List of Figures

Figure 1.1Conceptualized aging rates for physics-of-failure mechanisms
Figure 1.2First law energy flow to system: (a) heat-in, work-out; and (b) heat-in and work-in
Figure 1.3Fatigue S–N curve of cycles to failure versus stress, illustrating a fatigue limit in steel and no apparent limit in aluminum
Figure 1.4Elastic stress limit and yielding point 1
Figure 2.1The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero
Figure 2.2Cell fatigue dislocations and cumulating entropy
Figure 2.3Gaussian white noise
Figure 2.4Noise limit heart rate variability measurements of young, elderly, and CHF patients [10]
Figure 2.5Noise limit heart rate variability chaos measurements of young and CHF patients [10]
Figure 2.6Graphical 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 2.11Some key types of white, pink, and brown noise that might be observed from a system
Figure 2.121/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 2.13Autocorrelation noise measurement detection system
Figure 2.14Insulating cylinder divided into two sections by a frictionless piston
Figure 2.15System (capacitor) and environment (battery) circuit
Figure 2.16The system expands against the atmosphere
Figure 2.17Mechanical work done on a system
Figure 2.18Loss of available work due to increase in entropy damage
Figure 2.19A simple system in contact with a heat reservoir
Figure 2.20A system’s free energy decrease over time and the corresponding total entropy increase
Figure 3.1Conceptual view of cyclic cumulative damage
Figure 3.2Cyclic work plane
Figure 3.3Carnot cycle in P, V plane
Figure 3.4Cyclic engine damage Area 1 > Area 2
Figure 4.1Creep strain over time for different stresses where σ4 > σ3 > σ2 > σ1
Figure 4.2Example of creep of a wire due to a stress weight
Figure 4.3Wear occurring to a sliding block having weight PW
Figure 4.4Graphical example of a sine test resonance
Figure 5.1Lead acid and alkaline MnO2 batteries fitted data
Figure 5.2A simple corrosion cell with iron corrosion
Figure 5.3Uniform electrochemical corrosion depicted on the surface of a metal
Figure 6.1Arrhenius activation free energy path having a relative minimum as a function of generalized parameter a
Figure 6.2Examples 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 6.3Log 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 6.5Aging with critical values tc prior to catastrophic failure
Figure 7.1Types of wear dependence on sliding distance (time)
Figure 7.2Capacitor leakage model
Figure 7.3Beta degradation on life test data
Figure 7.4Life 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 8.1System with n particles and nenv environment particles
Figure 8.2Diffusion concept
Figure 9.1Reliability bathtub curve model
Figure 9.2Power law fit to the wear-out portion of the bathtub curve
Figure 9.3Log time aging with parametric threshold tf
Figure 9.4PDF failure portion that drifted past the parametric threshold
Figure 9.5Creep curve with all three stages
Figure 9.6Creep rate power law model for each creep stage, similar to the bathtub curve in Figure 9.1
Figure 9.7Creep strain over time for different stresses where σ4 > σ3 > σ2 > σ1
Figure 9.8Crystal frequency drift showing time-dependent standard deviation
Figure A.1Reliability bathtub curve model
Figure A.2Demonstrating the power law on the wear-out shape
Figure A.3Modeling the bathtub curve with the Weibull power law
Figure A.4Weibull hazard (failure) rate for different values of β [1]
Figure A.5Weibull shapes of PDF and CDF with β = 2 [1]
Figure A.6Weibull shapes of PDF and CDF with β = 0.5 [1]
Figure A.7Normal distribution shapes of PDF and CDF; μ = 5, σ = 1 [1]
Figure A.8Lognormal hazard (failure) rate for different σ values [1]
Figure A.9Lognormal CDF and PDF for different σ values [1]
Figure A.10Cpk analysis
Figure A.11Life test: (a) Weibull analysis compared to (b) lognormal analysis test at 200°C [1]
Figure A.12Field data (Table A.4) displaying inflection point as sub and main populations [1]
Figure A.13Separating out the lower and upper distributions by the inflection point method [1]
Figure B.1Main accelerated stresses and associated common failure issues
Figure B.2Common accelerated qualification test plan used in industry [1]
Figure B.3Arrhenius plot of data given in Table B.1
Figure B.4MTTF stress plot of data given in Table B.2
Figure B.5Sine vibration amplitude over time example
Figure B.6Random vibration amplitude time series example
Figure B.7PSD of the random vibration time series in Figure B.6
Figure C.1S–N curve for human heart compared to metal N fatigue cycle life versus S stress amplitude
Figure C.2Simplified body repair
Figure C.3Charge and repair RC model for the human body
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