Introduction to Statistical Process Control

MUHAMMAD ASLAM, Ph.D., is a Professor in the Department of Statistics at King Abdulaziz University at Jeddah, Saudi Arabia. He was awarded the "Research Productivity Award for the year" in 2012 by Pakistan Council for Science and Technology. He is the founder of neutrosophic statistical quality control and neutrosophic inferential statistics. AAMIR SAGHIR, Ph.D., is a Professor in the Department of Mathematics at Mirpur University of Science and Technology. He received his Ph.D. in Statistics from Zhejiang University in China. LIAQUAT AHMAD, Ph.D., is an Associate Professor in the Department of Statistics and Computer Science at the University of Veterinary and Animal Sciences, Lahore, Pakistan. He's taught Statistics for over 24 years at the Ph.D. and M. Phil levels.

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• About the Authors xiPreface xiiiAcknowledgments xvii1 Introduction and Genesis 11.1 Introduction 11.2 History and Background of Control Charts 31.3 What is Quality and Quality Improvement? 5Types of Quality-Related Costs 71.4 Basic Concepts 9Continuous Probability Distributions 14Discrete Probability Distributions 181.5 Types of Control Charts 191.6 Meaning of Process Control 21References 222 Shewhart Type Control Charts for Attributes 232.1 Proportion and Number of Nonconforming Charts 24Variable Sample Size 28Improved p-Chart 292.2 Number of Nonconformities and Average Nonconformity Charts 32Dealing with Low Defect Levels 392.3 Control Charts for Over-Dispersed Data 402.4 Generalized and Flexible Control Charts for Dispersed Data 44Process Monitoring 47A Geometric Chart to Monitor Parameter θ 48The OC Curve 522.5 Other Recent Developments 52References 543 Variable Control Charts 573.1 Introduction 573.2 x̅ Control Charts 583.3 Range Charts 723.4 Construction of S-Chart 723.5 Variance S2-Charts 75References 874 Control Chart for Multiple Dependent State Sampling 914.1 Introduction 914.2 Attribute Charts Using MDS Sampling 914.3 Conway–Maxwell–Poisson (COM–Poisson) Distribution 984.4 Variable Charts 1064.5 Control Charts for Non-normal Distributions 1074.6 Control Charts for Exponential Distribution 1094.7 Control Charts for Gamma Distribution 111References 1185 EWMA Control Charts Using Repetitive Group Sampling Scheme 1215.1 Concept of Exponentially Weighted Moving Average (EWMA) Methodology 1215.2 Attraction of EWMA Methodology in Manufacturing Scenario 1265.3 Development of EWMA Control Chart for Monitoring Averages 1275.4 Development of EWMA Control Chart for Repetitive Sampling Scheme 1275.5 EWMA Control Chart for Repetitive Sampling Using Mean Deviation 1285.6 EWMA Control Chart for Sign Statistic Using the Repetitive Sampling Scheme 1395.7 Designing of a Hybrid EWMA (HEWMA) Control Chart Using Repetitive Sampling 147References 1546 Sampling Schemes for Developing Control Charts 1616.1 Single Sampling Scheme 1616.2 Double Sampling Scheme 1626.3 Repetitive Sampling Scheme 1656.4 Mixed Sampling Scheme 1766.5 Mixed Control Chart Using Process Capability Index 180References 1877 Memory-Type Control Charts for Attributes 1917.1 Exponentially Weighted Moving Average (EWMA) Control Charts for Attributes 191Performance Evaluation Measure 196Calculation of ARLs Using the Markov Chain Approach 196Geometric EWMA Chart 202Conway–Maxwell–Poisson (COM–Poisson) EWMA Chart 2047.2 CUSUM Control Charts for Attributes 209Performance Measure 2197.3 Moving Average (MA) Control Charts for Attributes 220References 2268 Multivariate Control Charts for Attributes 2318.1 Multivariate Shewhart-Type Charts 231Choice of Sample Size 2338.2 Multivariate Memory-Type Control Charts 243Design of MEWMA Chart 2448.3 Multivariate Cumulative Sum (CUSUM) Schemes 246References 248Appendix A: Areas of the Cumulative Standard Normal Distribution 251Appendix B: Factors for Constructing Variable Control Charts 253Index 255