Reliability Modeling Using Degradation Data - by Harry Guo

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Reliability Modeling Using Degradation Data - by Harry Guo

  1. 1. Reliability Modeling Using Degradation Data 利用退化数据进行可靠性 预计 Harry Guo
  2. 2. ASQ Reliability Division Chinese Webinar Series One of the monthly webinars on topics of interest to reliability engineers To view upcoming or recorded webinars visit us today at www.asqrd.org
  3. 3. ©1992-2014 ReliaSoft Corporation - ALL RIGHTS RESERVED 利用退化数据进行可靠性预计 (Reliability Modeling Using Degradation Data) 郭怀瑞 (Harry Guo) Ph.D., CRE, CQE, CRP
  4. 4. 4 Outlines Part 1: Failures caused by degradation Examples of integrated circuits (ICs) Examples of mechanical components Part 2: Using degradation data to predict component reliability Non-destructive inspection Destructive inspection Part 3: Accelerated degradation data analysis
  5. 5. 5 EDUCATION 5 Part I: Failures Caused by Degradation
  6. 6. 6 Why Failure Occurs Failures can occur for many different reasons. Design incapability Being overstressed Manufacturing defects Wearout User error …
  7. 7. 7 Wearout Failure Failures can be caused by component properties changing over time. Adequate initial quality doesn’t ensure high reliability. Component performance can decrease very quickly. Material strength decreases over time. Corrosion, insulation and voltage deteriorate with time. A failure occurs, when degradation reaches a critical value. Wearout failures are time dependent. Failure rate increases with time.
  8. 8. 8 Stress-Strength STRESS STRENGTHFail Region dxxRxfxxP stressstrengthstrengthstress )()()( 0   
  9. 9. 9 Stress-Strength vs. Age Age/Time Stress/StrengthUnitsProbabilityofFailure
  10. 10. 10 Failure Mechanisms of ICs (Integrated Circuits) Electromigration (EM) Can cause voids and accumulations at material boundaries due to metal ion drift caused by electron current. Results in increase of resistance and loss of connections in ICs. Stress migration (SM) Flow of metal atoms under the influence of mechanical stress. Results in increase of resistance and can even lead to an open circuit.
  11. 11. 11 Failure Mechanisms of ICs (cont'd) Corrosion Corrosion tests are usually conducted under high temperature and high humidity. Corrosion activity is measured by monitoring the resistance versus time. Time-Dependent Dielectric Breakdown (TDDB) Caused by dielectric degradation in electric fields. Current density increases dramatically and voltage drops to 0 when TDDB occurs. This is a destructive test. The component is destroyed after TDDB occurs.
  12. 12. 12 Failure Mechanisms of Mechanical Components Creep-Induced Failures Creep is caused by applying a constant stress (beyond the yield point of the material) on a component. Crack-Induced Failures Micro-cracks may be introduced during fabrication. Its length can increase under loading and lead to failure. Fatigue-Induced Failures Fatigue can arise when a material is continually put under cyclical stress conditions. Adhesion Failures The bonding force between materials decreases with time.
  13. 13. 13 EDUCATION 13 Part II: Using Degradation Data to Predict Reliability
  14. 14. 14 Degradation Analysis: Non-Destructive This type of analysis involves the measurement of degradation or performance over time. Degradation data is also called parameter data. Use a parameter or index to indicate the status of a component. The degradation path/curve can be described by a mathematical function. Failure can be directly related to the amount of degradation.
  15. 15. 15 Degradation Data – Crack Length Example An example of degradation data involves the length of cracks in turbine blades. A failure is defined as a crack length of 1.6 inches or greater. A specimen is tested to 120,000 cycles, at which point the crack length is 1.27 inches. Even though the crack in the test specimen did not reach the critical length, it is a simple matter to extrapolate the test data to the point at which the degradation would reach the critical level (177,480 cycles). 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0 50000 100000 150000 200000 Cycles Cracklength(inches) 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0 50000 100000 150000 200000 Cycles Cracklength(inches) 177480
  16. 16. 16 Mathematical Models for Degradation Path The commonly used degradation models are the following simple models: Linear: 𝒚 = 𝒂 ∙ 𝒕 + 𝒃 Exponential: 𝒚 = 𝒃 ∙ 𝒆 𝒂∙𝒕 Power: 𝒚 = 𝒃 ∙ 𝒕 𝒂 Logarithmic: 𝒚 = 𝒂 ∙ 𝒍𝒏 𝒕 + 𝒃 where • 𝑦 represents the degradation performance or the percentage of change from the initial value, • 𝑡 represents time, and 𝑎 and 𝑏 are model parameters to be solved for.
  17. 17. 17 Example 1: Voltage Decreasing The threshold voltage of an electronics component decreases with time. Voltage readings are obtained from a test. Use a model to describe the changes of voltage with time. Predict the voltage reading after 1,000 hours. Time (hr) Voltage 0 1.500 100 1.384 200 1.363 300 1.348 400 1.334 500 1.320 600 1.312
  18. 18. 18 Solution for Example 1 The following power model is used 𝑉𝑡 = 𝑉0(1 − 𝑏 × 𝑡 𝑎 ) This function can be converted to a simple linear regression function: 𝑌 = 𝑏′ + 𝑎 × 𝑙𝑛(𝑡) where: 𝑌 = ln( 𝑉0−𝑉 𝑡 𝑉0 ) , 𝑏′ = ln 𝑏 . The final function is: 𝑉𝑡 = 1.5 (1 − 0.021 × 𝑡 0.278 )
  19. 19. 19 Solution for Example 1 (cont'd) The predicted voltage at 1,000 hours is: 1.5 1 − 0.021 × 1,000 0.278 = 1.284
  20. 20. 20 Degradation with Multiple Stages Sometimes the degradation path is an S-shaped curve. This is for cases when degradation has multiple stages. Degradation behaviors are different at different stages. We can use either piecewise regression or an S- shaped curve to describe the degradation.
  21. 21. 21 Example 2: Pressure Drop of a Material A material is used in surgery to hold a certain pressure to prevent body fluid leakage. The pressure will decrease after the material is deployed. The material should meet the pressure requirement after a certain time of use. The engineering team wants to study how the pressure degrades and then make design changes to adjust the initial pressure value.
  22. 22. 22 Example 2: Pressure Drop of a Material (cont'd) Initial tests showed that the material degradation experienced different stages. Pressure quickly drops immediately after deployed. Drop rate then slows down. Commonly used degradation functions such as linear, power and logarithmic do not work well in this case.
  23. 23. 23 Example 2: Pressure Drop of a Material (cont'd)
  24. 24. 24 Example 2: Pressure Drop of a Material (cont'd) It was found that modeling the percentage of pressure drop is better than modeling the pressure directly. This can reduce the effect of the initial value of each test sample to the modeling. Percentage is a value between 0 and 1, so the function we are going to use should meet this constraint. The function should also account for the quick change at the beginning and slow change at the later stages.
  25. 25. 25 Example 2: Pressure of a Material (cont'd) • A Mixed Weibull distribution is used. • The curve can fit the observations very well. • Based on the pressure requirement at time t, we can calculate what the initial pressure of the material should be.
  26. 26. 26 From Degradation to Failure Time When degradation reaches a certain level, the component cannot function as designed. For example: If the bonding force is too small, then bonded materials will be separated. If the voltage dropped to a critical value, then a signal of 1 becomes a signal of 0. The wearout of a seal will cause gas or oil leakage. Crack length on turbine blades is too big which will cause vibration and break the blade.
  27. 27. 27 From Degradation to Failure Time  For each test unit, we can use a function to describe the degradation path.  Using this function, we can predict the time when degradation will reach a critical value.
  28. 28. 28 Reliability Prediction Using Failure Times Once we have “failure times,” we can use them to predict reliability. These failure times are “predicted” pseudo failure times from the degradation function. This is for cases when a quantitative parameter can be used to indicate the performance of a component.
  29. 29. 29 Example 3: Crack Propagation For the crack of a mechanical component, a failure occurs when its length is above a certain value (30 mm). Degradation tests are conducted for several samples. The data set is given in this table.
  30. 30. 30 Example 3: Crack Propagation (cont’d)
  31. 31. 31 Example 3: Crack Propagation (cont'd) The calculated reliability function using a Weibull distribution is: 8.055 519.55 ( ) t R t e       
  32. 32. 32 Degradation with Destructive Inspection For some degradation processes, we cannot get the degradation reading without destroying the test samples (e.g., the breakdown voltage of semiconductor components). Each test sample has only one degradation reading. Therefore, we cannot build a degradation path for each individual test sample as we discussed before.
  33. 33. 33 Example 4: Dielectric Breakdown Voltage The dielectric breakdown strength of insulation specimens decreases with time. Each test sample was held for a certain time period at a constant temperature, and then its breakdown voltage was measured (a destructive test). The insulation fails when the breakdown voltage degrades below the design voltage 1.0 kV. We need to estimate the reliability of the insulation specimen based on the destructive test data.
  34. 34. 34 Example 4: Dielectric Breakdown Voltage (cont'd) Sample ID Week Breakdown Voltage (KV) Sample ID Week Breakdown Voltage (KV) 1 1 14 17 16 6 2 1 13 18 16 6 3 1 14 19 16 5 4 1 11.5 20 16 5.5 5 2 13 21 32 2.7 6 2 11.5 22 32 2.7 7 2 13 23 32 2.5 8 2 12.5 24 32 2.4 9 4 10 25 48 1.2 10 4 11.5 26 48 1.5 11 4 11 27 48 1 12 4 9.5 28 48 1.5 13 8 6.5 29 64 1.5 14 8 5.5 30 64 1 15 8 6 31 64 1.2 16 8 6 32 64 1.2
  35. 35. 35 Example 4: Dielectric Breakdown Voltage (cont'd) At a given time, the degradation value is assumed to be a random variable following a distribution. The location parameter of the distribution is a function of time. The probability of getting a degradation value beyond the critical value at time t is the unreliability at time t. ( ) Pr( ( ) )critF t x t D 
  36. 36. 36 Example 4: Dielectric Breakdown Voltage (cont'd) We assume the degradation follows a Weibull distribution. The scale parameter eta (𝜂) is a function of time: The probability of failure at time t is: 1 ( ) n t K t      ( ) ( ) Pr( ( ) ) 1 1 crit n crit D t crit D K t F t x t D e e                   For example, when t = 100, the probability of failure F(100) is 0.2454.
  37. 37. 37 EDUCATION 37 Part III: Accelerated Degradation Data Analysis
  38. 38. 38 Accelerated Degradation Test It may take too long to test a component at the normal use condition. The degradation rate may be higher at elevated stress conditions. By testing components at higher stresses, we can get degradation data more quickly and use the data for reliability prediction.
  39. 39. 39 Accelerated Degradation Data Analysis The method used to analyze accelerated degradation data is the same as the method used for degradation data obtained at the normal stress condition. The degradation value is not only affected by time, it is also affected by the stress level. The stress level affects degradation rate.
  40. 40. 40 Non-Destructive Accelerated Degradation Data Analysis High Temperature Low Temperature
  41. 41. 41 Example 5: Accelerated Degradation – Non-Destructive Consider a chemical solution (e.g., ink formulation, medicine, etc.) that degrades with time. A quantitative measure of the quality of the product can be obtained. This measure (QM) is said to be around 100 when the product is first manufactured and decreases with age. Any QM higer than 50 is acceptable. Products with QM equal to or lower than 50 are considered to be out of compliance or failed. Engineering analysis has indicated that at higher temperatures the QM has a higher rate of decrease. Assuming that the product’s normal use temperature is 20oC (or 293K), the goal is to determine the shelf life of the product via an accelerated degradation test. “Shelf life” is defined as the time by which 10% of the products will have a QM that is out of compliance.
  42. 42. 42 Example 5: Accelerated Degradation – Non-Destructive (cont'd) For this experiment, 15 samples of the product were tested, with 5 samples in each of three accelerated stress environments: 323K, 373K and 383K. Once a month, for a period of seven months, the QM for each sample was measured and recorded.
  43. 43. 43 Example 5: Accelerated Degradation – Non-Destructive (cont'd)
  44. 44. 44 Degradation Results Data for all samples were entered and individually fitted to multiple exponential curves. From each respective curve, a time-to-failure (i.e., the time the product is expected to go out of compliance) was automatically extrapolated.
  45. 45. 45 B10 Life Line B10 Life
  46. 46. 46 Where to Get More Information 1. http://www.itl.nist.gov/div898/handbook/ 2. www.weibull.com 3. http://www.ReliaWiki.org/index.php/ReliaSoft_Books

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