Response Modeling Methodology: Empirical Modeling For Engineering And Science

by Shore, Haim

• ISBN13: 9789812561022
• ISBN10: 9812561021
• Format: Hardcover
• Copyright: 2005-04-26
• Publisher: Textstream

Summary

- Demonstrates how the new approach (RMM) differs from current approaches in that both the structure of the model and its parameters are determined via data-driven procedures- Demonstrates that a single comprehensive methodology may provide a good platform for empirical modeling of both systematic variation (relational modeling) and random variation (variation that is captured by a statistical distribution with stable parameters)- Provides handy procedures to apply to the new methodology, accompanied by detailed numerical examples for the implementation of these procedures

Table of Contents

Preface	vii
References,	xi
1 Introduction	1	(12)
References,	12	(1)
PART I. CURRENT MODELS AND MODELING METHODOLGIES	13	(86)
2 Relational Models in Engineering and the Sciences	15	(14)
(Monotone Convex/Concave Relationships)
2.1. Introduction,	15	(2)
2.2. Chemistry and Chemical Engineering,	17	(2)
2.3. Physics,	19	(3)
2.4. Electrical Engineering,	22	(1)
2.5. Hardware Reliability Engineering,	22	(1)
2.6. Software Reliability-Growth Modeling,	23	(2)
2.7. Growth Models,	25	(1)
References,	25	(4)
3 Shared Features and "The Ladder"	29	(8)
3.1. Introduction,	29	(1)
3.2. Shared Features,	30	(4)
3.3. "The Ladder of Fundamental Uniformly Convex/Concave Functions",	34	(3)
4 Approaches to Model Systematic Variation	37	(16)
4.1. Introduction,	37	(2)
4.2. Linear Regression Analysis,	39	(2)
4.3. Box-Cox Power Transformations,	41	(3)
4.4. Generalized Linear Models,	44	(5)
4.5. Conclusions,	49	(2)
References,	51	(2)
5 Approaches to Model Random Variation	53	(26)
5.1. Introduction,	53	(4)
5.2. Parameter-Rich Families of Distributions, Transformations and Expansions,	57	(8)
5.2.1. The Pearson family of distributions,	58	(1)
5.2.2. Other families of distributions (Burr, Tukey's g- and h-systems, generalized Lambda, Shore, the exponential family),	59	(4)
5.2.3. Transformations (Johnson, Box-Cox) and expansions,	63	(2)
5.3. Moments and Their Role in Empirical Modeling of a Distribution,	65	(5)
5.3.1. Why moment matching?,	65	(2)
5.3.2. How many moments to match,	67	(3)
5.4. Heuristic Methods in Empirical Modeling of Random Variation,	70	(3)
5.5. An Alternative Approach to Four-Moment Matching,	73	(1)
References,	74	(5)
6 The Requirements and Evaluation of Compliance	79	(22)
6.1. Introduction,	79	(2)
6.2. Desirable Requirements of a General Methodology for Empirical Modeling,	81	(10)
6.3. An Evaluation of Compliance of Current Methodologies,	91	(6)
6.3.1. Modeling systematic variation,	91	(4)
6.3.2. Modeling random variation,	95	(2)
References,	97	(2)
PART II. RMM - DEVELOPING AND EVALUATING THE GENERAL APPROACH	99	(128)
7 The RMM Model	101	(16)
7.1. Introduction,	101	(2)
7.2. An Axiomatic Derivation of the RMM Model,	103	(7)
7.2.1. The model assumptions,	103	(1)
7.2.2. The general model,	104	(1)
7.2.3. Deriving f2,	105	(1)
7.2.4. Deriving f1,	106	(1)
7.2.5. The RMM Model,	107	(3)
7.3. The Response Moments,	110	(3)
7.4. Exploring the Relationship between the CV and η,	113	(2)
References,	115	(2)
8 Estimating the Relational Model	117	(34)
8.1. Introduction,	117	(3)
8.2. Phase 1 - Estimating the Linear Predictor (LP),	120	(5)
8.2.1. Introduction and motivation,	120	(3)
8.2.2. Stage I Approximating a transformed response via a Taylor series expansion and estimating the parameters via CCA,	123	(2)
8.2.3. Stage II Stepwise linear regression analysis with canonical scores as response values,	125	(1)
8.3. Issues Related to Implementation of Phase 1,	125	(8)
8.4. Phase 2 - Estimating the RMM Model,	133	(6)
8.4.1. Introduction,	133	(1)
8.4.2. Stage I Estimating the RMM parameters {α, λ μ2},	134	(3)
8.4.3. Stage II Estimating the RMM "Error Parameters" {ρσepsilon1,σepsilon2},	137	(1)
8.4.4. Summary of the estimation procedure (Phase 2),	138	(1)
8.5. Two Numerical Examples,	139	(8)
8.5.1. Example 1 The Wave-Soldering Process,	139	(5)
8.5.2. Example 2 The Resistivity Data,	144	(3)
References,	147	(1)
Appendix A Canonical Correlation Analysis - Background,	147	(2)
Appendix B The Assumptions of CCA and Major Threats to the Reliability and Validity of Results,	149	(2)
9 The RMM Error Distribution	151	(10)
9.1. Introduction,	151	(1)
9.2. Derivation of the RMM Error Distribution,	152	(2)
9.3. Properties of the Error Distribution,	154	(5)
9.4. Variations of the RMM Error Distribution,	159	(1)
References,	160	(1)
10 Fitting Procedures (for the Error Distribution)	161	(16)
10.1. Introduction,	161	(2)
10.2. Brief Review of Current Methodologies,	163	(3)
10.3. Fitting via "Moment Matching",	166	(5)
10.4. Fitting via "Quantile Matching",	171	(2)
10.5. Two Numerical Examples,	173	(3)
10.5.1. A moment-matching example,	173	(1)
10.5.2. A quantile-matching example,	174	(2)
References,	176	(1)
11 Estimating the Error Distribution	177	(26)
11.1. Introduction,	177	(3)
11.2. Percentile-Based Estimation,	180	(9)
11.2.1. The estimation procedure,	180	(4)
11.2.2. Two numerical examples (percentile-based estimation),	184	(5)
11.3. Moment-Based Estimation,	189	(12)
11.3.1. Introduction,	189	(5)
11.3.2. Procedure I,	194	(2)
11.3.3. Procedure II,	196	(2)
11.3.4. Two numerical examples (moment-based estimation),	198	(3)
References,	201	(2)
12 Special Cases of the RMM Model	203	(16)
12.1. Current Relational Models as Special Cases of RMM,	203	(6)
12.1.1. Chemistry and Chemical Engineering,	204	(3)
12.1.2. Physics,	207	(1)
12.1.3. Electrical engineering,	208	(1)
12.1.4. Growth models,	209	(1)
12.2. Current Models of Random Variation as RMM Models,	209	(8)
12.2.1. The Johnson families of distributions,	209	(1)
12.2.2. Tukey g- and h-Systems of distributions,	210	(1)
12.2.3. Fisher's transformation of the sample correlation,	211	(1)
12.2.4. Haldane power-transformation and Wilson-Hilferty approximation to Χ²,	212	(1)
12.2.5. Box-Cox normalizing transformation,	213	(1)
12.2.6. Cauchy distribution,	214	(1)
12.2.7. Generalized Inverse Gaussian distribution and the Levy distribution,	214	(2)
12.2.8. Generalized Gamma distributions,	216	(1)
References,	217	(2)
13 Evaluating RMM for Compliance	219	(8)
13.1. Introduction,	219	(1)
13.2. Compliance for Modeling Systematic Variation,	219	(4)
13.3. Compliance in Modeling Random Variation,	223	(3)
References,	226	(1)
PART III. MODELING SYSTEMATIC VARIATION - APPLICATIONS	227	(88)
14 Comparative Solutions for Relational Models	229	(22)
14.1. Introduction,	229	(1)
14.2. Two New Problems,	230	(11)
14.2.1. Example 1 The Windshield Experiment,	230	(5)
14.2.2. Example 2 The Economist Big Mac Parity Index,	235	(6)
14.3. Two Familiar Problems (Cont'd from Chapter 8),	241	(5)
14.3.1. Example 3 The Wave-Soldering Process,	241	(3)
14.3.2. Example 4 The Resistivity data,	244	(2)
14.4. Comparison of Models,	246	(2)
14.4.1. Mallow's Cp,	246	(1)
14.4.2. Akaike's Information Criterion (AIC),	247	(1)
References,	248	(3)
15 Reliability Engineering (with Censoring)	251	(14)
15.1. Introduction,	251	(1)
15.2. RMM Estimating with Censored Data,	252	(5)
15.3. A Numerical Example - The RFL model,	257	(6)
References,	263	(2)
16 Software Reliability-Growth Models	265	(12)
16.1. Introduction,	265	(1)
16.2. Example 1 Musa's M1 Data-Set,	266	(5)
16.3. Example 2 Musa's M3 Data-Set,	271	(5)
References,	276	(1)
17 Modeling a Chemo-Response	277	(20)
17.1. Introduction,	277	(1)
17.2. Applying RMM to a Chemo-Response- First Variation,	278	(9)
17.2.1. Example 1 Temperature dependence of vapor pressure,	278	(6)
17.2.2. Example 2 Temperature dependence of solid heat capacity,	284	(3)
17.3. Applying RMM to a Chemo-Response- Second Variation,	287	(7)
17.3.1. Example 1 Temperature dependence of vapor pressure,	288	(2)
17.3.2. Example 2 Heat capacity of solids and liquids,	290	(3)
17.3.3. Other temperature-dependent properties,	293	(1)
References,	294	(3)
18 Forecasting S-Shaped Diffusion Processes	297	(18)
18.1. Introduction,	297	(1)
18.2. Theoretical Background for S-shaped Diffusion Processes,	298	(5)
18.3. Modeling and Forecasting S-shaped Processes,	303	(4)
18.4. Numerical Examples,	307	(3)
18.4.1. Forecasting Tp, given P,	307	(3)
18.4.2. Forecasting PT, given T,	310	(1)
References,	310	(1)
Appendix A. Current Forecasting Models,	311	(1)
Appendix B. Description of Data Sets,	312	(3)
PART IV. MODELING RANDOM VARIATION - APPLICATIONS	315	(102)
19 RMM Distributional Approximations	317	(18)
19.1. Introduction,	317	(1)
19.2. Fitting RMM with Normal or Log-normal Errors,	318	(4)
19.3. Fitting with a Logistic Error Term,	322	(1)
19.4. Approximations for the Normal and the Poisson Distributions,	323	(11)
19.4.1. Approximating the Poisson quantile,	324	(1)
19.4.2. Approximating the CDF of the Standard Normal,	325	(9)
References,	334	(1)
20 Inverse Normalizing Transformations	335	(18)
20.1. Introduction,	335	(1)
20.2. Derivation of the "Origin" INT,	336	(1)
20.3. Four-Moment Matching - The Problem and a Solution,	337	(5)
20.4. Parameter-Reduced INTs,	342	(3)
20.4.1. Off-spring INT I,	342	(1)
20.4.2. Off-spring INT II,	343	(1)
20.4.3. Off-spring INT III,	343	(2)
20.4.4. Off-spring INT IV,	345	(1)
20.5. Distribution Fitting Procedures,	345	(5)
20.5.1. Fitting procedures for INT I (Section 20.4.1),	346	(1)
20.5.2. A fitting procedure for INT II (Section 20.4.2),	346	(1)
20.5.3. A fitting procedure for INT III (Section 20.4.3),	347	(1)
20.5.4. Fitting procedures for INT IV (Section 20.4.4),	348	(2)
20.6. Normalizing Transformations,	350	(1)
References,	351	(2)
21 Piece-Wise Linear Approximations	353	(16)
21.1. Introduction,	353	(3)
21.2. The Basic Modified (Normal) Approximation,	356	(1)
21.3. A Variation of the Basic Model with a Fitting Procedure,	357	(4)
21.4. A Simplified Fitting Procedure,	361	(2)
21.5. A Fitting Procedure Using First- and Second-Degree Moments,	363	(1)
21.6. Review of Related Published References,	364	(1)
21.7. A Numerical Example,	365	(2)
References,	367	(2)
22 General Control Charts	369	(28)
22.1. Introduction,	369	(1)
22.2. General Control Schemes for Attributes,	370	(14)
22.2.1. Introduction,	370	(3)
22.2.2. Modified control limits for attributes,	373	(2)
22.2.3. Simplified limits,	375	(2)
22.2.4. Probability limits with "inflated" skewness,	377	(2)
22.2.5. Probability limits for some attribute distributions,	379	(1)
22.2.6. Numerical assessment,	380	(4)
22.3. General Control Schemes for Variables,	384	(11)
22.3.1. Introduction,	384	(3)
22.3.2. 1NT-based control schemes for variables,	387	(8)
References,	395	(2)
23 Inventory Analysis	397	(20)
23.1. Introduction,	397	(1)
23.2. First Approach The Quantile Function and the Loss Function,	398	(3)
23.3. Second Approach The Quantile Function and Loss Function,	401	(6)
23.4. First Approach Newsboy Problem with Order-up-to Policy,	407	(2)
23.5. Second Approach Two Examples,	409	(6)
23.5.1. The Continuous-Review (Q,R) Model,	409	(3)
23.5.2. Safety lead-times for purchased components,	412	(3)
References,	415	(2)
Review Questions	417	(4)
Author Index	421	(6)
Subject Index	427