Distribution theory of runs and patterns and its application / James C. Fu, W.Y. Wendy Lou.

Includes bibliographical references and index.

Ch. 1. Introduction -- Ch. 2. Finite Markov Chain Imbedding -- 2.1. Finite Markov Chain -- 2.2. Chapman-Kolmogorov Equation -- 2.3. Tree-Structured Markov Chain -- 2.4. Runs and Patterns -- 2.5. Finite Markov Chain Imbedding -- 2.6. Absorbing State -- 2.7. First-Entry Probability -- Ch. 3. Runs and Patterns in a Sequence of Two-State Trials -- 3.1. Introduction -- 3.2. Number of Non-Overlapping Consecutive k Successes -- 3.3. Number of Success Runs of Length Greater Than or Equal to k -- 3.4. Number of Overlapping Consecutive k Successes -- 3.5. Number of Runs of Exactly k Successes -- 3.6. The Distribution of the Longest Success Run -- 3.7. Waiting-Time Distribution of a Success Run -- 3.8. Numerical Examples -- 3.9. Number of Successes in Success Runs of Length Greater Than or Equal to k -- Ch. 4. Runs and Patterns in Multi-State Trials -- 4.1. Introduction -- 4.2. Forward and Backward Principle with Non-Overlap Counting -- 4.3. Overlap Counting -- 4.4. Series Pattern -- 4.5. Joint Distribution -- Ch. 5. Waiting-Time Distributions -- 5.1. Introduction -- 5.2. The Waiting Time of A Simple Pattern -- 5.3. The Waiting Time of A Compound Pattern -- 5.4. Probability Generating Function -- 5.5. Mean of Waiting Time W([Lambda]) -- 5.6. More About Generating Functions -- 5.7. Spectrum Analysis and Large Deviation Approximation -- 5.8. Probability Generating Function of W(r, [Lambda]) -- 5.9. Scan Statistics -- Ch. 6. Random Permutations -- 6.1. Introduction -- 6.2. Successions -- 6.3. Eulerian and Simon Newcomb Numbers -- Ch. 7. Applications -- 7.1. Introduction -- 7.2. System Reliability -- 7.3. Hypothesis Testing -- 7.4. Sequential Continuity -- 7.5. Quality Control Schemes.