The geometric process and its applications

Yeh Lam9789812700032, 981-270-003-X

A geometric process is a simple monotone process that was first introduced by the author in 1988. It is a generalization of renewal process. This book captures the extensive research work on geometric processes that has been done since then in both probability and statistics theory and various applications. Some results are published for the first time.A reference book for researchers and a handbook for practioners, it is also a useful textbook for postgraduate or senior undergraduate students.

---

Table of contents :
Contents……Page 12
Preface……Page 8
1.1 Introduction……Page 16
1.2 The Poisson Process……Page 17
1.3 The Renewal Process……Page 23
1.4 Stochastic Order and Class of Lifetime Distributions……Page 33
1.5 Martingales……Page 41
1.6 The Rate of Occurrence of Failures……Page 46
1.7 Notes and References……Page 51
2.2 Geometric Process……Page 52
2.3 Age, Residual Life and Total Life……Page 57
2.4 Limit Theorems for Geometric Process……Page 60
2.5 A Geometric Process with Exponential Distribution……Page 65
2.6 Notes and References……Page 68
3.1 Introduction……Page 70
3.2 Geometric Equation……Page 71
3.3 Existence of Geometric Function……Page 72
3.4 General Solution to Geometric Equation……Page 76
3.5 Analytic Solution to Geometric Equation……Page 78
3.6 Numerical Solution to Geometric Equation……Page 94
3.7 Approximate Solution to Geometric Equation……Page 98
3.8 Comparison with Simulation Solution to Geometric Equation……Page 104
3.9 Exponential Distribution Case……Page 113
3.10 Notes and References……Page 115
4.2 Hypothesis Testing for Geometric Process……Page 116
4.3 Estimation of Parameters in Geometric Process……Page 119
4.4 Asymptotic Distributions of the Estimators……Page 121
4.5 Parametric Inference for Geometric Process……Page 128
4.6 Notes and References……Page 133
5.1 Introduction……Page 136
5.2 Data Analysis by Geometric Process Model……Page 137
5.3 Data Analysis by Poisson Process Models……Page 138
5.4 Real Data Analysis and Comparison……Page 140
5.5 Analysis of Data by a Threshold Geometric Process Model……Page 157
5.6 Notes and References……Page 167
6.1 Introduction……Page 170
6.2 A Geometric Process Maintenance Model……Page 171
6.3 Optimal Replacement Policy……Page 176
6.4 Monotonicity of the Optimal Policy for a Deteriorating System……Page 179
6.5 A Monotone Process Model for a Multistate System……Page 183
6.6 A Geometric Process ShockModel……Page 197
6.7 A Geometric Process δ-ShockModel……Page 208
6.8 A Threshold Geometric Process Maintenance Model……Page 216
6.9 A Geometric Process Preventive Maintenance Model……Page 225
6.10 Notes and References……Page 238
7.2 Reliability Analysis for a Series System……Page 242
7.3 Reliability Analysis for a Parallel System……Page 249
7.4 Reliability Analysis for a Cold Standby System……Page 254
7.5 A Geometric Process Maintenance Model for a Cold Standby System……Page 264
7.6 Notes and References……Page 267
8.2 A Geometric Process M/M/1 Queueing Model……Page 270
8.3 A Geometric Process Warranty Model……Page 289
8.4 Notes and References……Page 299
Appendix A SARS Data Sets……Page 300
A.1 Hong Kong SARS Daily Infected Case Data……Page 301
A.2 Singapore SARS Daily Infected Case Data……Page 302
A.3 Ontario SARS Daily Infected Case Data……Page 303
A.4 Taiwan SARS Daily Infected Case Data……Page 304
Bibliography……Page 306
Index……Page 312