Contents -- Preface -- 1. Preliminaries -- 1.1 Introduction -- 1.2 The Poisson Process -- 1.3 The Renewal Process -- 1.4 Stochastic Order and Class of Lifetime Distributions -- 1.5 Martingales -- 1.6 The Rate of Occurrence of Failures -- 1.7 Notes and References -- 2. Geometric Process -- 2.1 Introduction -- 2.2 Geometric Process -- 2.3 Age, Residual Life and Total Life -- 2.4 Limit Theorems for Geometric Process -- 2.5 A Geometric Process with Exponential Distribution -- 2.6 Notes and References -- 3. Geometric Function -- 3.1 Introduction -- 3.2 Geometric Equation -- 3.3 Existence of Geometric Function -- 3.4 General Solution to Geometric Equation -- 3.5 Analytic Solution to Geometric Equation -- 3.6 Numerical Solution to Geometric Equation -- 3.7 Approximate Solution to Geometric Equation -- 3.8 Comparison with Simulation Solution to Geometric Equation -- 3.9 Exponential Distribution Case -- 3.10 Notes and References -- 4. Statistical Inference of Geometric Process -- 4.1 Introduction -- 4.2 Hypothesis Testing for Geometric Process -- 4.3 Estimation of Parameters in Geometric Process -- 4.4 Asymptotic Distributions of the Estimators -- 4.5 Parametric Inference for Geometric Process -- 4.6 Notes and References -- 5. Application of Geometric Process to Data Analysis -- 5.1 Introduction -- 5.2 Data Analysis by Geometric Process Model -- 5.3 Data Analysis by Poisson Process Models -- 5.4 Real Data Analysis and Comparison -- 5.5 Analysis of Data by a Threshold Geometric Process Model -- 5.6 Notes and References -- 6. Geometric Process Maintenance Model -- 6.1 Introduction -- 6.2 A Geometric Process Maintenance Model -- 6.3 Optimal Replacement Policy -- 6.4 Monotonicity of the Optimal Policy for a Deteriorating System -- 6.5 A Monotone Process Model for a Multistate System -- 6.6 A Geometric Process ShockModel.

6.7 A Geometric Process δ-ShockModel -- 6.8 A Threshold Geometric Process Maintenance Model -- 6.9 A Geometric Process Preventive Maintenance Model -- 6.10 Notes and References -- 7. Application to Analysis of System Reliability -- 7.1 Introduction -- 7.2 Reliability Analysis for a Series System -- 7.3 Reliability Analysis for a Parallel System -- 7.4 Reliability Analysis for a Cold Standby System -- 7.5 A Geometric Process Maintenance Model for a Cold Standby System -- 7.6 Notes and References -- 8. Applications of Geometric Process to Operational Research -- 8.1 Introduction -- 8.2 A Geometric Process M/M/1 Queueing Model -- 8.3 A Geometric Process Warranty Model -- 8.4 Notes and References -- Appendix A SARS Data Sets -- A.1 Hong Kong SARS Daily Infected Case Data -- A.2 Singapore SARS Daily Infected Case Data -- A.3 Ontario SARS Daily Infected Case Data -- A.4 Taiwan SARS Daily Infected Case Data -- Bibliography -- Index.