Robust Reliability in the Mechanical Sciences, Softcover reprint of the original 1st ed. 1996

The aim of the book is to develop methodology for reliablity analysis which is particularly suited to the types of partial information characteristic of mechanical systems and structures.
The book is designed as an upper-level undergraduate or first-year graduate text on robust reliability of mechanical systems. It will give the student or engineer a working knowledge of robust reliability which will enable him to analyse the reliability of mechanical systems. Each chapter is introduced with a brief conceptual survey of the main ideas, which are then developed through examples. Problems at the end of each chapter give the student the opportunity to strengthen and extend his or her understanding.

1 Preview of Robust Reliability.- 1.1 Flexible Solar Panel.- 1.2 Quality Control of Thin Shells.- 1.3 Fatigue Failure and Reliability.- 1.4 Plastic Extrusion Manufacturing.- 1.5 Summary.- 2 Convexity and Uncertainty.- 2.1 Complex Uncertainty and Limited Information: Four Examples.- 2.2 Some Convex Models.- 2.3 Expansion of Convex Models.- 2.4 The Structure of Convex Sets.- 2.4.1 Definition of Convexity.- 2.4.2 Extreme Points and Convex Hulls.- 2.4.3 Extrema of Linear Functions on Convex Sets.- 2.4.4 Hyperplane Separation of Convex Sets.- 2.4.5 Linear Systems Driven by Convex Input Sets.- 2.5 Clustering of Uncertain Events: The Convexity Theorem.- 2.6 Problems.- 3 Robust Reliability of Static Systems.- 3.1 Introduction.- 3.2 Beam With An Uncertain Distributed Load.- 3.2.1 Uniform Load Uncertainty.- 3.2.2 Shifted Uniform Load Uncertainty.- 3.2.3 Load-Uncertainty Envelope.- 3.2.4 Fourier Ellipsoid-Bound Uncertainty.- 3.3 Cooling Fin in an Uncertain Flow Field: Reliability and Design.- 3.3.1 Uniform Blade.- 3.3.2 Optimal Thickness Profile.- 3.3.3 Optimal Width and Thickness Profiles.- 3.3.4 Minimum Weight Design.- 3.3.5 Parameter Sensitivity of the Reliability.- 3.4 Beam in Compression With Uncertain Initial Imperfections.- 3.4.1 Band-Limited Energy-Bound Convex Model.- 3.4.2 Fourier Representation of Y (?, N0, N1).- 3.4.3 Maximum Additional Bending Moment.- 3.4.4 Critical-Energy Failure Criterion.- 3.5 Radial Buckling of Thin-Walled Shells; Reliability and Quality Control.- 3.5.1 Localized Imperfections.- 3.5.2 Fourier Ellipsoid-Bound.- 3.6 Reliability of Serial and Parallel Networks.- 3.7 Problems.- 4 Robust Reliability of Time-Varying Systems.- 4.1 Mass and Spring System.- 4.2 Seismic Safety of Secondary Equipment.- 4.2.1 Dynamics.- 4.2.2 Reliability with the Fourier-Envelope Model.- 4.3 Multi-Dimensional Vibrating Structures.- 4.3.1 Formulation.- 4.3.2 Reliability: Hyperplane Separation.- 4.3.3 Input Reliability.- 4.4 Modal Reliability.- 4.4.1 Formulation.- 4.4.2 Coordinate Transformations.- 4.5 Axially Loaded Thin-Walled Shell With Imperfect Initial Shape.- 4.5.1 Dynamics.- 4.5.2 Fourier Ellipsoid Bound.- 4.6 Fatigue Failure and Reliability With Uncertain Loading.- 4.6.1 Damage Evolution.- 4.6.2 Uncertain Load Histories and Maximum Damage Increment.- 4.6.3 The Least-Lifetime Recursion.- 4.6.4 Least-Lifetime With Uncertain Harmonic Loads.- 4.6.5 Fatigue Reliability With Uncertain Harmonic Loads.- 4.6.6 Fatigue Reliability With Complex Uncertain Loads.- 4.7 Problems.- 5 Fault Diagnosis, System Identification and Reliability Testing.- 5.1 Benchmark Diagnostic Resolution: Simple Examples.- 5.1.1 Formulation.- 5.1.2 Single Measurement.- 5.1.3 Variable Measurement Position.- 5.1.4 Multiple Measurements.- 5.1.5 Hyperplane Separation.- 5.1.6 Reliability With Two Measurements.- 5.2 Multi-Hypothesis Diagnosis of Anomalous Inputs.- 5.2.1 Multi-Hypothesis Diagnosis.- 5.2.2 Criterion for Successful Diagnosis 1ll.- 5.2.3 Example.- 5.2.4 Robust Reliability.- 5.3 Least-Squares Estimation.- 5.3.1 Formulation of the Least-Squares Problem.- 5.3.2 Variation of the Least-Squares Solution.- 5.3.3 Estimating a Spectral Centroid.- 5.3.4 Reliability of “Regularized ” Solution.- 5.4 Multi-Hypothesis Diagnosis of a Crack.- 5.4.1 The Eigenvalue Equation.- 5.4.2 The Multi-Hypothesis Algorithm.- 5.4.3 Performance Criterion for the Diagnosis.- 5.4.4 A Useful Theorem.- 5.4.5 Reliability of the Diagnosis.- 5.5 Robust Reliability of Model-Order Determination.- 5.5.1 Formulation.- 5.5.2 Examples.- 5.6 Ill-Posed Problems.- 5.6.1 Column-Space Analysis.- 5.6.2 Multiplicity of Solutions.- 5.7 Selective Sensitivity.- 5.7.1 Basic Concept of Selective Sensitivity.- 5.7.2 Example: 2-Dimensional System.- 5.7.3 Example: Structural Integrity of a Building.- 5.8 Problems.- 6 Reliability of Mathematical Models.- 6.1 Models, Decisions and Reliability.- 6.2 Cooling Fin With Uncertain Geometry.- 6.3 Modal Truncation of a High-Dimensional Model.- 6.4 Robust Multi-Hypothesis System Identification.- 6.4.1 System Formulation.- 6.4.2 Uncertainty in the Nominal Model.- 6.4.3 Multi-Hypothesis Identification.- 6.4.4 Robustness of Asymptotic Multi-Hypothesis Algorithms.- 6.4.5 Robustness of Finite Multi-Hypothesis Algorithms.- 6.4.6 Hierarchical Multi-Hypothesis Algorithms.- 6.5 Problems.- 7 Convex and Probabilistic Models of Uncertainty.- 7.1 Uncertainty Is Not Necessarily Probabilistic: The Three-Box Riddle.- 7.2 Models of Uncertainty: A Comparison.- 7.3 Limitations of Probability.- 7.4 Sensitivity of the Failure Probability: An Example.- 7.4.1 Uncertainty in the PDF of the Load.- 7.4.2 Sensitivity of the Failure Probability.- 7.4.3 Design Implications.- 7.5 Problems.- 8 Robust Reliability and the Poisson Process.- 8.1 The Poisson Distribution.- 8.2 Dynamic System with Uncertain Loads.- 8.3 Shells With Geometric Imperfections.- 8.4 Damage and Annealing Processes.- 8.4.1 Birth and Death Process.- 8.4.2 Damage and Annealing: I.- 8.4.3 Damage and Annealing: II.- 8.5 Problems.- 9 Last But Not Final.- 9.1 Recapitulation of Robust Reliability.- 9.2 Subjective Calibration of Robust Reliability.- 9.2.1 Calibration by Consequence Severity.- 9.2.2 Calibration by the Information Gap.- 9.3 Reliability and Social Acceptability.- 9.4 Robustness as a Managerial Strategy.- References.- Author Index.

The aim of the book is to develop methodology for reliability analysis which is particularly suited to the types of partial information characteristic of mechanical systems and structures. It will give the student or engineer a working knowledge of robust reliability which will enable him to analyse the reliability of mechanical systems. Each chapter is introduced with a brief conceptual survey of the main ideas, which are then developed through examples. Problems at the end of each chapter give the student the opportunity to strengthen and extend his or her understanding.