ADT

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1 December 2015 Journal of Beijing University of Aeronautics and Astronautics Vol 41 No 12 http bhxb buaa edu cn buaa edu cn DOI /j bh * AD AD B114 3 A AD www cnki net /kcms /detail / V html YWF-14-KKX liule89@ gmail com * 1980 leexy@ buaa edu cn J Liu L Li X Y Jiang M Evaluation method for accelerated degradation testing with interval analysis J Journal of Beijing University of Aeronautics and Astronautics in Chinese

2 b 2 f u b 1 b 2 = 槡 2πu 3 - b 2 2 u - b 1 [ ] u > 0 2b 2 1u R t C σ μ = Φ( C - μλ t σ 槡 Λ t ) - exp ( 2μC 2 ) Φ σ ( - C + μλ t ) 5 σ 槡 Λ t t r = Λ -1 R -1 μ C σ R = r 6-1 r X - X - μ μ - μ Wiener 15 Z Y = A Y = A 0 + A 1 y A p y p 7 Y = 1 y X t 1 y p p X t = μλ t + σb Λ t 1 A = A 0 A 1 A p X 0 0 X t = X t - A i = a i c i a i c i X 0 σ B A i 7 Λ t t μ Z= a 0 c 0 + a 1 c 1 y j1 + + a p c p y jp = a y j c y j 8 Arrhenius a = a 0 a 1 a p c = c 0 c 1 c p Eyring ln μ = β 0 + β 1 φ s 2 y j = 1 y j1 y jp φ s β 0 β 1 ΔX i ~ N μδt i σ 2 Δt i 3 ΔX i = X t i - X t i - 1 Δt i = Λ t i - Z * Y = A * Y = A * 0 + A * 1 y A * p y p 9 Λ t i - 1 Z * Y = A * Y = A * 0 + A * 1 y A * p y p C 10 Λ ~ IG C /μ C 2 /σ 2 IG b 1 b 2 A * i = a i d i A * i = a i b 1 > 0 b 2 > 0 c i

3 12 min a d d ( n 2227 y j y j ) d + ξa a a y j + d y j Z - subject a y j - d y j Z - to d i 0 i = 0 1 p max a c 2 n c ( n y j y j ) c + ξc c a y i + c y i Z - subject a y j - c y j Z - to c i 0 i = 0 1 p 2 n Z Y Z * Y Z Y Z * Y A * i d i c i + d i d i 0 7 min a c d d ( n y j y j ) d + ξ a a + c c a y j + c y j + d y j Z - a y j - c y j - d y j Z - subject a y i + c y i Z - to a y j - c y j Z - c i 0 d i 0 i = 0 1 p 2 n m j t ijk 1 E X t = μλ t Λ t - X - X - 1 μ - ij μ μ - ij σ Fig 1 Flowchart of interval accelerated degradation testing analysis CSAD x - ijk x - ijk i i = 1 2 K j 2 n i k k = t 2 1 ijk x - ijk x - ijk 7 p = A 1 μ - ij μ - ij σ

4 σ K σ 2 i = 1 = n i m j k = 2 e ijk - e ij k K n i m j Δt ijk i = 1 k = 2 e ijk e ijk = 3 1 x ijk - μ ijk Λ t ijk e * ijk = x - * ijk - x - 18 ijk 2 * 2 + x - ijk - - x 槡 ijk σ 2 μ - 0 μ able 1 Information on accelerated wear degradation i μ - ij μ - testing for metal alloy ij μ - i μ - i n { i μ - i = min { μ - ij μ - } μ - n i i = max { μ - ij μ - 17 } s i μ - i μ - i 7 p 14 a c d s 0 μ - 0 μ Fig 2 Degradation data for accelerated wear testing under 5 6 three applied weights 2 1 μ - 0 μ - 0 σ 1 Δ i Δ i ~ N m ζm m ζ R R - t - R t C σ μ 0 μ - 0 μ - 0 = C σ μ - 0 R t t - - r t r = Λ -1 R -1 μ - 0 Λ -1 R -1 μ - 0 C σ - μ 0 C σ R = r C σ R = r /g /h ζ = 0 02 ζ = 0 2 i ± Δ i m m

5 μm m C = 50 μm 1 5 g 2 φ s = W W 2 Λ t = ln t m = 0 5 μm ζ = m μ - ij μ - ij σ = W i μ - i μ - i 14 3 μ - 0 μ - 0 = exp h Fig μ Draft coefficient μ under three applied weights 5 ~ 7 μ 0 σ 5 a m b μ 0 m μ 0 σ 6 4 Fig 4 m = 0 5 μm Interval reliability curves when m = 0 5 μm m m Fig 5 Center and radius of draft coefficients under different m values in two cases

6 m Fig 6 Diffusion coefficients under different m values in two cases 3 Fig 7 m R = 0 9 R = 0 9 under different m values in two cases m σ a 7 b 1 m 2 m 4 11 Ye Z S μ μ 0 σ References 1 Nelson W B Accelerated testing Statistical models test plans and data analysis M New York John Wiley & Sons Meeker W Q Escobar L A Lu C J Accelerated degradation tests Modeling and analysis J echnometrics J Deng A M Chen X Zhang C H et al A comprehensive review of accelerated degradation testing J Acta Armamentarii in Chinese 4 Wang Z Huang H Z Du L Reliability analysis on competitive failure processes under fuzzy degradation data J Applied Soft Computing Gonzalez-Gonzalez D S Alejo R J P Cantu-Sifuentes M et al A non-linear fuzzy regression for estimating reliability in a degradation process J Applied Soft Computing Alefeld G Mayer G Interval analysis heory and applications Center and radius of reliable lifetimes when J Journal of Computational and Applied Mathematics anaka H Lee H Interval regression analysis by quadratic programming approach J IEEE ransactions on Fuzzy Systems J Wang J Qiu Z P Wang X J Interval analysis for stress intensity factors J Acta Aeronautica et Astronautica Sinica in Chinese 9 Yu I Chang C L Applying Bayesian model averaging for quantile estimation in accelerated life tests J IEEE ransactions on Reliability Chateauneuf A Accelerated life testing and degradation modeling J Reliability Engineering & System Safety Xie M Stochastic modelling and analysis of degradation

7 12 for highly reliable products J Applied Stochastic Models in Business and Industry Park C Padgett W J Stochastic degradation models with several accelerating variables J IEEE ransactions on Reliability Pan Z Q Balakrishnan N Multiple-steps step-stress accelerated degradation modeling based on Wiener and Gamma processes J Communications in Statistics-Simulation and Computation Li X Y Jiang M Sun F Q et al Constant stress AD for superluminescent diode and parameter sensitivity analysis J Eksploatacja I Niezawodnosc-Maintenance and Reliability Wang X Jiang P Guo B et al Real-time reliability evaluation with a general Wiener process-based degradation model J Quality and Reliability Engineering International Escobar L A Meeker W Q A review of accelerated test models J Statistical Science Chhikara R S Folks J L he inverse Gaussian distribution heory methodology and applications M New York CRC Press Meeker W Q Escobar L A Statistical methods for reliability data M New York John Wiley & Sons Evaluation method for accelerated degradation testing with interval analysis LIU Le 1 2 LI Xiaoyang * 1 2 JIANG ongmin 1 1 School of Reliability and Systems Engineering Beijing University of Aeronautics and Astronautics Beijing China 2 Science and echnology on Reliability and Environmental Engineering Laboratory Beijing China Abstract raditional evaluation methods of accelerated degradation testing AD are based on precise degradation data to conduct reliability and lifetime assessment However with interfere of the uncertainties from human factors the test data can be imprecise represented by interval rather than precise data Under this consideration an interval analysis method for AD evaluation was proposed based on Wiener process which included possibility and necessity models Interval regression method was firstly used to transfer the problems of modeling interval degradation data under different accelerated stress levels into quadratic programming problems he interval drift coefficients under different stress levels with possibility model and diffusion coefficient were obtained hen the interval drift coefficients were extrapolated to normal stress condition with accelerated model under necessity model and further to analyze the relationship between measurement uncertainty and reliability and lifetime evaluation results Finally the numerical study was used to present and verify the proposed methodology and conduct uncertainty sensitivity analysis he results show that both reliability and lifetime evaluation results are effected by epistemic uncertainty of measurement and their correctness can be ensured with decreasing epistemic uncertainty Key words accelerated degradation testing AD interval analysis reliability life evaluation epistemic uncertainty sensitivity analysis

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