List of Figures

Figure 1.1 Conceptualized aging rates for physics-of-failure mechanisms Figure 1.2 First law energy flow to system: (a) heat-in, work-out; and (b) heat-in and work-in Figure 1.3 Fatigue S-N curve of cycles to failure versus stress, illustrating a fatigue limit in steel and no apparent limit in aluminum Figure 1.4 Elastic stress limit and yielding point 1 Figure 2.1 The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero Figure 2.2 Cell fatigue dislocations and cumulating entropy Figure 2.3 Gaussian white noise Figure 2.4 Noise limit heart rate variability measurements of young, elderly, and CHF patients [10] Figure 2.5 Noise limit heart rate variability chaos measurements of young and CHF patients [10] Figure 2.6 Graphical representation of the autocorrelation function Figure 2.7 (a) Sine waves at 10 and 15 Hz with some randomness in frequency; and (b) Fourier transform spectrum. In (b) we cannot transform back without knowledge of which sine tone occurred first Figure 2.8 (a) White noise time series; (b) normalized autocorrelation function of white noise; and (c) PSD spectrum of white noise Figure 2.9 (a) Flicker (pink) 1/f noise; (b) normalized autocorrelation function of 1/f noise; and (c) PSD spectrum of 1/f noise Figure 2.10 (a) Brown 1/f?2 noise; (b) normalized autocorrelation function of 1/f?2 noise; and (c) PSD spectrum of 1/f?2 noise Figure 2.11 Some key types of white, pink, and brown noise that might be observed from a system Figure 2.12 1/f noise simulations for resistor noise. Note the lower noise for larger resistors (power of 2) and higher noise for smaller resistors (power of 1.5) Figure 2.13 Autocorrelation noise measurement detection system Figure 2.14 Insulating cylinder divided into two sections by a frictionless piston Figure 2.15 System (capacitor) and environment (battery) circuit Figure 2.16 The system expands against the atmosphere Figure 2.17 Mechanical work done on a system Figure 2.18 Loss of available work due to increase in entropy damage Figure 2.19 A simple system in contact with a heat reservoir Figure 2.20 A system's free energy decrease over time and the corresponding total entropy increase Figure 3.1 Conceptual view of cyclic cumulative damage Figure 3.2 Cyclic work plane Figure 3.3 Carnot cycle in P, V plane Figure 3.4 Cyclic engine damage Area 1?>?Area 2 Figure 4.1 Creep strain over time for different stresses where s4?>?s3?>?s2?>?s1 Figure 4.2 Example of creep of a wire due to a stress weight Figure 4.3 Wear occurring to a sliding block having weight PW Figure 4.4 Graphical example of a sine test resonance Figure 5.1 Lead acid and alkaline MnO2 batteries fitted data Figure 5.2 A simple corrosion cell with iron corrosion Figure 5.3 Uniform electrochemical corrosion depicted on the surface of a metal Figure 6.1 Arrhenius activation free energy path having a relative minimum as a function of generalized parameter a Figure 6.2 Examples of ln(1?+?B time) aging law, with upper graph similar to primary and secondary creep stages and the lower graph similar to primary battery voltage loss Figure 6.3 Log time compared to power law aging models Figure 6.4 (a) Continuous function with numerous energy states. (b) Relative minimum energy states having different degradation mechanisms Figure 6.5 Aging with critical values tc prior to catastrophic failure Figure 7.1 Types of wear dependence on sliding distance (time) Figure 7.2 Capacitor leakage model Figure 7.3 Beta degradation on life test data Figure 7.4 Life test data of gate-source MESFET leakage current over time fitted to the ln(1?+?Bt) aging model. Junction rise was about 30°C Figure 8.1 System with n particles and nenv environment particles Figure 8.2 Diffusion concept Figure 9.1 Reliability bathtub curve model Figure 9.2 Power law fit to the wear-out portion of the bathtub curve Figure 9.3 Log time aging with parametric threshold tf Figure 9.4 PDF failure portion that drifted past the parametric threshold Figure 9.5 Creep curve with all three stages Figure 9.6 Creep rate power law model for each creep stage, similar to the bathtub curve in Figure 9.1 Figure 9.7 Creep strain over time for different stresses where s4?>?s3?>?s2?>?s1 Figure 9.8 Crystal frequency drift showing time-dependent standard deviation Figure A.1 Reliability bathtub curve model Figure A.2 Demonstrating the power law on the wear-out shape Figure A.3 Modeling the bathtub curve with the Weibull power law Figure A.4 Weibull hazard (failure) rate for different values of ß [1] Figure A.5 Weibull shapes of PDF and CDF with ß?=?2 [1] Figure A.6 Weibull shapes of PDF and CDF with ß?=?0.5 [1] Figure A.7 Normal distribution shapes of PDF and CDF; µ?=?5, s?=?1 [1] Figure A.8 Lognormal hazard (failure) rate for different s values [1] Figure A.9 Lognormal CDF and PDF for different s values [1] Figure A.10 Cpk analysis Figure A.11 Life test: (a) Weibull analysis compared to (b) lognormal analysis test at 200°C [1] Figure A.12 Field data (Table A.4) displaying inflection point as sub and main populations [1] Figure A.13 Separating out the lower and upper distributions by the inflection point method [1] Figure B.1 Main accelerated stresses and associated common failure issues Figure B.2 Common accelerated qualification test plan used in industry [1] Figure B.3 Arrhenius plot of data given in Table B.1 Figure B.4 MTTF stress plot of data given in Table B.2 Figure B.5 Sine vibration amplitude over time example Figure B.6 Random vibration amplitude time series example Figure B.7 PSD of the random vibration time series in Figure B.6 Figure C.1 S-N curve for human heart compared to metal N fatigue cycle life versus...