Discrete stochastic models are tools that allow us to understand, control, and optimize engineering systems and processes. This book provides real-life examples and illustrations of models in reliability engineering and statistical quality control and establishes a connection between the theoretical framework and their engineering applications.
The book describes discrete stochastic models along with real-life examples and explores not only well-known models, but also comparatively lesser known ones. It includes definitions, concepts, and methods with a clear understanding of their use in reliability engineering and statistical quality control fields. Also covered are the recent advances and established connections between the theoretical framework of discrete stochastic models and their engineering applications.
An ideal reference for researchers in academia and graduate students working in the fields of operations research, reliability engineering, quality control, and probability and statistics.
Author(s): Serkan Eryilmaz
Publisher: CRC Press
Year: 2022
Language: English
Pages: 182
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Author Biography
Chapter 1: An Overview of Discrete Stochastic Modeling
1.1. Discrete random variable
1.2. Conditioning
1.3. Discretization
1.4. Combinatorial methods
1.5. Recursive equations
1.6. Simulation
Chapter 2: Discrete Probability Distributions
2.1. Binomial model
2.2. Waiting time models
2.3. Poisson model
2.4. Compound models
2.5. Models via discretization of continuous distributions
2.6. Bivariate binomial and geometric models
2.7. Discrete reliability indices
2.8. Discrete renewal process
Chapter 3: Markov Chains
3.1. Markov binomial model
3.2. Simulation of a Markov chain
3.3. Testing the order of Markov dependence
3.4. Markov chain with a change point
Chapter 4: Phase-type Distributions
4.1. Definition and characteristics
4.2. Closure and other properties
4.3. Bivariate phase-type distributions
Chapter 5: Matrix-geometric Distributions
5.1. Definition and characteristics
5.2. Properties
5.3. Two-unit cold standby repairable system via matrix-geometric distributions
Chapter 6: Some Particular Models/Classes of Discrete Distributions
6.1. Order statistics
6.2. System signature
6.3. Power series class of distributions
6.4. Panjer’s family of distributions
Chapter 7: Other Discrete Stochastic Models Involving Dependency
7.1. Exchangeable dependence
7.2. Previous-sum dependent model
7.3. The distribution of the number of successes
7.4. m-dependent sequence of random variables
Chapter 8: Applications
8.1. System reliability models
8.2. Shock models
8.3. Age replacement policies
8.4. Quality control
8.5. Start-up demonstration tests
Index
