Process Capability Analysis: Estimating Quality presents a systematic exploration of process capability analysis and how it may be used to estimate quality. The book is designed for practitioners who are tasked with insuring a high level of quality for the products and services offered by their organizations. Along with describing the necessary statistical theory, the book illustrates the practical application of the techniques to data that do not always satisfy the standard assumptions.
The first two chapters deal with attribute data, where the estimation of quality is restricted to counts of nonconformities. Both classical and Bayesian methods are discussed. The rest of the book deals with variable data, including extensive discussions of both capability indices and statistical tolerance limits. Considerable emphasis is placed on methods for handling non-normal data. Also included are discussions of topics often omitted in discussions of process capability, including multivariate capability indices, multivariate tolerance limits, and capability control charts. A separate chapter deals with the problem of determining adequate sample sizes for estimating process capability.
Features:
Comprehensive treatment of the subject with consistent theme of estimating percent of nonconforming product or service.
Includes Bayesian methods.
Extension of univariate techniques to multivariate data.
Demonstration of all techniques using Statgraphics data analysis software.
Neil Polhemus is Chief Technology Officer at Statgraphics Technology and the original developer of the Statgraphics program for statistical analysis and data visualization. Dr. Polhemus spent 6 years on the faculty of the School of Engineering and Applied Science at Princeton University before moving full-time to software development and consulting. He has taught courses dealing with statistical process control, design of experiments and data analysis for more than 100 companies and government agencies.
Preface
Introduction
Relative Frequency Histogram
Summary Statistics
Measures of central tendency
Measures of variability
Measures of shape
Box-and-Whisker Plot
Plotting Attribute Data
Estimating the Percentage of Nonconformities
Proportion nonconforming
Defects per million
Six Sigma and World Class Quality
What’s ahead
Capability Analysis Based on Proportion of Nonconforming Items
Estimating the proportion of nonconforming items
Confidence intervals and bounds
Plotting the likelihood function
Determining quality levels
The information in zero defects
Incorporating prior information
Uniform prior
Non-uniform prior
Capability Analysis Based on Rate of Nonconformities
Estimating the mean nonconformities per unit
Determining quality levels
Sample size determination
Incorporating prior information
Capability Analysis of Normally Distributed Data
The normal distribution
Parameter estimation
Individuals versus Subgroup Data
Levels of variability
Capability versus performance
Estimating long-term variability
Estimating short-term variability from subgroup data
Estimating short-term variability from individuals’ data
Estimating the percentage of nonconforming items
Estimating quality indices
Z-scores
Cp/Pp
CR/PR
Cpk/Ppk
CM/PM
Cpm
CCpk
K
SQL – The Sigma Quality Level
Confidence bound for proportion of nonconforming items
Confidence limits for one-sided specifications
Confidence limits for two-sided specifications
Summary
Capability Analysis of Non-Normal Data
Tests for Normality
Power Transformations
Box-Cox Transformations
Calculating Process Capability
Confidence limits for capability indices
Fitting Alternative Distributions
Selecting a Distribution
Testing Goodness-of-Fit
Calculating Capability Indices
Confidence Limits for Capability Indices
Non-Normal Capability Indices and Johnson Curves
Comparison of Methods
Statistical Tolerance Limits
Tolerance Limits for Normal Distributions
Tolerance Limits for Non-Normal Distributions
Tolerance Limits Based on Power Transformations
Tolerance Limits Based on Alternative Distributions
Nonparametric Statistical Tolerance Limits
Multivariate Capability Analysis
Visualizing Bivariate Data
The Multivariate Normal Distribution
Multivariate Tests for Normality
Multivariate Capability Indices
Confidence Intervals
Multivariate Normal Statistical Tolerance Limits
Multivariate Tolerance Regions
Simultaneous Tolerance Limits
Analysis of Non-Normal Multivariate Data
Sample Size Determination
Sample Size Determination for Attribute Data
Sample Size Determination for Proportion of Nonconforming Items
Sample Size Determination for Rate of Nonconformities
Sample Size Determination for Capability Indices
Sample Size Determination for Cp and Pp
Sample Size Determination for Cpk and Ppk
Sample Size Determination for Statistical Tolerance Limits
Control Charts for Process Capability
Capability Control Charts
Control chart for proportion of nonconforming items
Control chart for rate of nonconformities
Control charts for Cp and Pp
Control charts for Cpk and Ppk
Sample size determination for capability control charts
Acceptance Control Charts
Conclusion
Appendix A Probability Distributions
Appendix B Guide to Capability Analysis Procedures in Statgraphics
Introduction
Capability Analysis Based on Proportion of Nonconforming Items
Capability Analysis Based on Rate of Nonconformities
Capability Analysis of Normally Distributed Data
Capability Analysis of Non-Normal Data
Statistical Tolerance Limits
Multivariate Capability Analysis
Sample Size Determination
Control Charts for Process Capability
Biography
Dr. Polhemus is Chief Technology Officer for Statpoint Technologies, Inc. and directs the development of STATGRAPHICS. He received his B.S.E. and Ph.D. degrees from the School of Engineering and Applied Science at Princeton University, under the tutelage of Dr. J. Stuart Hunter. Dr. Polhemus spent two years as an assistant professor in the Graduate School of Business Administration at the University of North Carolina at Chapel Hill and six years as an assistant professor in the Engineering School at Princeton University.Dr. Polhemus founded Statistical Graphics Corporation in 1980 to develop and promote the STATGRAPHICS software program. In 1983, he founded Strategy Plus, Inc., which developed EXECUSTAT for DOS. Dr. Polhemus founded NWP Associates, Inc., in 1993 to develop STATLETS, a set of Java applets which permit statistical data analysis over the Internet. In 1999 development of STATGRAPHICS was assumed by Statpoint Technologies, Inc.Dr. Polhemus lives in northern Virginia with his wife Caroline and is the proud father of four sons: Christopher, Gregory, Leland, and Michael.
