Introduction to Statistical Process Control

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Muhammad Amir Aslam. Introduction to Statistical Process Control

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Introduction to Statistical Process Control

About the Authors

Preface

Acknowledgments

1 Introduction and Genesis. 1.1 Introduction

1.2 History and Background of Control Charts

1.3 What Is Quality and Quality Improvement?

Types of Quality‐Related Costs

1.4 Basic Concepts. 1.4.1 Descriptive Statistics

Example 1.1

Example 1.2

Example 1.3

1.4.2 Probability Distributions

Continuous Probability Distributions. Normal Probability Distribution

Student's t‐Distribution

Gamma Distribution

Discrete Probability Distributions. Binomial Probability Distribution

Poisson Probability Distribution

1.5 Types of Control Charts

1.5.1 Attribute Control Charts

1.5.2 Variable Control Charts

1.6 Meaning of Process Control

References

Note

2 Shewhart Type Control Charts for Attributes

2.1 Proportion and Number of Nonconforming Charts

2.1.1 Proportion of Nonconforming Chart (p‐Chart)

Example 2.1

Solution

Variable Sample Size

Improved p‐Chart

2.1.2 Number of Nonconforming Chart (np‐Chart)

2.1.3 Performance Evaluation Measures

2.2 Number of Nonconformities and Average Nonconformity Charts

2.2.1 Number of Nonconformities (c‐) Chart

Example 2.2

Solution

2.2.2 Average Nonconformities (u‐) Chart

Example 2.3

Solution

2.2.3 The Performance Evaluation Measure

Dealing with Low Defect Levels

2.3 Control Charts for Over‐Dispersed Data. 2.3.1 Dispersion of Counts Data

2.3.2 g‐Chart and h‐Chart

Example 2.4

Solution

2.4 Generalized and Flexible Control Charts for Dispersed Data

2.4.1 The gc‐ and the gu‐Charts

2.4.2 Control Chart Based on Generalized Poisson Distribution

Process Monitoring

A Geometric Chart to Monitor Parameter θ

2.4.3 The Q‐ and the T‐Charts

The OC Curve

2.5 Other Recent Developments

References

3 Variable Control Charts. 3.1 Introduction

3.2 Control Charts

3.2.1 Construction of and R Charts

Example 3.1

3.2.2 Phase II Control Limits

3.2.3 Construction of Chart for Burr Distribution Under the Repetitive Sampling Scheme

3.3 Range Charts

3.4 Construction of S‐Chart

3.4.1 Construction of Chart

3.4.2 Normal and Non‐normal Distributions for and S‐Charts

3.5 Variance S2‐Charts

3.5.1 Construction of S2‐Chart

3.5.2 The Construction of Variance Chart for Neutrosophic Statistics

3.5.3 The Construction of Variance Chart for Repetitive Sampling

References

Note

4 Control Chart for Multiple Dependent State Sampling. 4.1 Introduction

4.2 Attribute Charts Using MDS Sampling

4.2.1 The np‐Control Chart

4.3 Conway–Maxwell–Poisson (COM–Poisson) Distribution

4.4 Variable Charts

4.5 Control Charts for Non‐normal Distributions

4.6 Control Charts for Exponential Distribution

4.7 Control Charts for Gamma Distribution

References

5 EWMA Control Charts Using Repetitive Group Sampling Scheme. 5.1 Concept of Exponentially Weighted Moving Average(EWMA) Methodology

5.2 Attraction of EWMA Methodology in Manufacturing Scenario

5.3 Development of EWMA Control Chart for Monitoring Averages

5.4 Development of EWMA Control Chart for Repetitive Sampling Scheme

5.5 EWMA Control Chart for Repetitive Sampling Using Mean Deviation

5.6 EWMA Control Chart for Sign Statistic Using the Repetitive Sampling Scheme

5.7 Designing of a Hybrid EWMA (HEWMA) Control Chart Using Repetitive Sampling

References

Note

6 Sampling Schemes for Developing Control Charts. 6.1 Single Sampling Scheme

6.2 Double Sampling Scheme

6.3 Repetitive Sampling Scheme

6.3.1 When a Shift of μ1 = μ + kσ Occurs in the Process

6.4 Mixed Sampling Scheme

6.4.1 Mixed Control Chart Using Exponentially Weighted Moving Average (EWMA) Statistics

6.5 Mixed Control Chart Using Process Capability Index

6.5.1 Analysis Through Simulation Approach

References

Note

7 Memory‐Type Control Charts for Attributes. 7.1 Exponentially Weighted Moving Average (EWMA) Control Charts for Attributes

7.1.1 Binomial EWMA Charts

7.1.2 Poisson EWMA (PEWMA) Chart

Performance Evaluation Measure

Calculation of ARLs Using the Markov Chain Approach

Example 7.1

Solution

7.1.3 Other EWMA Charts

Geometric EWMA Chart

Conway–Maxwell–Poisson (COM–Poisson) EWMA Chart

Example 7.2

Solution

7.2 CUSUM Control Charts for Attributes

7.2.1 Binomial CUSUM Chart

7.2.2 Poisson CUSUM Chart

7.2.3 Geometric CUSUM Chart

7.2.4 COM–Poisson CUSUM Chart

Performance Measure

7.3 Moving Average (MA) Control Charts for Attributes

7.3.1 Binomial MA Chart

7.3.2 Poisson MA Chart

7.3.3 Other MA Charts

References

8 Multivariate Control Charts for Attributes. 8.1 Multivariate Shewhart‐Type Charts

8.1.1 Multivariate Binomial Chart

Choice of Sample Size

8.1.2 Multivariate Poisson (MP) Chart

Example 8.1

Solution

8.1.3 Multivariate Conway–Maxwell–Poisson (COM–Poisson) Chart

Example 8.2

Solution

8.2 Multivariate Memory‐Type Control Charts. 8.2.1 Multivariate EWMA Charts for Binomial Process

Design of MEWMA Chart

8.2.2 Multivariate EWMA Charts for Poisson Process

8.3 Multivariate Cumulative Sum (CUSUM) Schemes

8.3.1 Multivariate CUSUM Chart for Poisson Data

References

Appendix A Areas of the Cumulative Standard Normal Distribution

Appendix B Factors for Constructing Variable Control Charts

Index. a

b

c

d

e

f

g

h

i

l

m

n

o

p

q

r

s

t

u

v

w

x

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Отрывок из книги

Muhammad Aslam

Aamir Saghir

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The mean deviation is defined as the average of the deviations from the mean or median; the deviations are taken without algebraic sign. So the average deviation calculated from mean is known as the mean deviation from mean and is defined as

And the mean deviation from median and is defined as

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