Quality Improvement With Design of Experiments: A Response Surface Approach

by Vuchkov, Ivan Nikolov

• ISBN13: 9780792368274
• ISBN10: 0792368274
• eBook ISBN(s): 9789400900097
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-03-01
• Publisher: SPRINGER
• More Book Details

Summary

This book presents a model-based approach to quality improvement through design of experiments. After a description of statistical methods for data analysis and design of experiments it addresses the following topics: -Taguchi's approach to quality improvement; -Reduction of errors transmitted from factors to the response; -Robustness against errors in product/process parameters and external noise factors; -Optimization procedures for product/process design; -Quality improvement through mechanistic models; -Quality improvement of products with both qualitative and quantitative factors; and -Quality improvement based on replicated observations. The book provides systematic and detailed practical guidance to a model-based approach to quality engineering problems. All methods are illustrated by real-world examples that make them readily accessible to readers. All mathematical proofs are given in appendices to the relevant chapters. The book is written for a wide range of engineers, quality engineering professionals, engineering designers, engineering statisticians, and all those who want to apply design of experiments to solving quality improvement problems. The text is appropriate for undergraduate and graduate students in engineering and statistics.

Table of Contents

Introduction to Quality Improvement	1	(13)
Why do deviations occur?	1	(1)
Random variations	2	(2)
On-line and off-line quality control	4	(3)
Performance characteristics, product parameters and noises	7	(1)
Design of experiments and data analysis	8	(4)
Model-based robust engineering design	12	(2)
Statistical Methods for Data Analysis	14	(82)
Analysis of variance	15	(16)
One Way Classification	15	(1)
Main results	15	(3)
Simplified formulae	18	(1)
Computational procedure	19	(3)
Anova Multiple Classification	22	(9)
Introduction to design of experiments	31	(8)
Problem Formulation	31	(1)
Completely Randomized Designs	31	(1)
Randomized Block Designs	32	(2)
Latin Squares	34	(2)
Graeko-Latin and Hyper Graeko-Latin Squares	36	(2)
Other Designs	38	(1)
Regression analysis	39	(45)
Defining the Problem	39	(1)
Factors and Regions of Interest	40	(2)
Regression Models	42	(2)
Assumptions of Linear Regression Analysis	44	(1)
Least Squares Method	45	(8)
Confidence Intervals and Significance of Regression Coefficients	53	(3)
Lack of Fit Tests	56	(1)
Defining the problem	56	(1)
Analysis of variance for testing model adequacy	57	(2)
Lack of fit tests based on repeated observations	59	(2)
Multiple correlation coefficient	61	(5)
Stepwise Regression and all Possible Regressions	66	(7)
Graphical Tools for Residual Analysis	73	(1)
Introduction	73	(1)
Residual plots	74	(3)
Normal and half-normal plots	77	(3)
Transformations of Variables	80	(2)
Weighted Least Squares	82	(2)
Bibliography	84	(12)
Basic equation of the analysis of variance	84	(1)
Derivation of the simplified formulae (2.10) and (2.11)	85	(1)
Basic properties of least squares estimates	86	(2)
Sums of squares for tests for lack of fit	88	(2)
Properties of the residuals	90	(6)
Design of Regression Experiments	96	(94)
Introduction	96	(2)
Variance-optimality of response surface designs	98	(8)
Two level full factorial designs	106	(17)
Definitions and Construction	106	(3)
Properties of Two Level Full Factorial Designs	109	(4)
Regression Analysis of Data Obtained Through Two Level Full Factorial Designs	113	(1)
Parameter estimation	113	(3)
Effects of factors and interactions	116	(2)
Statistical analysis of individual effects and test for lack of fit	118	(5)
Two level fractional factorial designs	123	(10)
Construction of Fractional Factorial Designs	123	(7)
Fitting Equations to Data Obtained by Fractional Factorial Designs	130	(3)
Blocking	133	(2)
Steepest ascent	135	(7)
Second order designs	142	(11)
Introduction	142	(2)
Composite Designs	144	(1)
Rotatable central composite designs	145	(1)
D-optimal composite designs	146	(1)
Hartley's designs	146	(1)
Other Three Level Second Order Designs	147	(1)
Statistical Analysis of Data Obtained Through Symmetric Second Order Designs	148	(5)
Sequential generation of D-optimal designs	153	(6)
Procedures for Sequential Generation of D-Optimal Designs	153	(3)
Asymmetrical Second Order D-Optimal Designs	156	(2)
Symmetrical Second Order D-Optimal Designs	158	(1)
Dependence of the variance-optimal designs on the assumptions about the model and the region of interest	159	(9)
Model-Dependence	159	(3)
Dependence on the Size and Shape of the Region of Interest	162	(6)
Interpreting models	168	(16)
Optimization Procedures and Graphical Tools for Model Interpretation	168	(7)
Canonical Representation of Second Order Models	175	(7)
Confidence Region on the Location of the Stationary Point	182	(2)
Bibliography	184	(6)
Proof of formula (3.24)	184	(1)
Sequential generation of D-optimal designs	185	(1)
Derivation of canonical form B	186	(2)
Covariance matrix of δ = b + 2Bx	188	(2)
Taguchi's Approach to Quality Improvement	190	(47)
Introduction	190	(1)
Loss function	190	(3)
Stages of product design	193	(1)
Parameter design	194	(2)
Orthogonal arrays	196	(4)
Split plot designs	200	(1)
Linear graphs	201	(1)
Signal-to-noise ratio	202	(2)
Data analysis and decision making	204	(6)
Some practical problemes	210	(2)
Choice of Experimental Condition and Factor Levels	210	(1)
Repeated Observations	211	(1)
Confirmatory Experiments	212	(1)
Computer Simulations	212	(1)
Tolerance design	212	(1)
Taguchi method: summary	213	(1)
Advantages and disadvantages of the Taguchi method	213	(3)
Examples	216	(17)
Bibliography	233	(4)
Loss function	235	(1)
Expected loss	235	(2)
Quality Improvement Through Reduction of the Errors Transmitted from the Factors to the Response	237	(50)
Transmission of errors from product parameters to the response	237	(1)
Models of the mean value and the variance in mass production	238	(13)
Defining the Problem	238	(1)
Models of Mean Value and Variance for a Product with Two Parameters	239	(4)
Generalizations	243	(1)
Models of mean value and variance in mass production based on second and third order polynomials	243	(4)
Models of the mean value and the variance in matrix notations	247	(4)
Estimation of noise distribution parameters	251	(5)
Estimation of Error Distribution Moments Through Observations	250	(4)
Variance Estimation Using Tolerance Intervals	254	(2)
Further generalizations	256	(4)
Accuracy of the predicted mean value and variance in mass production	260	(15)
Influence of the Regression Model Structure	260	(2)
Influence of High Order Error Distribution Moments and High Order Terms on the Variance Model	262	(3)
Influence of the Inaccuracy of Estimation	265	(10)
Bibliography	275	(12)
Derivation of mean value and variance models for second order polynomials with m factors	275	(5)
Unbiased estimation of variance in mass production	280	(3)
Derivation of matrix Ψ for a full second order polynomial model	283	(4)
Optimization Procedures for Robust Design of Products and Processes with Errors in the Factors	287	(57)
Introduction	287	(1)
Optimality criteria for robust process and product design	288	(4)
Loss Function Minimization	288	(2)
Conditional Minimization of the Variance	290	(1)
Maximization of Signal-to Noise Ratio	291	(1)
Robustness against errors in product parameters: the larger the better and the smaller the better cases	292	(8)
Defining the Problem	292	(2)
A Simple Case Single Parameter Product	294	(3)
Multivariable Analytical Solution	297	(3)
Model-based product design in cases when a specific target value is best	300	(11)
Analytical Solution for Second Regression Models	300	(5)
A Special Case Error Free Product Parameters	305	(6)
Model based decision making in quality improvement	311	(14)
Products with Several Performance Characteristics	311	(4)
Use of Numerical Optimization Procedures	315	(3)
Practical Problems	318	(7)
Model based tolerance design	325	(3)
Summary of the model based approach to quality improvement through reduction of the transmitted error	328	(1)
Friction welding example	328	(10)
Bibliography	338	(6)
Development of the algorithm of subsection 6.4.1	338	(4)
Development of the algorithm of subsection 6.4.2	342	(2)
Robustness Against Both Errors in Product Parameters and External Noise Factors	344	(44)
Introduction	344	(2)
Design of experiments	346	(3)
Model building	349	(18)
Models of Mean Value and Variance in Mass Production Based on Second Order Models	349	(3)
Models with Error Free Product Parameters	352	(11)
General Second Order Models Revisited	363	(4)
Optimization Procedures	367	(13)
Problem Formulation	367	(2)
Optimization by Lagrange Multipliers	369	(1)
Introduction	369	(1)
Unconstrained optimization by Lagrange multipliers	369	(5)
Constrained optimization by Lagrange multipliers in a spherical region of interest	374	(1)
Numerical Optimization Procedures	375	(5)
Bibliography	380	(8)
Development of models for mean value and variance with both errors in product parameters and external noise factors	381	(4)
Derivation of algorithm for unconstrained optimization by Lagrange multipliers	385	(3)
Quality Improvement Through Mechanistic Models	388	(34)
Introduction	388	(2)
Computing performance characteristic's mean value and variance using mechanistic models	390	(9)
Case with Errors Only in Product Parameters	390	(7)
Performance Characteristic's Variations Due to Both Errors in Factors and External Noises	397	(2)
Mixed models for mean value and variance	399	(5)
Response surface approach based on polynomial approximations	404	(4)
Other methods for quality improvement based on mechanistic models	408	(1)
Using Combined Arrays and Optimizing Loss Statistics Via Modelling the Underlying Response	408	(1)
Monte Carlo Experiments	409	(1)
Use of Taguchi Method With Mechanistic Models	409	(1)
Specific problems of quality improvement based on mechanistic models	409	(3)
Bibliography	412	(10)
Derivation of formulae (8.4) and (8.6)	412	(4)
Development of formulae (8.11) and (8.12)	416	(3)
Derivation of mean and variance models for third order polynomials	419	(3)
Quality Improvement of Products Depending on Both Qualitative and Quantitative Factors	422	(31)
Introduction	422	(1)
Models of Performance characteristics depending on both qualitative and quantitative factors	423	(7)
Dummy Variables	423	(1)
Regression Models with Both Qualitative and Quantitative Factors	423	(1)
Models without external noise factors	424	(3)
Models with external noise factors	427	(3)
Design and analysis of experiments with both qualitative and quantitative factors	430	(1)
Models of mean value and variance in mass production and use of the product	431	(2)
Optimization procedures	433	(2)
Introduction	433	(1)
Analytical Solutions of the Optimization Problem in Cases when Only the Errors in Product Parameters are Taken into Account	433	(1)
The smaller the better and the larger the better cases	433	(1)
A specific target value is best	434	(1)
Other optimization problems	435	(1)
Examples	436	(16)
Bibliography	452	(1)
Other Methods for Model Based Quality Improvement	453	(29)
Introduction	453	(1)
Model building based on replicated observations	454	(12)
Problem Statement	454	(1)
Regression Models for the Mean Value and Variance	454	(2)
Variance Estimates Based on Residuals	456	(6)
Graphical Tools for Studying Location and Disperssion Effects	462	(4)
Location and dispersion effects from non-replicated observations	466	(7)
More about the optimization procedures for robust product design	473	(1)
Parameter estimation in the case with errors in factor levels	474	(3)
Introduction	474	(1)
Weighted Least Squares Estimation Based on Repeated Observations	475	(1)
Weighted Least Squares Unreplicated Case	476	(1)
Response surface approach to robust design of signal-dependent systems	477	(4)
Bibliography	481	(1)
Bibliography	482	(18)
Subject Index	500	(3)
Author Index	503