Contents

Dedication

Preface

Synopsis of the Contents

Foreword

I. BACKGROUND MATERIAL AND MATHEMATICAL MODELING

    1. Introduction

        1.1 Main Areas of Manufacturing

        1.2 Main Problems of Production Systems Engineering

            1.2.1 Complicating phenomena

            1.2.2 Analysis, continuous improvement, and design problems

            1.2.3 Fundamental laws of Production Systems Engineering

            1.2.4 Techniques used in this textbook

        1.3 Summary

        1.4 Problems

        1.5 Annotated Bibliography

    2. Mathematical Tools: Elements of Probability Theory

        2.1 Random Events

            2.1.1 Terminology

            2.1.2 Axioms of probability and their corollaries

            2.1.3 Conditional probability

            2.1.4 Independence

            2.1.5 Total probability formula

            2.1.6 Bayes's formula

        2.2 Random Variables

            2.2.1 Terminology

            2.2.2 Discrete random variables

            2.2.3 Continuous random variables

            2.2.4 Expected value, variance, and coefficient of variation

            2.2.5 Vector random variables

            2.2.6 Asymptotic properties of sums of random variables

        2.3 Random Processes

            2.3.1 Terminology

            2.3.2 Continuous time, continuous space random processes

            2.3.3 Markov processes

        2.4 Summary

        2.5 Problems

        2.6 Annotated Bibliography

    3. Mathematical Modeling of Production Systems

        3.1 Types of Production Systems

            3.1.1 Serial production lines

            3.1.2 Assembly systems

        3.2 Structural Modeling

        3.3 Mathematical Models of Machines

            3.3.1 Timing issues

            3.3.2 Machine reliability models

            3.3.3 Notations

            3.3.4 Machine model identification

            3.3.5 Calculating parameters of aggregated machines

            3.3.6 Machine quality models

        3.4 Mathematical Models of Buffers

            3.4.1 Modeling

            3.4.2 Buffer parameters identification

        3.5 Modeling Interactions between Machines and Buffers

            3.5.1 Slotted time case

            3.5.2 Continuous time case

        3.6 Performance Measures

            3.6.1 Production rate and throughput

            3.6.2 Work-in-process and finished goods inventory

            3.6.3 Probabilities of blockages and starvations

            3.6.4 Due-time performance

            3.6.5 Transient characteristics

            3.6.6 Evaluating performance measures on the factory floor

        3.7 Model Validation

        3.8 Steps of Modeling, Analysis, Design, and Improvement

            3.8.1 Modeling

            3.8.2 Analysis, continuous improvement, and design

        3.9 Simplification: Transforming Exponential Models into Bernoulli Ones

            3.9.1 Motivation

            3.9.2 Exponential and Bernoulli lines considered

            3.9.3 The exp-B transformation

            3.9.4 The B-exp transformation

            3.9.5 Exp-B and B-exp transformations for assembly systems

        3.10 Case Studies

            3.10.1 Automotive ignition coil processing system

            3.10.2 Automotive paint shop production system

            3.10.3 Automotive ignition module assembly system

        3.11 Summary

        3.12 Problems

        3.13 Annotated Bibliography

II. SERIAL PRODUCTION LINES WITH BERNOULLI MODEL OF MACHINE RELIABILITY

    4. Analysis of Bernoulli Lines

        4.1 Two-machine Lines

            4.1.1 Mathematical description

            4.1.2 Steady state probabilities

            4.1.3 Formulas for the performance measures

            4.1.4 Asymptotic properties

        4.2 M > 2-machineLines

            4.2.1 Mathematical description and approach

            4.2.2 Aggregation procedure and its properties

            4.2.3 Formulas for the performance measures

            4.2.4 Asymptotic properties of M > 2-machine lines

            4.2.5 Accuracy of the estimates

        4.3 System-Theoretic Properties

            4.3.1 Static laws of production systems

            4.3.2 Reversibility

            4.3.3 Monotonicity

        4.4 Case Studies

            4.4.1 Automotive ignition coil processing system

            4.4.2 Automotive paint shop production system

        4.5 Summary

        4.6 Problems

        4.7 Annotated Bibliography

    5. Continuous Improvement of Bernoulli Lines

        5.1 Constrained Improvability

            5.1.1 Resource constraints and definitions

            5.1.2 Improvability with respect to WF

            5.1.3 Improvability with respect to WF and BC simultaneously

            5.1.4 Improvability with respect to BC

        5.2 Unconstrained Improvability

            5.2.1 Definitions

            5.2.2 Identification of bottlenecks in two-machine lines

            5.2.3 Identification of bottlenecks in M > 2-machine lines

            5.2.4 Potency of buffering

            5.2.5 Designing continuous improvement projects

        5.3 Measurement-based Management of Production Systems

        5.4 Case Studies

            5.4.1 Automotive ignition coil processing system

            5.4.2 Automotive paint shop production system

        5.5 Summary

        5.6 Problems

        5.7 Annotated Bibliography

    6. Design of Lean Bernoulli Lines

        6.1 Parametrization and Problem Formulation

        6.2 Lean Buffering in Bernoulli Lines with Identical Machines

            6.2.1 Two-machine lines

            6.2.2 Three-machine lines

            6.2.3 M > 3-machine lines

        6.3 Lean Buffering in Serial Lines with Non-identical Bernoulli Machines

            6.3.1 Two-machine lines

            6.3.2 M > 2-machine lines

        6.4 Case Studies

            6.4.1 Automotive ignition coil processing system

            6.4.2 Automotive paint shop production system

        6.5 Summary

        6.6 Problems

        6.7 Annotated Bibliography

    7. Closed Bernoulli Lines

        7.1 System Model and Problem Formulation

            7.1.1 Model

            7.1.2 Problems addressed

        7.2 Performance Analysis, Monotonicity, Reversibility, and Unimpeding Closed Lines

            7.2.1 Two-machine lines

            7.2.2 M > 2-machine lines

        7.3 Improvability

            7.3.1 Two-machine lines

            7.3.2 M > 2-machine lines

            7.3.3 Comparisons

        7.4 Bottleneck Identification

            7.4.1 Two-machine lines

            7.4.2 M > 2-machinelines

        7.5 Leanness

        7.6 Case Study

            7.6.1 Modeling and model validation of closed automotive paint shop production system

            7.6.2 S-improvability

            7.6.3 Lean system design

        7.7 Summary

        7.8 Problems

        7.9 Annotated Bibliography

    8. Product Quality in Bernoulli Lines

        8.1 Bernoulli Lines with Non-perfect Quality Machines

            8.1.1 Model and problem formulation

            8.1.2 Performance analysis

            8.1.3 Bottlenecks

            8.1.4 Design

        8.2 Bernoulli Lines with Quality-Quantity Coupling Machines

            8.2.1 Model and problem formulation

            8.2.2 Monotonicity properties

            8.2.3 Bottlenecks

        8.3 Bernoulli Lines with Rework

            8.3.1 Model and problem formulation

            8.3.2 Performance analysis

            8.3.3 Bottleneck identification

        8.4 Summary

        8.5 Problems

        8.6 Annotated Bibliography

    9. Customer Demand Satisfaction in Bernoulli Lines

        9.1 Modeling and Parametrization

            9.1.1 Production-inventory-customer (PIC) model

            9.1.2 Due-time performance measure

            9.1.3 Parametrization

        9.2 Analysis of DTP

            9.2.1 Evaluating DTP in PIC systems with one-machine PS

            9.2.2 Evaluating DTP in PIC systems with M-machine PS

        9.3 Design of Lean FGB for Desired DTP

            9.3.1 Lean FGB

            9.3.2 Conservation of filtering

        9.4 Analysis of DTP for Random Demand

            9.4.1 Random demand modeling

            9.4.2 Evaluating DTP for random demand

            9.4.3 DTP degradation as a function of demand variability

            9.4.4 Dependence of DTP on the shape of demand pmf's

        9.5 Case Study

        9.6 Summary

        9.7 Problems

        9.8 Annotated Bibliography

    10. Transient Behavior of Bernoulli Lines

        10.1 Problem Formulation

            10.1.1 Mathematical description

            10.1.2 Second largest eigenvalue problem

            10.1.3 Pre-exponential factor problem

            10.1.4 Settling time problem

            10.1.5 Production losses problem

        10.2 Analysis of the Second Largest Eigenvalue

            10.2.1 Two-machine lines

            10.2.2 Three-machine lines

        10.3 Analysis of the Pre-exponential Factors

        10.4 Analysis of the Settling Time

            10.4.1 Behavior of PR(n) and WIP(n)

            10.4.2 Analysis of tsPR and tsWIP

        10.5 Analysis of the Production Losses

            10.5.1 Approach

            10.5.2 Percent of loss when the buffers are empty at the beginning of the shift

            10.5.3 Percent of loss when the buffers are not empty at the beginning of the shift

        10.6 Summary

        10.7 Problems

        10.8 Annotated Bibliography

III. SERIAL PRODUCTION LINES WITH CONTINUOUS TIME MODELS OF MACHINE RELIABILITY

    11. Analysis of Exponential Lines

        11.1 Synchronous Exponential Lines

            11.1.1 Two-machine case

            11.1.2 M > 2-machine case

        11.2 Asynchronous Exponential Lines

            11.2.1 Two-machine case

            11.2.2 M > 2-machinecase

        11.3 Case Studies

            11.3.1 Automotive ignition coil processing system

            11.3.2 Crank shaft production line

        11.4 Summary

        11.5 Problems

        11.6 Annotated Bibliography

    12. Analysis of Non-Exponential Lines

        12.1 Systems Considered

            12.1.1 Mathematical description

            12.1.2 Second-order-similar production lines

        12.2 Sensitivity of PR and TP to Machine Reliability Model

        12.3 Empirical Formulas for PR and TP

        12.4 Summary

        12.5 Problems

        12.6 Annotated Bibliography

    13. Improvement of Continuous Lines

        13.1 Constrained Improvability

            13.1.1 Resource constraints and definitions

            13.1.2 Improvability with respect to CT

            13.1.3 Improvability with respect to BC

        13.2 Unconstrained Improvability

            13.2.1 Definitions

            13.2.2 One-machine lines

            13.2.3 Two-machine synchronous exponential lines

            13.2.4 Asynchronous exponential lines

            13.2.5 M ≥ 2-machine non-exponential lines

            13.2.6 Buffering potency and measurement-based management

        13.3 Case Study

        13.4 Summary

        13.5 Problems

        13.6 Annotated Bibliography

    14. Design of Lean Continuous Lines

        14.1 Parametrization and Problem Formulation

        14.2 Lean Buffering in Synchronous Lines with Identical Exponential Machines

            14.2.1 Two-machine lines

            14.2.2Three-machinelines

            14.2.3 M > 3-machinelines

        14.3 Lean Buffering in Synchronous Lines with Non-identical Exponential Machines

            14.3.1 Two-machine lines

            14.3.2 A special class of three-machine lines

            14.3.3 M > 2-machinelines

        14.4 Lean Buffering in Synchronous Lines with Non-exponential Machines

            14.4.1 Approach

            14.4.2 Sensitivity of kE to machine reliability models

            14.4.3 Empirical formulas for kE

        14.5 Summary

        14.6 Problems

        14.7 Annotated Bibliography

    15. Customer Demand Satisfaction in Continuous Lines

        15.1 Modeling and Parametrization

            15.1.1 Production-inventory-customer (PIC) system

            15.1.2 DTP Definition

            15.1.3 Parametrization

        15.2 DTP Evaluation in PIC Systems with Exponential Machines

            15.2.1 DTP in PIC systems with one-machine PS

            15.2.2 DTP in PIC systems with M-machine PS

        15.3 Lean FGB and Conservation of Filtering in PIC Systems with Exponential Machines

            15.3.1 Lean FGB

            15.3.2 Typical behavior of νDTP vs. τ

        15.4 DTP in the Case of Random Demand

            15.4.1 Random demand modeling

            15.4.2 DTP for random demand in PIC systems with exponential machines

            15.4.3 DTP degradation as a function of demand variability

            15.4.4 Dependence of DTP on the shape of demand pmf

        15.5 Summary

        15.6 Problems

        15.7 Annotated Bibliography

IV. ASSEMBLY SYSTEMS

    16. Assembly Systems with Bernoulli Model of Machine Reliability

        16.1 Analysis of Bernoulli Assembly Systems

            16.1.1 Three-machine assembly systems

            16.1.2 M > 3-machine assembly systems

        16.2 Continuous Improvement of Bernoulli Assembly Systems

            16.2.1 Constrained improvability

            16.2.2 Unconstrained improvability

        16.3 Design of Lean Bernoulli Assembly Systems

        16.4 Customer Demand Satisfaction in Bernoulli Assembly Systems

        16.5 Case Studies

            16.5.1 Automotive ignition module assembly system

            16.5.2 Injection molding assembly system

        16.6 Summary

        16.7 Problems

        16.8 Annotated Bibliography

    17. Assembly Systems with Continuous Time Models of Machine Reliability

        17.1 Analysis of Assembly Systems with Exponential Machines

            17.1.1 Systems addressed

            17.1.2 Synchronous case

            17.1.3 Asynchronous case

        17.2 Analysis of Non-exponential Assembly Systems

        17.3 Improvement of Assembly Systems with Continuous Time Models of Machine Reliability

            17.3.1 Constrained improvability

            17.3.2 Unconstrained improvability

        17.4 Design on Lean Assembly Systems with Continuous Machines

        17.5 Customer Demand Satisfaction in Assembly Systems with Continuous Machines

        17.6 Case Studies

        17.7 Summary

        17.8 Problems

        17.9 Annotated Bibliography

V. SUMMARY, PSE TOOLBOX, AND PROOFS

    18. Summary of Main Facts of Production Systems Engineering

        18.1 Individual Machines

        18.2 Serial Lines

            18.2.1 Performance analysis

            18.2.2 Continuous improvement

            18.2.3 Design

        18.3 Assembly Systems

    19. PSE Toolbox

        19.1 Architecture and Functions

        19.2 Modeling Function

            19.2.1 Aggregation of parallel machines

            19.2.2 Aggregation of consecutive dependent machines

            19.2.3 Exp-B transformation for serial lines

            19.2.4 B-exp transformation for serial lines

            19.2.5 Exp-B transformation for assembly systems

            19.2.6 B-exp transformation for serial lines

        19.3 Performance Analysis Function

            19.3.1 Analysis of serial lines with Bernoulli machines

            19.3.2 Analysis of synchronous serial lines with exponential machines

            19.3.3 Analysis of asynchronous serial lines with exponential machines

            19.3.4 Analysis of closed lines with Bernoulli machines

            19.3.5 Analysis of assembly systems with Bernoulli machines

        19.4 Continuous Improvement Function

            19.4.1 Unimprovable allocation of WF in Bernoulli serial lines

            19.4.2 Unimprovable allocation of WF and BC simultaneously in Bernoulli serial lines

            19.4.3 WF-continuous improvement procedure for Bernoulli serial lines

            19.4.4 BC-continuous improvement procedure for Bernoulli serial lines

            19.4.5 S-continuous improvement procedure for closed Bernoulli lines

        19.5 Bottleneck Identification Function

            19.5.1 BN-m and BN-b in serial lines with Bernoulli machines

            19.5.2 c-BN and BN-b in serial lines with exponential machines

            19.5.3 c-BN and BN-b in serial lines with general model of machine reliability

            19.5.4 BN-m and BN-b in closed lines with Bernoulli machines

        19.6 Lean Buffer Design Function

            19.6.1 Lean buffering for serial lines with identical Bernoulli machines

            19.6.2 Lean buffering for serial lines with non-identical Bernoulli machines

        19.7 Product Quality Function

            19.7.1 Analysis of Bernoulli lines with non-perfect quality machines and inspection operations

        19.8 Customer Demand Satisfaction Function

            19.8.1 DTP in PIC system with one Bernoulli machine

        19.9 Simulation Function

            19.9.1 Simulation of serial lines with Bernoulli machines

            19.9.2 Simulation of serial lines with exponential machines

            19.9.3 Simulation of serial lines with general model of machine reliability

            19.9.4 Simulation of assembly systems with Bernoulli machines

    20. Proofs

        20.1Proofs for Part II

            20.1.1 Proofs for Chapter 4

            20.1.2 Proofs for Chapter 5

            20.1.3 Proofs for Chapter 6

            20.1.4 Proofs for Chapter 7

            20.1.5 Proofs for Chapter 8

            20.1.6 Proofs for Chapter 10

        20.2 Proofs for Part III

            20.2.1 Proofs for Chapter 12

        20.3 Proofs for Part IV

Epilogue