CONTENTS -- Preface -- List of Contributors -- Part A Foundation of Stochastic Operations Research -- A Probabilistic Proof of an Identity Related to the Stirling Number of the First Kind M. Tamaki -- 1. Introduction -- 2. Probabilistic Proof -- 2.1. Derivation by a forward-looking argument -- 2.2. Derivation by a backward-looking argument -- Acknowledgement -- References -- A Sequential Decision Problem based on the Rate Depending on a Markov Process T. Nakai -- 1. Introduction -- 2. Evaluation based on Outcomes and Decisions -- 3. Sequential Expenditure Problem -- 3.1. Stochastic process and outcomes -- 3.2. Sequential expenditure problem -- 4. Sequential Expenditure Problem on a Markov Process -- 4.1. Stochastic order relation -- 4.2. Transition probability of a Markov process -- 4.3. Sequential decision model -- 5. Partially Observable Markov Process and Learning Procedure -- 5.1. Partially observable Markov process and information -- 5.2. Learning procedure -- 5.3. Gradually condition -- 5.4. Monotonic property -- 5.5. Sequential expenditure problem: an incomplete information case -- 6. Conclusion -- Acknowledgements -- References -- Search for 90/150 Cellular Automata Sequences with Maximum Minimum-Phase-Spacing M. Fushimi, T. Furuta and A. Ito -- 1. Introduction -- 2. Designing the Maximum Period-Length 90/150 CA -- 3. Computing Phase Shifts of 90/150 CA Sequences -- 4. Computational Results -- 5. Conclusion -- Acknowledgement -- References -- Difference and Similarity between MONANOVA and OLS in Conjoint Analysis H. Kono, H. Ishii and S. Shiode -- 1. Introduction -- 2. MONANOVA -- 3. OLS -- 4. Proposal Methods -- 4.1. Proposal method -- 4.2. Numerical example -- 5. Conclusion -- References -- Part B Stochastic Modeling -- A Datum Search Game and an Experimental Verification for Its Theoretical Equilibrium R. Hohzaki and Y. Ida.

1. Introduction -- 2. Datum Search Game and Theoretical Results -- 2.1. A model of datum search game and formulation -- 2.2. Lower bound estimation -- 2.3. Upper bound estimation -- 3. Simulator for Datum Search Game -- 4. Experiment for a Datum Search Game -- 5. Conclusions -- References -- An Optimal Wait Policy in Two Discrete Time Queueing Systems J. Koyanagi, D. Nanba and H. Kawai -- 1. Introduction -- 2. Model -- 3. Numerical Example -- 4. Conclusion -- References -- Analysis of Finite Oscillating GIX/M(m)//N Queueing Systems F. Ferreira, A. Pacheco and H. Ribeiro -- 1. Introduction -- 2. GIX/M(m)//N Systems -- 3. Batch Prearrival State Process -- 4. Customer Prearrival State Process -- 5. Continuous-Time State Process -- 6. Numerical Results -- References -- A Continuous-Time Seat Allocation Model with Up-Down Resets K. Sato and K. Sawaki -- 1. Introduction -- 2. An Airline Seat Inventory Control with the Booking Limits of Upward and Downward Resets -- 2.1. The model and sequence of operations -- 2.2. A case of low fare demand large enough -- 2.3. Spill rates -- 3. A Seat Inventory Control of Callable Seats with Up-Down Resets -- 3.1. Optimal seat allocation with cancellation -- 3.2. The model with callable property -- 3.3. A case of low fare demand large enough with callable property -- 4. Numerical Examples -- 4.1. Computational results of section 2 -- 4.2. Computational results of section 3 -- 5. Conclusion -- References -- Part C Reliability and Maintenance -- Simulation of Reliability, Availability and Maintenance Costs P. Hagmark and S. Virtanen -- 1. Introduction -- 2. Failure and Operation Structures -- 2.1. The case example - power generation unit -- 2.2. Definition of a stochastic failure logic -- 2.3. Operation strategies and wait states -- 2.4. Rescue of a gate -- 3. Dependability Data and Simulation -- 3.1. Repair time.

3.2. Failure tendency and failure profile -- 3.3. Generation of failure points -- 3.4. Simulation procedure and the logbook -- 4. Reliability and Availability Calculation -- 4.1. Main results for the product -- 4.2. Reliability performance of the product -- 4.3. Entities involved in TOP downtime -- 4.4. Results for state combinations -- 5. Cost and Resource Calculation -- 5.1. Additional inputs concerning failures -- 5.2. Costs and resources due to failures -- 5.3. Documentation of preventive maintenance -- 5.4. Costs and resources due to scheduled procedures -- 6. The Summary of the Case Example -- References -- Stochastic Profit Models under Repair-Limit Replacement Program T. Dohi, N. Kaio and S. Osaki -- 1. Introduction -- 2. Repair-Time Limit Replacement Model -- 2.1. Notation -- 2.2. Model description -- 3. Analysis -- 3.1. Long-run average profit -- 3.2. Expected total discounted profit -- 4. Graphical Methods -- 4.1. Long-run average profit -- 4.2. Expected total discounted profit -- 5. Non-Parametric Estimation -- Acknowledgements: -- References -- Investigation of Equivalent Step-Stress Testing Plans E. A. Elsayed, Y. Zhu, H. Zhang and H. Liao -- 1. Introduction -- 2. Definitions of Equivalency -- 3. Equivalency of Step-Stress and Constant-Stress ALT Plans -- 4. Numerical Example and Simulation Study -- 4.1. Numerical example -- 4.2. Sensitivity study -- 4.3. Simulation study -- 5. Conclusion and Future Work -- References -- Optimal Policy for a Two-Unit System with Two Types of Inspections S. Mizutani and T. Nakagawa -- 1. Introduction -- 2. Expected Cost -- 3. Optimal Policy -- 4. Numerical Example -- 5. Conclusions -- References -- Redundancy Optimization in Multi-Level System Using Metaheuristics I. H. Chung, W. Y. Yun and H. G. Kim -- 1. Introduction -- 2. Model Description -- 3. Ant Colony Optimization -- 3.1. Solution representation.

3.2. State transition rule -- 3.3. Method for generating a feasible neighborhood solution -- 3.4. Pheromone trail -- 4. Numerical Examples -- 4.1. Three level case -- 4.2. Four and five level cases -- 4.3. Sensitivity analysis in the SA -- 5. Conclusion -- Acknowledgements -- References -- Optimal Censoring Policies for the Operation of a Damage System K. Ito and T. Nakagawa -- 1. Introduction -- 2. Model 1 -- 3. Model 2 -- 4. Numerical Illustrations -- 5. Conclusions -- References -- Part D Dependable Computing -- Optimal Sequential Checkpoint Intervals for Error Detection K. Naruse, T. Nakagawa and S. Maeji -- 1. Introduction -- 2. Sequential Checkpoint Interval -- 3. Model 2 -- 4. Conclusions -- References -- Effective Algorithms to Estimate the Optimal Software Rejuvenation Schedule under Censoring K. Rinsaka and T. Dohi -- 1. Introduction -- 2. Semi-Markov Models -- 2.1. Model 1 -- 2.2. Model 2 -- 3. The TTT Concept -- 4. The Kaplan-Meier Estimator -- 5. The Kernel Density Estimation -- 6. Simulation Experiments -- 7. Concluding Remarks -- Acknowledgments -- References -- Optimal Backup Interval of a Database System Using a Continuous Damage Model S. Nakamura, T. Nakagawa and H. Kondo -- 1. Introduction -- 2. Expected Cost -- 3. Optimal Policy -- 4. Numerical Example -- 5. Conclusions -- References -- Operational Software Performance Evaluation based on the Number of Debuggings with Two Kinds of Restoration Scenario K. Tokuno and S. Yamada -- 1. Introduction -- 2. Software Availability Model -- 2.1. Model Description -- 2.2. Traditional Software Availability Measures -- 2.2.1. Distribution of transition time between state W -- 2.2.2. Operational state occupancy probability and software availability -- 3. Model Analysis -- 4. Derivation of Software Performance Measures -- 5. Numerical Examples -- 6. Concluding Remarks -- Acknowledgments.

References -- Software Reliability Assessment with 2-Types Imperfect Debugging Activities S. Inoue and S. Yamada -- 1. Introduction -- 2. Imperfect Debugging Modeling -- 2.1. NHPP model -- 2.2. Modeling with two kinds of imperfect debugging activities -- 3. Software Reliability Assessment Measures -- 3.1. Software reliability function -- 3.2. Mean time between software failures -- 3.3. Hazard rate -- 4. Parameter Estimation -- 5. Numerical Examples -- 6. Model Comparison -- 7. Concluding Remarks -- References -- Flexible Stochastic Differential Equation Modeling for Open-Source-Software Reliability Assessment Y. Tamura and S. Yamada -- 1. Introduction -- 2. Stochastic Differential Equation Modeling -- 3. Method of Maximum-Likelihood -- 4. Software Reliability Assessment Measures -- 4.1. Expected numbers of detected faults and their variances -- 4.2. Mean times between software failures -- 4.3. Coefficient of variation -- 5. Numerical Illustrations -- 5.1. Data for numerical illustrations -- 5.2. Reliability assessment results considering fault levels -- 5.3. Sensitivity analysis in terms of model parameters -- 6. Concluding Remarks -- Acknowledgements -- References.