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Reliability estimation from accelerated degradation testing

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Accelerated tests are conducted at various stages of the product life cycle. When accelerated life tests yield few or no failures at low stress levels, it is difficult or impossible to estimate reliability at the design stress level. In such situations, accelerated degradation tests may be used. This presentation introduces accelerated degradation test methods, degradation models, estimation of model parameters, relationships between degradation and reliability, and estimation of reliability at the design stress level. Several practical examples are presented.

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Reliability estimation from accelerated degradation testing

  1. 1. Reliability Estimation from  Accelerated Degradation Testing 基于加速退化试验的可靠性估 计 Guangbin Yang (杨广斌), Ph.D.
 ©2011 ASQ & Presentation Yang Presented live on Jan 08th, 2011http://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_‐_Chinese/Webinars_‐_Chinese.html
  2. 2. ASQ Reliability Division  Chinese Webinar  Series One of the monthly webinars  on topics of interest to  reliability engineers. To view recorded webinar (available to ASQ Reliability  Division members only) visit asq.org/reliability To sign up for the free and available to anyone live  webinars visit reliabilitycalendar.org and select English  Webinars to find links to register for upcoming eventshttp://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_‐_Chinese/Webinars_‐_Chinese.html
  3. 3. Reliability Estimation fromAccelerated Degradation Testing基于加速退化试验的可靠性估计 Guangbin Yang (杨广斌), Ph.D.Ford Motor Company, Dearborn, Michigan, U.S.A. Email: gbyang@ieee.org
  4. 4. Overview ALT (Accelerated Life Test) and ADT (Accelerated Degradation Test) Reliability Estimation from Pseudo-Lifetimes ADT with Destructive Inspections Takeaways 2
  5. 5. ALT Purpose and Test Method The primary purpose of ALT is to estimate the reliability of a product at the design condition in a shorter time. To do an ALT, a number of units are sampled and divided into two or more groups. Each group is tested at a different accelerating condition. The test at an accelerating condition continues until all units fail, or until a pre-specified time or number of failures is reached. 3
  6. 6. ALT Data Analysis The life data of all groups are combined to estimate the reliability at the design condition through an acceleration relationship. acceleration S relationship S2       S1       S0 0 t 4
  7. 7. Why ADT? The time allowed for testing is continuously reduced, and thus the test at low stress levels often yields few or no failures. This is especially the case when we test high-reliability products. With few or no failures, it is difficult or impossible to analyze the life data and make meaningful inferences about product reliability. In these situations, we should consider ADT. 5
  8. 8. What Products Are Suitable for ADT? Soft failure: failure is defined by a performance characteristic degrading to an unacceptable level. Degradation is irreversible; that is, the performance characteristics monotonically increase or decrease with time. For convenience of data analysis, a product should have a critical performance characteristic, which describes the dominant degradation process and is closely related to reliability. Such a characteristic is fairly obvious to identify for many products. 6
  9. 9. ADT Method ADT are similar to ALT. During ADT, however, measurements of the critical performance characteristic are taken at various time intervals. Most ADT apply constant stress. Other types of stress (e.g., step stress) may be used, but are not common in practice because of complexity in data analysis and stress application. 7
  10. 10. Methods for Degradation Data Analysis Degradation data obtained at higher stress levels are used to estimate the reliability at the design level. The estimation requires a degradation model that relates performance characteristic to aging time and stress level. The primary methods for reliability estimation include  Pseudo-lifetime analysis.  Random-process method.  Random-effect method. 8
  11. 11. Advantages of ADT An ADT allows reliability to be estimated even before a test unit fails. Thus an ADT greatly reduces the test time and cost. An ADT often yields more accurate estimates than those from life data analysis, especially when a test is highly censored. 9
  12. 12. Disadvantages of ADT Reliability estimation from degradation data often requires intensive computations. An ADT requires frequent measurement of performance characteristics during testing. This increases workload if it cannot be done automatically. 10
  13. 13. Reliability Estimation from Pseudo Lifetimes 伪寿命及可靠性估计 11
  14. 14. Pseudo Life A pseudo life is not an observation. A pseudo life is obtained by extrapolating a degradation path. y G 0 t0 t1 t2 tn t 12
  15. 15. Estimation of Life Distributions y S2 S1 G 0 t21 t23 t11 t13 t 13
  16. 16. Reliability Estimation from PseudoLifetimes at the Design Stress Level The methods for ALT life data analysis apply to pseudo lifetimes. The analysis can be done using commercial software. acceleration S relationship S2       S1       S0 0 t 14
  17. 17. Application Example: Electrical Connector Problem statement  Electrical connectors fail often due to excessive stress relaxation.  Stress relaxation can be measured by the ratio s / s0 (%), where s0 is the initial stress and s is the stress loss.  For an electrical connector, failure is defined by the stress relaxation exceeding 30%.  Estimate its failure probability at the design life of 15 years and the operating temperature of 40C. 15
  18. 18. Application Example: Electrical Connector Test method  A sample of 18 units was randomly selected from a production lot and equally divided into three groups. Each group had 6 units.  The test temperatures were 65, 85 and 100C.  The censoring times were 2848 hours at 65C, 1842 hours at 85C, and 1238 hours at 100C. 16
  19. 19. Application Example: Electrical Connector Stress relaxation data 30 s 100C s0 25 20 85C 65C 15 10 5 0 0 500 1000 1500 2000 2500 3000 t (hr) 17
  20. 20. Application Example: Electrical Connector Degradation model s B  Ea   At exp   s0  kT  where Ea is the activation energy, k is the Boltzmann’s constant, A and B are unknowns. Here A usually varies from unit to unit, and B is a fixed effect parameter. 18
  21. 21. Application Example: Electrical Connector Linearized degradation model At a given temperature, the degradation model can be written as ln( s s0 )  1   2 ln(t ), where 1  ln( A)  Ea / kT , and  2  B. 19
  22. 22. Application Example: Electrical Connector The linearized degradation model is fitted to each of the 18 degradation paths. 1 and 2 are estimated for each unit using the least squares method. The pseudo lifetime of each test unit is calculated from ˆ  ln( 30)  1  tˆ  exp  .  ˆ2  20
  23. 23. Application Example: Electrical Connector The lifetimes at the three temperatures are lognormal. The shape parameter is reasonably constant. 21
  24. 24. Application Example: Electrical Connector Acceleration relationship From the degradation model, we can assume the acceleration relationship as    0  1 / T , where  is the lognormal scale parameter, T is the absolute temperature, 0 and 1 are unknown parameters. 22
  25. 25. Application Example: Electrical Connector Estimation of acceleration model parameters Using Minitab (or other software), we obtain the ML estimates: ˆ0  14.56,  1  8373.35,   0.347. ˆ ˆ 23
  26. 26. Application Example: Electrical Connector Failure Probability at the Use Temperature The estimate of the scale parameter at 40C is   14.56  8373.35 / 313.15  12.179. ˆ Then the failure probability at 15 years (131,400 hours) is  ln(131,400)  12.179  F (131,400)      0.129.  0.347  24
  27. 27. ADT with Destructive Inspections 破坏性加速退化试验 25
  28. 28. Destructive Inspections For some products, inspection to measure performance characteristics must damage the function of the test units.  Example 1: A solder joint must be sheared or pull off to get its strength.  Example 2: An insulator must be broken down to measure its dielectric strength. After destructive inspection, units cannot restart with the same function as before the inspection, and are removed from testing. 26
  29. 29. Destructive Inspections A unit is inspected once and generates only one measurement. The performance characteristics usually are monotonically decreasing strengths. The degradation analysis methods described earlier are not applicable. Instead, the random- process method can be used. 27
  30. 30. Test Method, Degradation Data, andAnalysis y S0                 S1         G      S2  t0 t 28
  31. 31. Application Example: Copper Wire Bond Problem statement  To reduce cost, it was planned to replace gold wire with copper wire to provide an electrical interconnection for a new semiconductor device.  The shear strength of wire bonds is the critical characteristic. If it is less than 15 grams force, a bond is said to have failed.  We wanted to estimate the reliability of the wire bonds after the use of 8500 cycles at a temperature profile of –25C to 75C. 29
  32. 32. Application Example: Copper Wire Bonds Test plan Sample High T Low T Group Inspection Cycles Size (C) (C) A 100 125 –55 50, 100, 300, 600, 900 B 100 110 –45 100, 300, 600, 900, 1200 C 100 95 –35 300, 600, 900, 1200, 1500 30
  33. 33.  Shear Strength (gf) 15 0 20 40 60 80 100 A50 A100 A300 A600 Shear strength data A900 B100 B300 B600 B900 B1200 C300 C600 C900 C1200 C1500 Application Example: Copper Wire Bonds31
  34. 34. Application Example: Copper Wire Bonds Lognormal fits to the strength data of group A 99 A50 95 A100 A300 90 A600 A900 80 70 60 Percent 50 40 30 20 10 5 1 5 10 20 40 60 80 120 Shear Strength 32
  35. 35. Application Example: Copper Wire Bonds Lognormal fits to the strength data of group B 99 B100 95 B300 B600 90 B900 B1200 80 70 60 Percent 50 40 30 20 10 5 1 10 20 40 60 80 100 120 Shear Strength 33
  36. 36. Application Example: Copper Wire Bonds Lognormal fits to the strength data of group C 99 C300 95 C600 C900 90 C1200 C1500 80 70 60 Percent 50 40 30 20 10 5 1 10 20 40 60 80 100 120 Shear Strength 34
  37. 37. Application Example: Copper Wire Bonds Plots of estimates of µy vs. log inspection cycles for all groups 4.5 y ˆ 4 3.5 3 Group A 2.5 Group B Group C 2 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 ln(t) 35
  38. 38. Application Example: Copper Wire Bonds Degradation model  The effect of thermal cycling is often described by the Coffin-Manson relationship. From the previous plots, we have  y  1   2 ln(t )   3 ln( T ), where T is the temperature range.  Multiple linear regression analysis suggests this model is reasonable. 36
  39. 39. Application Example: Copper Wire Bonds Estimation of model parameters Consider the degradation model as a two-variable acceleration relationship, where t is also treated as a stress. Using Minitab, we obtain 1  28.1165,  2  0.6445,  3  4.1416,  y  0.2205. ˆ ˆ ˆ ˆ 37
  40. 40. Application Example: Copper Wire Bonds Reliability at the use temperature profile  The estimate of y after 8500 cycles at the use condition (T = 100C) is  y  3.212 ˆ  The reliability at 8500 cycles is  ln(G )   y  ˆ  ln(15)  3.2124  R(8500 )  Pr( y  G )  1      1     0.9889   y ˆ    0.2205  38
  41. 41. Takeaways ADT is more efficient than ALT, and should be used whenever possible. Pseudo-lifetime method applies to nondestructive inspections. Random-process method can be used for both destructive and nondestructive inspections. 39

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