trapezoidal cyclic stress accelerated life test method, comprising the following steps 1-5.

[0008] Step 1: Obtain relevant information and test data for the product's trapezoidal cyclic stress accelerated life test.

[0009] Information related to the product's trapezoidal cyclic stress accelerated life test can be described as follows:

[0010] Trapezoidal cyclic stress accelerated life test profile of the product as shown Figure 1 As shown. Within one stress cycle T, the interval [t0, t1] represents the high stress level S. H During the maintenance phase, t H =t1-t0 is the holding time of the high stress level, and the stress in the interval (t1,t2) changes from the high stress level S H Gradually reduce to low stress level S L (S H >S L >S0, where S0 is the stress level in use), t D =t2-t1 represents the time from high stress level to low stress level, and the interval (t2,t3] represents the low stress level S. L During the maintenance phase, t L =t3-t2 is the holding time of the low stress level, and the stress in the interval (t3,t4) changes from the low stress level S L Gradually rising to high stress level S H , t A =t4-t3 represents the time required for the stress level to rise from a low stress level to a high stress level. The rate of decrease in stress level is D. s =(S H -S L The stress level rise rate is A / (t2-t1). s =(S H -S L ) / (t4-t3). The cyclic stress period is T=t4-t0.

[0011] The stress-time variation model S(t) within one cyclic stress cycle can be described as:

[0012]

[0013] The product's trapezoidal cyclic stress accelerated life test data are as follows:

[0014] Randomly select n test samples to conduct cyclic accelerated life tests, and use test equipment to apply stress to these samples as follows: Figure 1 The cyclic stress shown is applied until the test time reaches τ, or the number of cycles reaches N. The test yields the failure time data t′1, t′2, ..., t′ of the samples.r r represents the total number of failures at the end of the test.

[0015] Step 2: Select the life distribution model and acceleration model based on the characteristics of the product's trapezoidal cyclic stress accelerated life test.

[0016] A lifetime distribution model refers to the probability distribution function that a product's lifetime (as a random variable) follows. For electronic products, insulating oils and liquids, dielectrics, and products that have entered the random failure stage after screening, the lifetime distribution generally uses an exponential distribution model. For metal fatigue lifetime, semiconductor lifetime, diodes, gallium arsenide field-effect transistor lifetime, and electrical insulation material lifetime distribution, a log-normal distribution model is generally used. For bearings, electronic products, ceramics, capacitors, dielectrics, and "weakest ring type" products, the Weibull distribution model is generally chosen. The exponential distribution model is a special case of the Weibull distribution model with a shape parameter of 1. The log-normal distribution model can also be approximated by the Weibull distribution model. That is, in this invention, the Weibull distribution model can be used as the lifetime distribution model for all products. The Weibull distribution model is expressed as follows: the product lifetime distribution function is F(t) = 1 - exp[-(t / η)] m ], where F(t) is the failure probability of the product at time t, m is the shape parameter, and η is the characteristic lifetime parameter.

[0017] The acceleration model in this invention is expressed as: lnη=a0+a1·x, where η is the characteristic lifetime parameter, a0 and a1 are acceleration model parameters, x is the conversion stress and x=φ(S), S is the acceleration stress, and φ(S) is a monotonic function of S. When S is temperature, x=φ(S)=1 / (273+S), and the above formula is the Arrhenius model; when S is electrical stress, x=φ(S)=lnS is generally taken, and the above formula is the inverse power law model.

[0018] The cumulative damage model is a mathematical model that connects the cumulative failure distribution of a product under cyclic stress with the failure distribution of a product under constant stress. According to the acceleration model, since stress x(t) = φ[S(t)] is a function of time, the characteristic lifetime parameter η(x) of the lifetime distribution is also a function of time, i.e., η(t) = η[x(t)]. The corresponding cumulative damage can be expressed as:

[0019]

[0020] Therefore, the cumulative failure distribution function of the product under cyclic stress can be expressed as:

[0021] F0(t)=1-exp{-[ε(t)] m} (2)

[0022] Step 3: Based on the experimental data, establish a maximum likelihood estimation model for the trapezoidal cyclic stress accelerated life test of the product. The construction process is as follows:

[0023] First, the specific expression for the cumulative damage of the specimen is derived from the cumulative damage model in step 2, and then the expressions for the cumulative failure distribution function and its distribution density function are obtained. Since x(t)=φ[S(t)], the change of transformed stress with time can be described as:

[0024]

[0025] Among them, D x =(x H -x L ) / (t2-t1), A x =(x H -x L ) / (t4-t3), x H =φ(S H ), x L =φ(S L ), D x For the rate of decrease of the transformed stress level, A x Let the rate of increase of the transformation stress level be x. H To convert high stress levels, x L To convert to low stress levels;

[0026] Let the failure time of the sample be t. First, we derive the expression for the cumulative damage when t∈[t0,t4]. Then, we derive the expression for the cumulative damage in the general case. The expression for the cumulative damage when [t0,t4] can be divided into four cases, as follows:

[0027] In the first case, when t∈[t0,t1]:

[0028]

[0029] Where, η H =exp(a0+a1x) H ), η H Here, u is an intermediate parameter, and u is the integration variable;

[0030] In the second case, when t∈(t1,t2]:

[0031]

[0032] Where ξ=η H / η L η L =exp(a0+a1x) L ), ξ、η L t is an intermediate parameter. H=t1-t0 is the holding time at the high stress level, t D =t2-t1 is the time it takes for the stress level to drop from high to low.

[0033] The third case is when t∈(t2,t3]:

[0034]

[0035] The fourth case is when t∈(t3,t4]:

[0036]

[0037] Among them, t L =t3-t2 is the holding time at the low stress level, t A =t4-t3 is the time it takes for the stress level to rise from a low stress level to a high stress level;

[0038] Specifically, let t = t4, that is, the cumulative damage to the specimen after one cycle of cyclic stress acceleration test T can be expressed as:

[0039]

[0040] Where Δε1, Δε2, Δε3, and Δε4 represent the cumulative damage to the specimen caused by the cyclic stress accelerated test within the intervals [t0,t1], (t1,t2], (t2,t3], and (t3,t4], respectively, and:

[0041]

[0042] Therefore, generally speaking, if the sample fails at time t, let t = b·T + ω, ω∈[t0,t4], where b and ω are intermediate parameters; then its cumulative damage can be expressed as:

[0043]

[0044] Therefore, the cumulative failure distribution function F0(t) of the product under cyclic stress can be expressed as:

[0045] F0(t)=1-exp{-[ε(t)] m} (11)

[0046] Furthermore, the cumulative failure distribution density function f0(t) is obtained as follows:

[0047]

[0048] The derivative of the cumulative damage function with respect to time, dε(t) / dt, can be obtained by differentiating equation (10). In fact, since 1 / η(x(t)) is a continuous function with respect to t, therefore:

[0049]

[0050] Right now:

[0051]

[0052] Based on the cumulative failure distribution density function, the likelihood function L of the sample is obtained as follows:

[0053]

[0054] Further, we obtain the log-likelihood function, i.e., the maximum likelihood estimation model, as follows:

[0055]

[0056] Where, f0(t) i F0(τ) can be obtained from equations (12), (10) and (14), and F0(τ) can be obtained from equations (11) and (10).

[0057] Based on the cumulative failure distribution density function f0(t), we can obtain:

[0058]

[0059] in:

[0060]

[0061] In the formula, ε i E is the cumulative damage function. i The time derivatives of the cumulative damage function, ε(t) and dε(t) / dt, can be obtained from equations (10) and (14), respectively.

[0062] From equation (11), we can obtain:

[0063]

[0064] Where, ε τ We can let t = τ and obtain it from equation (10);

[0065] Therefore, the maximum likelihood estimation model is obtained as follows:

[0066]

[0067] In the formula, l is the log-likelihood function of the trapezoidal cyclic stress accelerated life test sample, and ε τ For cumulative damage, ε iE is the cumulative damage function. i This is the time derivative of the cumulative damage function.

[0068] Step 4: Estimate the parameters of the lifetime distribution model and the acceleration model based on the maximum likelihood estimation model.

[0069] The maximum likelihood estimation problem for the parameters θ = [m, a0, a1] in the maximum likelihood estimation model in step 3 can be transformed into an extremum problem.

[0070]

[0071] Where Ω is the feasible region of θ, Ω={m,a0,a1|,m∈R,a0∈R,a1∈R,m>0,-∞ <a0<∞,-∞<a1<∞}。

[0072] The derivation of the gradient and Hessian matrix of the log-likelihood function l is complex, and the extreme value problem shown in equation (21) implicitly contains the constraint m>0. Since the interior-point method is very effective for this type of nonlinear optimization problem, this invention uses the interior-point method to solve the above extreme value problem. In the method described in this invention, there are no special restrictions on the choice of optimization method for solving the above extreme value problem; in addition to the interior-point method, other optimization methods can also be selected.

[0073] Step 5: Based on the estimation results of the lifetime distribution model parameters and the acceleration model parameters, calculate the reliability parameters of the product under operating stress.

[0074] Based on the estimation results in step 4, the failure distribution F(t) of the product at time t under the service stress level S0 is calculated as follows:

[0075] F(t)=1-exp[-(t / η0)] m ]

[0076] =1-exp[-(t·exp(-a0-a1x0)) m ] (twenty two)

[0077] =1-exp[-(t·exp(-a0-a1φ(S0))) m ]

[0078] Where, x0=φ(S0), lnη0=a0+a1·x0;

[0079] Based on the failure distribution of the product at time t under the service stress level S0, the product reliability function under the service stress is obtained as follows:

[0080]

[0081] Where R(t) represents the reliability of the product at time t under the operating stress level S0.

[0082] Compared with existing technologies, the present invention has the following technical effects:

[0083] 1. This invention utilizes cyclic stress as accelerated stress to conduct accelerated life tests, which can simulate the cyclic stress loading mode experienced by the product during service, making the test data more effective and the prediction results more accurate.

[0084] 2. This invention uses cyclic stress profiles, which are more efficient than traditional constant stress and step stress accelerated life testing methods, and can significantly shorten the testing time and reduce testing costs. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0086] Figure 1 This is a schematic diagram of a trapezoidal cyclic stress loading cross-section in an embodiment of the present invention;

[0087] Figure 2 This is the trapezoidal cyclic stress accelerated life test method in the embodiments of the present invention;

[0088] Figure 3 This is a schematic diagram of the iterative convergence process of the log-maximum likelihood function optimization in an embodiment of the present invention;

[0089] Figure 4 This is a schematic diagram of the reliability curve of the miniature electromagnetic relay at 30°C in an embodiment of the present invention.

[0090] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0091] The technical solutions in the embodiments of this invention will be clearly and completely described below, based on the practical experience of trapezoidal cyclic stress accelerated life test analysis and prediction of miniature electromagnetic relay products. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0092] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0093] refer to Figure 1 The trapezoidal cyclic stress accelerated life test method for the miniature electromagnetic relay product in this embodiment specifically includes the following steps 1-5.

[0094] Step 1: Obtain relevant information and test data for the trapezoidal cyclic stress accelerated life test of the miniature electromagnetic relay product. Specifically:

[0095] A miniature electromagnetic relay operates at a temperature of 30°C with a DC load of 24V and 0.5A. To evaluate the reliability of this miniature electromagnetic relay at 30°C, n=300 relays were randomly selected from this batch for accelerated life testing using a trapezoidal cyclic stress profile. The operating frequency of the miniature electromagnetic relay during the test was 10 cycles / minute. The high-temperature stress level S within one cycle of the trapezoidal cyclic stress profile is shown. H =125℃, low temperature stress level S L =69℃, holding time of high temperature stress level t H =t1-t0=1 hour, t0=0 hours, the holding time of the low temperature stress level t L =t3-t2=1 hour, the time t for the stress level to decrease from the high temperature level to the low temperature level. D =t2-t1=0.2 hours, the time t for the stress level to rise from the low temperature level to the high temperature level. A =t4-t3=0.2 hours, cyclic stress period T=t4-t0=2.4 hours. The trapezoidal cyclic stress accelerated life test continued until 7.5040 hours. The simulation data of the temperature cyclic stress accelerated life test of the miniature electromagnetic relay are shown in Table 1. That is, the failure data of the miniature electromagnetic relay are shown in Table 1: t1′=0.0047 hours, t2′=0.0155 hours, ..., t r ′=7.5040 hours, r=191 is the total number of failures at the end of the test, and τ=7.5040 hours is the test time.

[0096] Table 1: Simulation data of accelerated life test under temperature cycling stress for a miniature electromagnetic relay (unit: hours)

[0097]

[0098]

[0099] Step 2: Based on the characteristics of the trapezoidal cyclic stress accelerated life test of a certain miniature electromagnetic relay product, select the life distribution model and the acceleration model. The specific implementation process is as follows:

[0100] Since miniature electromagnetic relays are electronic products, and based on engineering experience and historical data, the Weibull distribution model is more suitable for describing their lifetime distribution. Therefore, the Weibull distribution model is chosen to describe the lifetime distribution of miniature electromagnetic relays.

[0101] F(t) = 1 - exp[-(t / η)] m ]

[0102] Where F(t) is the failure probability of the miniature electromagnetic relay at time t, m is the shape parameter, and η is the characteristic lifetime parameter.

[0103] Since the accelerating stress is temperature, the Arrhenius model is chosen as the acceleration model, as follows:

[0104] lnη=a0+a1·x=a0+a1 / (273+S)

[0105] Where η is the characteristic lifetime parameter, a0 and a1 are the acceleration model parameters, x is the conversion stress and x = φ(S) = 1 / (273 + S), and S is the temperature acceleration stress.

[0106] Step 3: Establish a maximum likelihood estimation model for the trapezoidal cyclic stress accelerated life test of the product based on the experimental data. The specific implementation process is as follows:

[0107] From equation (20), the maximum likelihood estimation model for the trapezoidal cyclic stress accelerated life test of the miniature electromagnetic relay can be obtained as follows:

[0108]

[0109] Where r = 191 is the total number of failures at the end of the test, n = 300 is the sample size of the miniature electromagnetic relays used in the test, and τ = 7.5040 hours is the test cutoff time. Let t = τ, ε τ The calculation method for ε(τ) is as follows: b τ =[τ / T] F , [·] F Indicates rounding down; ω τ =τ-b τ ·T; according to ω τ The value of ε is calculated using the following formula. τ ,for:

[0110]

[0111] in,

[0112]

[0113] and

[0114]

[0115] η H =exp(a0+a1x) H ), η L =exp(a0+a1x) L ), ξ=η H / η L x H =φ(S H ) = 1 / (273 + S H ), x L =φ(S L )=1 / (273+S L ).

[0116] Let t = t i ′,i=1,2,…,r,ε i =ε(t) i The calculation method of ′) and ε τ The calculation method is similar and will not be repeated here. E in the above maximum likelihood estimation model... i The calculation method is as follows: Let t = t i ′,i=1,2,…,r,b i =[t i ′ / T] F , [·] F Indicates rounding down; ω i =t i ′-b i ·T; according to ω i The value of E is calculated using the following formula. i

[0117]

[0118] Step 4: Based on the maximum likelihood estimation model, estimate the parameters of the lifetime distribution model and the acceleration model. The specific implementation process is as follows:

[0119] The interior-point method is used to solve the extreme value problem corresponding to the maximum likelihood estimation model. The estimation results are m = 1.2782, a0 = -18.7991, a1 = 8.0094 × 10⁻⁶. 3 The maximum likelihood estimation extreme value search iterative process is as follows: Figure 3 As shown in the figure, the optimization process converges to the optimal solution after 28 iterations.

[0120] Step 5: Based on the estimation results of the lifetime distribution model parameters and the acceleration model parameters, calculate the reliability parameters of the product under service stress. The specific implementation process is as follows:

[0121] The failure distribution F(t) of the product at time t under temperature stress S = 30℃ is:

[0122] F(t)=1-exp[-(t / η0)] m ]

[0123] =1-exp[-(t·exp(-a0-a1x0)) m ]

[0124] =1-exp[-(t·exp(-a0-a1φ(S0))) m ] (twenty four)

[0125] =1-exp[-(t·exp(-a0-a1 / (273+S0))) m ]

[0126] =1-exp[-(t·exp(18.7991-8009.4 / (273+30)) 1.2782 ]

[0127] =1-exp[-(t·4.8340×10 -4 ) 1.2782 ]

[0128] Therefore, the reliability R(t) of the product under temperature stress S = 30℃ is:

[0129] R(t) = 1 - F(t)

[0130] =exp([-(t / η0) m (25)

[0131] =exp[-(t·4.8340×10] -4 ) 1.2782 ]

[0132] Reliability curve as shown Figure 4 As shown in Table 2, the reliability of the miniature electromagnetic relay corresponding to different working times can be calculated using equation (25), and the lifespan of the miniature electromagnetic relay corresponding to different reliability levels can also be calculated. In engineering, the lifespan of the miniature electromagnetic relay is generally expressed by the number of uses. Based on the fact that the operating frequency of the miniature electromagnetic relay in the experiment was 10 times / minute, the lifespan of the miniature electromagnetic relay corresponding to different reliability levels at 30℃ can be calculated using equation (25), as shown in Table 2.

[0133] Table 2: Reliable lifespan of miniature electromagnetic relays

[0134]

[0135] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A trapezoidal cyclic stress accelerated life test method, characterized in that, Includes the following steps: Step 1: Obtain test data from the trapezoidal cyclic accelerated life test of the product. The test data includes the number of test samples for which the cyclic accelerated life test was conducted. n A model of stress variation over time within a cyclic stress cycle. S ( t ), test time τ Or the number of loops N The failure time data of the samples were obtained through the experiment. t′ 1. t′ 2、···、 t′ r ,in, r To achieve the test time Or the number of cycles reaches N The number of failures of the test samples at that time; Step 2: Based on the characteristics of the product's trapezoidal cyclic stress accelerated life test, select the life distribution model and the acceleration model; Step 3: Establish a maximum likelihood estimation model for the product trapezoidal cyclic stress accelerated life test based on experimental data; Step 4: Estimate the parameters of the lifetime distribution model and the acceleration model based on the maximum likelihood estimation model; Step 5: Based on the estimation results of the lifetime distribution model parameters and the acceleration model parameters, calculate the reliability parameters of the product under service stress. The construction process of the maximum likelihood estimation model is as follows: Obtaining a lifetime distribution model F ( t )=1-exp[-( t / η ) m ], Acceleration model ln η = a 0+ a 1 x ,in, F ( t )for t The probability of product failure at any given time. m For shape parameters, η For characteristic lifetime parameters, a 0、 a 1 represents the parameters of the acceleration model. x For transforming stress and x = ( S ), S To accelerate stress, ( S )for S A monotonic function; Due to stress x ( t )= [ S ( t [Time] t The function of lifetime distribution, therefore the characteristic lifetime parameters η It is also time t The function, i.e. η ( t )= η [ x ( t The corresponding cumulative damage It can be represented as: Due to transformed stress x ( t )= [ S ( t [ ], and a model of stress variation over time within one cyclic stress cycle. S ( t Specifically: In the formula, S H For high stress level, S L For low stress level, D s For the rate of decrease of stress level, A s For the rate of increase of stress level, [ t 0, t 1] The interval is the stage of maintaining a high stress level, ( t 1, t 2] The interval is the stage of stress level decrease, ( t 2, t 3] The interval is the stage of maintaining a low stress level. t 3, t 4] This interval represents the stage of stress level increase; the cyclic stress period T = [ t 0, t 4]; The transformation stress over time can then be described as follows: in, D x =( x H - x L ) / ( t 2- t 1), A x =( x H - x L ) / ( t 4- t 3), x H = ( S H ), x L = ( S L ), D x The rate of decrease in the transformed stress level, A x The rate of increase of the transformation stress level; Let the failure time of the sample be... t ,available t ∈[ t 0, t Cumulative damage at 4] ,for: when t ∈[ t 0, t 1] time: in, η H =exp( a 0+ a 1 x H ); when t ∈( t 1, t 2] time: in, ξ = η H / η L , η L =exp( a 0+ a 1 x L ), t H = t 1- t 0 represents the holding time at high stress levels. t D = t 2- t 1 represents the time it takes for the stress level to decrease from a high stress level to a low stress level; when t ∈( t 2, t 3] when: when t ∈( t 3, t 4] time: in, t L = t 3- t 2 represents the holding time at low stress levels. t A = t 4- t 3 represents the time required for the stress level to rise from a low stress level to a high stress level; make t = t 4, meaning after one cycle T The cumulative damage to the specimen caused by cyclic accelerated stress testing can be expressed as: Where, Δ ε 1. Δ ε 2. Δ ε 3. Δ ε 4 represents the cyclic accelerated stress test in the interval [ t 0, t 1]、( t 1, t 2]、( t 2, t 3]、( t 3, t 4] The cumulative damage to the sample within the period, and: set up t = b T + ω , b ∈ ={0, 1, 2, …} ω ∈[ t 0, t 4], then its cumulative damage can be expressed as: Therefore, the cumulative failure distribution function of the product under cyclic stress It can be represented as: Further, the cumulative failure distribution density function is obtained. ,for: Based on the cumulative failure distribution density function, the likelihood function L of the sample is obtained as follows: In the formula, t′ 1. t′ 2、···、 t′ r To obtain failure time data for the samples in the experiment; Further, we obtain the log-likelihood function, i.e., the maximum likelihood estimation model, as follows: Based on cumulative failure distribution density function We can obtain: in, ; Based on the cumulative failure distribution function of products under cyclic stress We can obtain: in, ε τ Can make t = The maximum likelihood estimation model is obtained from the cumulative damage: in, For cumulative damage, For cumulative damage function, This is the time derivative of the cumulative damage function.

2. The trapezoidal cyclic stress accelerated life test method according to claim 1, characterized in that, In step 2, the lifetime distribution model is selected as an exponential distribution model, a log-normal distribution model, or a Weibull distribution model; The acceleration model is an Arrhenius model, an inverse power law model, an Eyring model, or a polynomial acceleration model.

3. The trapezoidal cyclic stress accelerated life test method according to claim 1 or 2, characterized in that, When accelerated stress S At temperature, the transformation stress x = ( S ) = 1 / (273+ S When accelerated stress S When it is electrical stress, the transformed stress x = ( S )=ln S .

4. The trapezoidal cyclic stress accelerated life test method according to claim 3, characterized in that, In step 4, the interior point method is used to solve for the extreme values ​​corresponding to the maximum likelihood estimation model, and the parameters of the lifetime distribution model are estimated. m and acceleration model parameters a 0、 a 1.

5. The trapezoidal cyclic stress accelerated life test method according to claim 4, characterized in that, Step 5 specifically involves: Calculate the product's stress level based on the estimation results in step 4. S 0 t Failure distribution at time F ( t )for: in, x 0= ( S 0), ln η 0= a 0+ a 1 x 0; Based on the product's stress level during use S 0 t The failure distribution at each time step yields the product reliability function under operating stress: in, R ( t The stress level of the product under use S 0 t Reliability at any given moment.

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