Method to Determine Test Profile in Step-Stress Accelerated RDT under Type-I Censoring Li Peng, Technology and Engineering Center for Space Utilization Dang Wei, Technology and Engineering Center for Space Utilization Xin Mincheng, Technology and Engineering Center for Space Utilization Liu Kai, Technology and Engineering Center for Space Utilization Zou Tianji, Technology and Engineering Center for Space Utilization Key Words: Reliability demonstration, type-I censoring, Acceleration Factor (AF), test profile SUMMARY & CONCLUSIONS Conventional Reliability Demonstration Test (RDT) based on statistical method is widely used in industry as it is simply and convenient to apply. But for the products with high reliability and long life, this test method fails to satisfy the demand for short cycle and low cost, and is liable to cause the phenomenon of over-test and short-test. This paper gives a step-stress accelerated RDT plan when the lifetime follows exponential distribution, making it faster to make decision of accept or reject. We summarize the method of stress sensitivity analysis, and use failure effect to characterize the failure mechanism by considering the non-linear phenomena between severity rating and failure effect. By raising the levels of environment stresses, the test time can be cut down remarkably. Combined with the stress profile in Reliability Qualification Test (RQT), the step-stress accelerated test profile is acquired. An example is given to illustrate the superior performance of the proposed method over traditional methods. The FIDES method based stress sensitivity analysis was studied, and the non-linear phenomena between severity rating and failure effect was considered, then the failure effect was used to characterize the failure mechanism. We proposed a step-stress accelerated reliability demonstration test plan, combining conventional statistical demonstration method with Physics of Failure (PoF), which can remarkably cut down the test time and cost. The detailed process on the establishment of accelerated test profile under multiple stresses and mechanisms was illustrated with a case example. 1 INTRODUCTION RDT is composed of the test plan and decision rules, and time-censoring (Type-I censoring) is commonly used in the engineering applications, as the total test time of this test type is pre-determined. However, for advanced products with high reliability and long lifetime, test duration and sample size become time and cost prohibitive [1]. The step-stress scheme allows the stress level to increase gradually at some pre978-1-5090-5284-4/17/$31.00 ©2017 IEEE
planned time points during the test for flexibility and adjustability [2][3]. 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 [4]. Yadav facilitates the development of reliability test plan by bring three-dimensional understanding of the product design while utilizing existing information and knowledge [5]. 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 [6]. 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 [11]. 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 [12], and failure effect can be analyzed by failure mode and effect analysis (FMEA) and Risk Priority Number (RPN) method [13]. 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
Mission phase
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.
Environment profile
Natural environment
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 [14]. 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.
Sensitivity analysis
Stress analysis n
j
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 [12] for a product is:
λ= λPhysical ⋅ ∏ Part manufacturing ⋅ ∏ Pr ocess
∏
λPhysical
Part manufacturing
represents
the
physical
j
(3)
j
3 FORMULATION OF TEST PROFILE OF STEP-STRESS ACCELERATED TEST
Stress sensitivity analysis
where
j
Stress analysis 1 …
Life profile
Environment profile 1 …
Stress analysis
…
Mission profile 1
(1)
contribution.,
Choose an appropriate time-censoring statistical test plan and establish the test profile of RQT based on GJB 899A-2009 [15]. 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
∏
Pr ocess
represents the
Fig. 3. Formulation process of test profile of step-stress accelerated test
3.1 Calculation of AF for each sensitive stress
k
1)
Thermal cycling According to the JESD94A in the JEDES standard [16], the thermal cycling follows Norris-Landzberg model: 1.9
ATC
1/3
∆T1 v1 exp 0.01(Tmax_ Test − Tmax ) ∆T2 v2
(4)
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 [17]: E = ATD exp a k B
1 1 − TTD + 273 TTD _ Test + 273
ATC =
TC _i
(8)
k
∑τ
i
Therefore the number of test cycles is: N = N AT 0 + 1 ATC
(9)
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
ATD =
i
i =1
TD _i
k
∑τ i
(10)
i =1
Thus the thermal dwell duration for each cycle in accelerated condition is given by
3
(6)
i
i =1
i =1
(5)
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
(11)
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 [18].
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
(7)
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
(12)
(13)
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
(14)
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
Thermal dwell
Thermal cycling
0.0704 3.976 0.0089 0.0196 0.0375 0.6398 4.7522 30.20%
1.3631 2.5341 0.2654 0.0954 0.0176 0.0084 4.284 27.23%
Mechanical environment 0.0628 0.1997 0.0679 0.1197 0.0146 3.1973 3.662 23.28%
Humidity
Chemical Environment
Total
0.0532 0 0 0.0112 0.1798 1.0030 1.2472 7.93%
0 0 0 0 1.7878 0 1.7878 11.36%
1.5495 6.7098 0.3422 0.2459 2.0373 4.8485 15.7332 -
Table 2 Results of failure effect analysis of the device (a=0.25) Components
Failure mode
Failure mechanism
Severity (S)
Modified severity ( S )
Occurrence (O)
Criticality (C)
Fatigue
4
2.7183
4
10.8732
3
2.117
Resistance drift
Strength Wear
1
2.1170
2
4.2340
Resistor Corrosion
3
2.117
2
4.2340
Electro migration
8
7.3891
6
44.3346
Short circuit
Fatigue Electro migration
7
5.7546
7 4
40.2822 23.0184
Insulating property Degradation
Packaging defect
5
3.4903
1
3.4903
Drift
Corrosion
5
3.4903
2
6.9806
Open circuit
Strength
4
2.7183
3
8.1549
Short circuit
Contamination
5
3.4903
2
6.9806
2.117
4
8.4680
Open circuit
Capacitor
Semiconductor
Corrosion Drift
Contamination
Chip failure
Metal oxygenation Mutual diffusion Age
Packaging
Moisture
Microcircuit
3
2.117
1
2.1170
8
7.3891
2 1 2
14.7782 7.3891 14.7782
2
1.6487
2
3.2974
Table 3 Statistical plan of RQT No. of plans 17
Nominal value
Decision making risks Actual value
α
β
α'
β'
20%
20%
17.5%
19.7%
Discrimination ratio d = θ 0 θ1
Test time ( θ1 )
3.0
4.3
Decision failures Rejection Acceptance (≤) (≥) 3 2
T(℃) 35℃ -5℃/min
+5℃/min 0
-55℃
74
60
554
568
(min)
g2/Hz Acceleration PSD 0.1
60
90
(min)
Fig. 4 Test profile of RQT for the equipment Table 4 Accelerated stress level and AFs of the device Stress level
THigh (℃)
∆T (℃)
ζ (℃/min)
W(g2 /Hz )
Thermal cycling ATC
Thermal dwell ATD
Vibration AVib
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
Non-accelerated Accelerated
4088 1750
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)
30 8.8
568 189
38700 5512.5
T(℃) 60℃ 50℃ 40℃ 35℃
-10℃/min
+10℃/min 0
60
69
95.5
96
122.5 123.5
150 151
177.5
189
(min)
-55℃ g2/Hz Acceleration PSD 0.2
60 68.8
(min)
Fig. 5 Test profile of step-stress accelerated reliability demonstration test There are five accelerated stress levels with S 1
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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.
