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planned time points during the test for flexibility and adjustability . In addition, there is no guidance on what the environmental and operational stresses should be applied during the test, and how the MTBF related to environment profile. Many researchers pay attention to accelerated demonstration testing. Kang has synthesized the risk from life distribution and model selection and found the equivalent dispersion of accelerated factor on system level, then the verification testing for system with one sample has been designed . Yadav facilitates the development of reliability test plan by bring three-dimensional understanding of the product design while utilizing existing information and knowledge . Chen proposes a method and procedure based on main failure mechanism analysis and the theoretical life models to determine the accelerated stress profile, which take the multiple failure mechanisms into consideration . Milena designs the accelerated sequential testing to demonstrate product’s reliability regarding its expected operational and environmental stresses with the required confidence in the test result [7-10]. David considers the step-stress model under time-censoring when the different risk factors have sindependent generalized exponential lifetime distributions . Most of the relative literatures focus on time-censoring or failure-censoring under constant accelerated stress, and little attention has been devoted to the determination of the step-stress accelerated test profile under multiple stresses and mechanisms. In this study, we connect reliability demonstration test based on statistical approach with PoF, and propose a stepstress accelerated test plan, which significantly shortens the test time and effectively cuts the cost. FIDES method is used to analyze stress sensitivity, and failure effect is considered as the criterion to determine failure mechanism. A case example is made to present the procedure to establish the accelerated test profile, stating the proposed method is better than traditional statistical method, and it can avoid the phenomena of over-test and short-test in verification.
2 DETERMINATION OF STRESS&FAILURE MECHANISM Survey the environmental stress criticality of all mission phases in typical life profile, and analyze each event that can change the environmental stresses, then the typical environment profile can be established. Combined with products’ structure and material, stress sensitivity can be analyzed by FIDES method , and failure effect can be analyzed by failure mode and effect analysis (FMEA) and Risk Priority Number (RPN) method . Therefore, main failure stress and mechanism are determined. Fig. 1. illustrates the flow chart for determining accelerated stress range and type, including stress sensitivity analysis and failure effect analysis. Structure& Material Stress&Failure analysis Environment profile
Sensitivity analysis (FIDES)
Accelerated stress type (main failure stress)
Failure effect analysis (FMEA&RPN)
Accelerated stress range (main failure mechanism)
2.2 Main failure mechanism
Fig. 1. Flow chart for stress and failure analysis based on PoF 2.1 Main failure stress analysis Stress sensitivity analysis is based on the temporal relations and data of each environment profile in the mission phase, and analyze environmental stresses the product would expose to, such as temperature, humidity, mechanical stress, chemical stress. Platform environment Stress quantification
Stress profile determination
quality and technical control over the development, manufacturing and usage process for the product containing the item. The procedure of stress sensitivity analysis is as follows: 1) Make use of the stresses in the established environment profile, and combine with the components of the product, then the environment stresses contributing factors for all the components during each mission phase can be calculated. 2) Based on all the environment stresses contributing factors, the contributing factors for each stress to cause the product failure in the life profile can be acquired. Then the main failure stress during the life profile is determined, which can provide the accelerated stress type in the accelerated test.
As failure of a mission critical system have potential effects on public safety and economy, the failure effect is used to determine main failure mechanism. According to the failure severity and the failure occurrence, failure effect analysis fully evaluates all the possible product’s failures, and provides a reference for the selection of accelerated stress type. The severity is an evaluation of how serious the effect would be if a given failure mechanism occurs, and occurrence is ranked according to the failure frequency and is regarded as the qualitative failure rate. Thus, on the basis of qualitatively criticality analysis performed in FMEA, RPN has been used to quantitatively characterize the failure effect. Let the product has j failure mechanisms with severity ranking S j , occurrence ranking O j . As we can see that the difference between S j =10 and S j =9 should be greater than the difference between S j =2 and S j =1, the non-linear phenomena between severity rating and failure effect should be considered . Then the modified severity ranking can be written in an exponential form: (2) S = exp ( aS ) j
Mission profile n
Environment profile n
So the modified RPN is expressed by C = S × O , j = 1, 2, , n.
Stress analysis n
Fig. 2. Procedure of stress sensitivity analysis We can quantify the impact on failure for each environmental stress with relative literatures. Then the accelerated stress type can be determined. The procedure of stress sensitivity analysis is shown in Fig. 2. The general failure rate model  for a product is:
λ= λPhysical ⋅ ∏ Part manufacturing ⋅ ∏ Pr ocess
3 FORMULATION OF TEST PROFILE OF STEP-STRESS ACCELERATED TEST
Stress sensitivity analysis
Stress analysis 1 …
Environment profile 1 …
Mission profile 1
Choose an appropriate time-censoring statistical test plan and establish the test profile of RQT based on GJB 899A-2009 . Accelerate each sensitive stress and calculate AFs, then the step-stress accelerated test profile is built. The whole procedure is shown in Fig. 3. Stress profile Statistic al plan
Test profile of RQT
AF of thermal cycle
Equivalent cycles in AT
AF of thermal dwell … AF of vibration
Equivalent duration in AT … Equivalent duration in AT
Test profile of step-stress accelerated test
represents the quality and technical control
over manufacturing of the item., and
Fig. 3. Formulation process of test profile of step-stress accelerated test
3.1 Calculation of AF for each sensitive stress
Thermal cycling According to the JESD94A in the JEDES standard , the thermal cycling follows Norris-Landzberg model: 1.9
where ΔT 1 、 ΔT 2 are thermal amplitudes, v 1 、 v 2 are temperature ramp rates, T max_Test , T max are highest exposure temperatures. 2) Thermal dwell For simplicity, the product is exposed to only a high temperature. Acceleration model of thermal dwell follows Arrhenius model : E = ATD exp a k B
Therefore the number of test cycles is: N = N AT 0 + 1 ATC
2) Thermal dwell duration in a cycle For stress synergism, combine thermal exposure with the thermal cycling, distributing the thermal exposure over the high temperature of the thermal cycling to determine thermal dwell at the high temperature. In RQT, as four applied step-stresses maintain the same time, the thermal dwell AF of a cycle is given by:
∑ (τ A ) k
Thus the thermal dwell duration for each cycle in accelerated condition is given by
where T TD , T TD_Test are exposure temperatures, Ea is activation energy (eV), k B is Boltzman’s constant =8.617*10-5eV/K 3) Vibration According to reliability methodology for electronic systems of FIDES, the AF for random vibration is given by:
T1 W2 AVib = = T2 W1
∑ (τ A )
t ATD _ cy =
tTD N 0 ⋅ ATD N AT
where T 1 、 T 2 are durations, W 1 、 W 2 are acceleration PSD, g2/Hz。 The vibration stress should have the same PSD whether the test is accelerated or not, and is accelerated by increasing the acceleration PSD .
3) Vibration duration in a cycle The vibration duration for each cycle in accelerated condition is given by
3.2 Determination of parameters in accelerated test profile
4) Duration of a test cycle The duration of an accelerated cycle is expressed as:
As the required test duration is apparently time prohibitive, each of the expected life environments to be applied in test should be accelerated. By raising stress level in the condition of unchanging failure mechanism of the product, the test time for each environment stress can be calculated. Select n specimens randomly from the same batch of products to carry out SSALT under k accelerated stress levels with S 1
t0 _ max N0 = +1 tcycle
1) Number of test cycles Convert the number of thermal cycles in RQT into the accelerated conditions, and the number of test cycles is equal to number of thermal cycles. Then the thermal cycling AF of a cycle is expressed as:
t AVib _ cy =
tVib N 0 ⋅ AVib N AT
t AT _ cy = tramp + t ATD _ cy + tcold
where t cold is the duration of low temperature, which should make sure the product is completely cold during the low temperature stage. 5) The test time of the accelerated test The total duration of the step-stress accelerated test is expressed as: t AT =t AT _ cy × N AT
4 CASE EXAMPLE In the section, we illustrate the proposed test plan with a dedicated time-frequency device of a vehicle military communication equipment. The reliability goal is MTBF≥9000h, then θ1 = 9000h . According the general failure rate model in (1), Table 1 shows the analysis results of sensitive stresses. We can see thermal dwell, thermal cycling and mechanical environment both account for more than 20% of the total failure rate. Apparently, the failure impact on the equipment caused by all the environment stresses are given by: Temperature > Mechanical environment > Humidity > Chemical
environment. Thus, the main failure stresses are temperature GJB 899A-2009 provides time-censoring, failureand vibration, then the accelerated stresses are thermal dwell, censoring and sequential test plans, and the following thermal cycling and vibration. statistical plan 17 is selected. The normal time-censoring test Table 2 presents the Results of failure effect analysis. parameters and decision criterion are shown in Table 3. Therefore the main failure mechanisms are fatigue leading to Through the analysis of sensitive stresses and main failure capacitor’s short circuit, and electro migration resulting in mechanism, the test profile of RQT is shown in Fig. 4. The resistor’s open circuit, both of whose criticality exceed 40. total test time of RDT is: t 0 =4.3 =38700h. A cycle time under Combined with the operating limits of products and the load normal condition is: t cycle =568min. Then the numbers of RDT capacity of the test equipment, the accelerated stress range can cycles are: N 0 =4088 be determined. Table 1 Results of stress sensitivity analysis of the device Failure rate Components Resistor Capacitor Inductor Semiconductor Connector Microcircuit Total Percentage
Fig. 4 Test profile of RQT for the equipment Table 4 Accelerated stress level and AFs of the device Stress level
W(g2 /Hz )
Thermal cycling ATC
Thermal dwell ATD
S0 S1 S2 S3 S4
35 40 50 60 70
90 95 105 115 125
5 10 10 10 10
0.1 0.2 0.2 0.2 0.2
1.4678 1.9619 2.5773 3.3374
1.662 4.3796 10.888 25.6686
8 8 8 8
Table 5 Comparison of non-accelerated RDT to the step-stress accelerated RDT Stress type
No. of test cycles
Thermal dwell duration in a cycle (min) 480 105.3
Vibration duration in a cycle (min)
duration of a cycle (min)
Total test time (h)
T(℃) 60℃ 50℃ 40℃ 35℃
-55℃ g2/Hz Acceleration PSD 0.2
Fig. 5 Test profile of step-stress accelerated reliability demonstration test There are five accelerated stress levels with S 1
REFERENCES 1. 2.
Nelson W., Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, Wiley, New York, 1990. Yungli Lee, Mingwei Lu. Damage-based models for stepstress accelerated life testing[J]. Journal of Testing and Evaluation, 2006, 34(6):1-10. Jiang Tongmin. Reliability and Life Test [M]. Beijing: National Defense Industry Press, 2012:230-240. Kang Rui, Wang Wenyu, Ma Xiaobing, Chen Qinfeng. System Level Accelerated Demonstration Tests Design: Approach and Application[C] Reliability and
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BIOGRAPHIES Li Peng Technology and Engineering Center for Space Utilization Chinese Academy of Sciences 9# Deng Zhuang South Road Haidian District, Beijing, 100094, P.R. China e-mail: [email protected] Mr. Peng Li received his master degree from Beihang University. Now he is an engineer in technology and Engineering Center for Space Utilization, CAS. His research interests are concentrated on reliability and environmental testing, and reliability assessment. Wei Dang Technology and Engineering Center for Space Utilization Chinese Academy of Sciences 9# Deng Zhuang South Road Haidian District, Beijing, 100094, P.R. China Mr. Wei Dang received his MS degree from University of CAS. He is an associate professor and the director of Reliability Assurance Center in CSU. His research interests are concentrated on reliability systems engineering, COTS components, accelerated testing and life estimation. Mincheng Xin Technology and Engineering Center for Space Utilization Chinese Academy of Sciences 9# Deng Zhuang South Road Haidian District, Beijing, 100094, P.R. China
Mr. Mincheng Xin received the PhD from University of CAS. He is a senior engineer in CSU. His main research interest include space electronics and environmental testing. Kai Liu Technology and Engineering Center for Space Utilization Chinese Academy of Sciences 9# Deng Zhuang South Road Haidian District, Beijing, 100094, P.R. China
Mr. Kai Liu received the PhD from University of CAS, and he is an engineer in CSU. His main research interests include accelerated testing, reliability evaluation. TianJi Zou Technology and Engineering Center for Space Utilization Chinese Academy of Sciences 9# Deng Zhuang South Road Haidian District, Beijing, 100094, P.R. China
Mr. TianJi Zou received his MS degree from Beihang University, and now he is an engineer in CSU. His research interests include the accelerated testing techniques, specifically in optimal design of accelerated degradation testing, accelerated testing data analysis, durability design and analysis.