ACCELERATED LIFE TESTING TRAINING Presented by Byron Jones 1/18/2012

1. MATERIALS IN THIS TRAINING SESSION WERE TAKEN FROM: ACCELERATED LIFE TESTING TRAININGPresented by Byron Jones1/18/2012 Reliability Statistics, by Robert A. Dovich ISBN 0-87389-086-8 Applied Reliability, by Paul A. Tobias & David C.Trindade ISBN 0-442-28310-5 MIL-HDBK-217 Practical Reliability Engineering 3rd, ed. by Patrick D.T. O’Connor ISBN 0-471-92696-5 & ISBN 0-471-92902-6

2. Purpose Of The Training Session Definition Of Useful Life Stages In Life Bath Tub Curve Mean Time To Failure (MTTF) Reliability Reliability Definitions Exponential Distribution Wear Out Distribution Weibull Distribution Accelerated Life Stresses That Contribute to Failure Arrhenius Model Accelerated Life Example Conclusion Appendices ACCELERATED LIFE TESTING TRAINING PROGRAM

3. USEFUL LIFE The number of life units from manufacture to when an item has an unrepairable failure or unacceptable failure rate.

4. STAGES IN LIFE • INFANT MORTALITY • Decreasing Failure Rate • Generally the result of manufacturing errors that are not caught in inspection prior to burn-in or placing in service. Failures resulting from time/stress dependent errors may occur in this period. • CONSTANT FAILURE MODE • Random – Constant Failure Rate • Generally least frequent failure rate which MTBF is based. The flat portion of the bath-tub curve. • WEAROUT PERIOD • Increasing Failure Rate • More predominant in mechanical systems than electrical systems, but wear-out actually begins the moment the product is put into service.

5. RELIABILITY BATHTUB CURVE Infant Mortality Period Wear Out Period Constant Failure Mode

6. MEAN TIME TO FAILURE A basic measure of system reliability for nonrepairable items: The total number of life units of an item divided by the total number of failures within that population, during a particular measurement interval under stated conditions.

7. The probability that an item will perform its intended function for a specified interval under stated environmental conditions. RELIABILITY

8. BASIC RELIABLITY DEFINITIONS • t = the time period (or cycles) under consideration. • e = the base of the natural logarithms (2.718281828). • R(t) = the reliability for a period of time (t) • F(t) = the unreliability for a period of time (t) • MTBF = the mean time between failures (or MCBF is mean cycles between failures) • λ = the failure rate, or the reciprocal of MTBF • Z = the normal probability distribution function statistic • σ = the standard deviation • AF = the acceleration factor

9. EXPONENTIAL DISTRIBUTION The exponential distribution is most often used in reliability engineering to predict the probability of survival to time (t). R(t) f (t) Time

10. PROBABILITY DENSITY FUNCTION R(t) PDF Time PDF = λe-λt = 1/Ø X e-t/Ø ; where t ≥ 0 λ = Failure Rate = 1/Ø Ø = MTBF F(t) = Unreliability = 1 – R(t) R(t) = e-λt or e-t/Ø; where t ≥ 0

11. EXAMPLEExersizes • A unitis run for 316 hours, during that time 4 failures occurred, what is the MTBF for the unit? Ans. 79 hours • What is the probability of the unit running 79 hours without failure? Ans. 36.79% • Some other assembliesfail on an average of 1 in every 500,000 cycles. What is the probability of survival 350,000 cycles? Ans. 49.66%

12. WEAR-OUT DISTRIBUTION The Wear-out phase of product life often follows the Gaussian (normal) frequency distribution model. See Appendix 1, for “Z” statistic conversion. The chance cause failure distribution will also continue to be present. Therefore, fall-out from both distributions must be considered. NORMAL FREQUENCY DISTRIBUTION Z = (W(t) – W(µ)) / σ TIMES EXPONENTIAL FREQUENCY DISTRIBUTION R(t) = e-λt ;where t ≥ 0

13. EXAMPLEExersizes • Some bearings have a wear-out distribution that is know to be normal. The distribution has a mean wear-out time of 2000 hours and a standard deviation of 25 hrs. The time of operation to this point has been 1900 hours. What is the probability that the bearings will survive (wear-out failures only) for the next 16 hours? Hint, R(t)/R(t1) ; where t>t1. Ans. 99.964% • What is the probability that the bearings will survive considering wear-out and chance cause failures? Ans. 99.16%

14. WEIBULL DISTRIBUTION f(t) = β.(t)β-1e[-(t/η)β] ηη for t ≥ 0, 0 for t < 0 and the survival function is e-[(t/η)β] β = shape parameter, which determines distribution shape η = scale parameter; 63.21% of the values fall below this parameter Ø = MTBF Γ(x) = gamma function of a variable (x). See Appendix 2. t = noted time of an individual characteristic. Weibull mean = µw = ηΓ ( 1 + 1/β) Weibull standard deviation = σw σw = η [Γ (1 + 2/β) – Γ2 (1 + 1/β)]½

15. WEIBULL DISTRIBUTION EXAMPLE An assembly was tested and the following were the results of the test: η = 20,000 and β = 2.5. Calculate the Weibull mean, standard deviation, and P(s) for 10,000 hours. Weibull mean = µw = 20,000 {Γ (1+1/2.5)} = 17,745 hrs. Weibull standard deviation = σw σw= 20,000 [{Γ (1+2/2.5)} - {Γ2 (1+1/2.5)}]½= 7593 hrs. P(s)= e-(10,000/20,000)2.5 = .838

16. ACCELERATED LIFE Increasing the stress(es) on the system shortens the expected life of the system. This can be studied and predicted statistically. For example, if the mean life, and standard deviation of a product line is known under normal use conditions, increasing the stress(es) of typical failure causes and noting the mean life and standard deviation under those conditions can shorten the life testing time to an equivalent life.

17. COMMON STRESSES THAT AFFECT PRODUCT LIFE • TEMPERATURE • VIBRATION • PRESSURE • VOLTAGE • CYCLING RATE • LOAD • ENVIRONMENT • Internal • External • FATIGUE • Combination of above

18. ARRHENIUS MODEL λb = K exp (-E/kt) Where: λb is the base failure rate of the item E is the activation energy (eV) for the process k is Boltzmann’s constant, 8.63X10-5 eV K-1 t is the absolute temperature (K°) K is constant For example: Capacitors, vacuum or gas, fixed or Variable, T = 125°C max. rated. At 50% stress level, The failure rate at 100°C is 0.68 per 106 hr, while at 110°C, the failure rate is 0.87 failures per 106 hr. The 110°C failure rate is 1.28 timers the 100° failure rate. At 120°C, the failure rate is 1.2 failures per 106 hr, for an increase of 40% over the 110°C failure rate. A causal rule of thumb for the Arrhenius effect states that for every 10°C increase in temperature, the chemical reactions for electronic and electrical components double, along with their respective failure rates. This general rule should be tempered with experience. This model shows that even small increases in temperature have dramatic increases in failure rates.

19. ACCELERATION FACTOR Under a linear acceleration assumption, we have the relationship (time to fail at stress S1) = AF x (time to fail at stress S2), where AF is the acceleration constant relating times to fail at the two stresses. “AF” is called the acceleration factor between the stresses.

20. ACCELERATED LIFE EXAMPLE A component, tested at 125°C in a laboratory, has an exponential distribution with MTTF 4500 hr. Normal use temperature for the component is 25°C. Assuming an acceleration factor of 35 between these two temperatures, what will the use failure rate be and what percent of these components will fail before the end of the expected useful life period of 40,000 hr? AF = Acceleration factor = 35 MTTF at 125° C = 4500 hrs. MTTF at 25° C is 4500hr. X 35 = 157,500 hr. λ = 1/157,500 = 6.349 x 10-6 F(t) = 1 - e-(40,000x 6.349x10-6) X 100% = 22.43% Ans. Use Failure Rate = 6.349 x 10-6 22.43% will fail by 40,000 hrs. of normal use.

21. EXPECTED RESULTS FROM ACCELERATED LIFE TESTING • SOON • KNOWLEDGE OF PRODUCT LIFE • WARRANTEE COST EXPECTATIONS • LATER • PREDICTIONS OF REPURCHASE TIMES • QUALITY/RELIABILITY IMPROVEMENT

22. APPENDICES