六西格玛设计：战略实验方法

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"Design for Six Sigma as Strategic Experimentation" 是一本专为在高度竞争市场中从事产品规划、设计、制造和服务的专业人士，如研究生工程师、统计学家和科学家编写的书籍。书中提出了一种实用的、基于科学的方法论，用于指导产品实现过程。这种方法将市场研究、产品规划、财务、设计、工程和制造的各项任务与责任整合到一个统一的产品实现流程中。六西格玛设计（Design for Six Sigma, DFSS）是一种旨在优化产品和服务质量的策略，目标是在设计阶段就达到六个标准偏差的性能水平，以确保产品的可靠性和客户满意度。书中强调了利用现金流量预测、市场份额和价格预测来选择最终设计方案的重要性。通过单一的正式框架，DFSS帮助不同领域的专业人员协同工作，确保所有决策都基于数据和统计分析。书中的内容涵盖了计算机辅助的健壮工程、项目管理、统计学在六西格玛绿带中的应用、六西格玛项目管理的口袋指南、业务过程的定义和分析以及实验设计等多个方面。此外，还提供了一个包含MS Excel宏、SDWs（Statistical Data Worksheets）和模板的CD-ROM，以及12个教程，这些工具旨在帮助读者实践和应用书中的理论知识。六西格玛方法论通常包括DMAIC（Define, Measure, Analyze, Improve, Control）和DFSS两个阶段。这本书侧重于DFSS，即在设计阶段就引入六西格玛原则，以减少缺陷，提高效率，从而在竞争激烈的市场中取得优势。通过这种方法，企业可以更有效地满足客户需求，降低运营成本，并增强市场竞争力。 "Design for Six Sigma as Strategic Experimentation" 是一本深度结合实践和理论的著作，不仅提供了一个全面的框架来指导产品开发，还包含了丰富的工具和资源，帮助读者在实际工作中实施六西格玛设计策略。对于那些希望提升产品品质，优化业务流程，并在市场中获得竞争优势的企业和个人来说，这是一本不可多得的参考书籍。

Table 5.1 Unweighted expressions for the three types of value curves. . . . . . . . . . . . . . 88

Figure 5.4 Shaft and bearing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 5.5 Curves for value, cost, and value minus cost for the shaft as a function of its

diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 5.6 Value and cost as a function of the standard deviation of the shaft. . . . . . . . . 94

Figure 5.7 Robustness increases from A to B to C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure 5.8 The shear pin diameter for the mower blade assembly acts as scaling factor. 95

Figure 5.9 Ranges of torque on blade shaft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Figure 5.10 Schematic representation of shear strength of the material with annealing

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Table 5.2 The 0s and 1s of an outer array have been added to the experimental design

shown in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Table 5.3 Hypothetical outcomes for each trial in Table 5.2. . . . . . . . . . . . . . . . . . . . . . 99

Table 5.4 Placement of the noise factors in the outer array of Table 5.3 .in a new inner

array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 5.11 Simulated distribution for the population variance: s

(q) = 1 and v(q) = 30. . 102

Figure 5.12 Simulated distribution for the population variance: s

(q) = 1 and v(q) = 2. . . 103

Figure 5.13 Simulated distribution for the population variance: s

(q) = 1 and v(q) = 4. . . 103

Figure 6.1 Superposition of the frequency distribution of pin shear strengths on the

value curve, illustrating the two failure modes. . . . . . . . . . . . . . . . . . . . . . . . 106

Table 6.1 Named variables and spreadsheet equations for a single simulation of the

alternative heat treatment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 6.2 The cumulative distribution for strengths outside the operational limits for

a sample variance of 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 6.3 The cumulative distribution for strengths outside the operational limits for

a sample variance of 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 6.4 Distribution for value improvement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Table 7.1 Levels of analysis for examining the outcomes of an experiment. . . . . . . . . . 116

Figure 7.1 Suggested organization of matrices within the spreadsheet. . . . . . . . . . . . . . . 118

Table 7.2 Development of the design, transpose, covariance, and solution matrices. . . 120

Table 7.3 The design matrix, lambda form, for the problem. . . . . . . . . . . . . . . . . . . . . . 123

Table 7.4 Outcomes for the experiment as displayed in the SDW. . . . . . . . . . . . . . . . . . 124

Table 7.5 Computation of the unknown coefficients and their EWE as taken from the

Level 1 worksheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Table 7.6 The solution matrix and the diagonal elements of the covariance matrix. . . . 126

Table 7.7 The model for coefficients deemed significant using the EWE test and the

resulting Level 1 model averages (YMODEL_1) as taken from the Level 1

worksheet. The computation of R2 is also shown. . . . . . . . . . . . . . . . . . . . . . 127

Table 7.8 Lack of Fit final model (KEEPLAM) formed by setting the weaker

coefficients to zero until a minimum is reached in the EWE column for the

most influential factors as taken from the LOF worksheet. . . . . . . . . . . . . . . 129

Table 7.9 F ratio Type I error for the sum square of the LOF variance and the pooled

sample variance for the final model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Table 7.10 Simulated crop yield as a function of farmer, seed type, and fertilizer. . . . . . 130

Table 7.11 Design matrix, crop yield, and model of yield. . . . . . . . . . . . . . . . . . . . . . . . . 131

Table 7.12 Analysis of the lambda coefficients and their EWE. . . . . . . . . . . . . . . . . . . . 131

Table 7.13 Solution matrix (XS) computed from the crop yield design matrix. . . . . . . . 132

Table 7.14 Residuals determined from the difference between outcomes and prediction

given by the reduced model in Table 7.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

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Figure 7.2 Plot of the residuals as a function of the average of the outcomes, Y(q). . . . . 133

Figure 7.3 Normal probability plot of the residuals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Figure 8.1 Flow chart for analyzing the significance of the factors on the mean. . . . . . 138

Table 8.1 L

) lambda design and solution matrices and diagonal of covariance

matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Table 8.2 Replications and outcomes of experiment as taken from the L4(2^3) SDW. 141

Table 8.3 Analysis of significance of the lambda coefficients as taken from the Lambda

Coefficients worksheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Figure 8.2 Plot of residuals showing higher scatter for trials 1 and 4. . . . . . . . . . . . . . . . 144

Table 8.4 Outcomes for Level 1 analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Figure 9.1 The flow diagram for assessing the influence of factors on sample variance.

For either outcome in A, there is no pooling of variances. . . . . . . . . . . . . . . 147

Table 9.1 The lambda form of the L

) OA used as the experimental design. . . . . . . 150

Table 9.2 The solution matrix for the lambda form of the L

) OA and the diagonal

elements of the covariance matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Table 9.3 Coefficients chosen for the mean (PLAM) and –10 log variance (PXI) for the

populations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Table 9.4 Population means and variances constructed from the coefficients for the

mean and –10 log variance in Table 9.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Table 9.5 Simulated outcomes used in the analysis provided by the L8(2^7) SDW.

The vector Y lists the sample variances, and YMODEL is the default model

for Y generated by the vector (REDLAM) of significant lambda coefficients

for the alpha shown. The vector SVAR lists the sample variances, and

SVARMODEL is the default model for the sample variances generated by the

vector (REDXI) of the significant XI coefficients for the alpha shown. . . . . 152

Table 9.6 Results of the individual test of the significance of the factors on log variance,

as taken from the Xi Coefficients worksheet. . . . . . . . . . . . . . . . . . . . . . . . . . 153

Table 9.7 Computations of Satterthwaite’s effective df and EWE for the lambda

coefficients as taken from the Lambda Coefficients worksheet. . . . . . . . . . . . 154

Table 9.8 Results of the computations for the significance of the factors on the Ln

variance based upon the Z test approximation. The last column shows the

EWE significance for ξ

ij,Ln

from the F test for comparison. . . . . . . . . . . . . . . 156

Table 9.9 Preparation of data for making a double-half-normal plot of the off-baseline

XILN results shown in Table 9.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Figure 9.2 Double-half-normal plot of the results shown in Table 9.9. . . . . . . . . . . . . . . 157

Figure 9.3 Results of 1000 simulations of the XI coefficients. . . . . . . . . . . . . . . . . . . . . 159

Table 9.10 Outcomes for a single Monte Carlo simulation of the XI coefficients. . . . . . 159

Figure 9.4 The nine allowable states for two factors at three levels each forming a 3

design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Table 9.11 Computation of a contrast vector c(R,R*) between the baseline and factor 11

at its off-baseline level as taken from the Contrasts worksheet. Its PWE is

given by PWERRstar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Figure 10.1 Value and cost curves (hypothetical) as a function of the attribute g. . . . . . . 166

Table 10.1 Parameters used to construct the value and cost curves. . . . . . . . . . . . . . . . . . 167

Table 10.2 Parameters used in the Monte Carlo simulations. . . . . . . . . . . . . . . . . . . . . . . 169

Table 10.3 Outcomes from a single simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Figure 10.2 Normal probability plot of the SN ratio lambda coefficients determined from

the Monte Carlo simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Figures and Tables xvii

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Figure 10.3 Distributions for ∆V

, and ∆V

11,41

, which is the distribution for the

combined 11 and 41 factors. The distribution for ∆V

is not plotted, as it is

just to left of the combined distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Table 11.1 Lambda form of L

) design matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Table 11.2 Solution matrix and diagonal of covariance matrix for design matrix in

Table 11.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Table 11.3 The design matrix actually used in the experiment. . . . . . . . . . . . . . . . . . . . . 176

Table 11.4 Solution matrix and diagonal of covariance matrix for the design matrix in

Table 11.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Table 11.5 Results of the simulated tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Table 11.6 Results of the individual test using two separate paired sets of df to arrive

at an upper and lower limit on the single-tail significance of the factors on

log variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Table 11.7 Monte Carlo simulation of the ξ

coefficients (name XIijSIM). . . . . . . . . . . 180

Table 11.8 The column for XIijSIM in Table 11.7 is transformed into a row so that the

repeats of the simulations are pushed down instead of across the

spreadsheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Figure 11.1 Results of 1000 simulations for XIijSIM plotted on normal

probability paper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

Table 11.9 Steps in constructing the effective df and significance for the factors. . . . . . . 181

Table 11.10 (a) L

) Design Array 1 and (b) The confounding matrix for Array 1. . . . . 182

Table 11.11 (a) Design Array 2 is formed by adding trial 8 to matrix 1. (b)

The confounding matrix for Array 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Table 11.12 Design Array 3 represented by the L

) design less triplet interaction. . . . . 183

Table 11.13 The assumed population mean and variance for the problem. . . . . . . . . . . . . 184

Table 11.14 The population lambda coefficients for the mean and –10 log variance. . . . . 184

Table 11.15 The replications, sample variances, and means for the first experiment

(Array 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Table 11.16 The independent analysis of the factors on –10 log variance for Arrays 1

through 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Table 11.17 The replications, sample variances, and means for the second experiment

(Array 2 used). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Table 11.18 The replications, sample variances, and means for the third experiment

(Array 3 used). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Table 11.19 Criteria for significance used in analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Table 11.20 The solution matrices and the diagonals of covariance matrices for the

three design matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Table 11.21 The L

) nonregular design matrix. Every factor is confounded with

two-factor interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

Table 11.22 The confounding matrix between the main effects and several selected

pairwise interactions for the L

) nonregular design. . . . . . . . . . . . . . . . . 189

Table 11.23 The solution matrix for the L

) design. . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Table 11.24 The development of a L

) design from a L

) design. The resulting

lambda form X matrix is also shown for completeness. . . . . . . . . . . . . . . . . . 190

Table 11.25 The solution matrix for the L

) design. . . . . . . . . . . . . . . . . . . . . . . . . . 190

Table 11.26 The transformation of the L

) design into an L

) design. . . . . . . . . . 191

Table 11.27 The design matrix for L

) design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

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Table 11.28 The L

) solution matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Table 11.29 The transformation of the L

) design into an L

) design. . . . . . . . . . 192

Table 11.30 The lambda form of the L

) design matrix. . . . . . . . . . . . . . . . . . . . . . . 193

Table 11.31 The lambda form of the L

) solution matrix. . . . . . . . . . . . . . . . . . . . . 193

Figure 12.1 Hypothetical value curve for telescope versus the number of defects in

mirror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Table 12.1 Financial parameters for problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Table 12.2 L

) OA used for the experimental design and the natural logs of the five

defect replications per trial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Table 12.3 Solution matrix for the design in Table 12.2. . . . . . . . . . . . . . . . . . . . . . . . . . 197

Table 12.4 Population statistics for the hypothetical problem. . . . . . . . . . . . . . . . . . . . . . 198

Table 12.5 Simulated experimental outcomes for defect concentrations. . . . . . . . . . . . . 199

Table 12.6 Sample means (name Y) and sample variance (name SVAR) for Ln(g) as

taken from the L9(3^4) SDW. The results for the models for the sample

means and variances are also shown for their default reduced models. . . . . . 199

Table 12.7 Independent test of factors on homogeneity of variance. . . . . . . . . . . . . . . . . 200

Table 12.8 Determination of the effective variance, VARij, and effective df, DFij, for

Satterthwaite’s test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Table 12.9 Typical Monte Carlo simulation of possible population variances and means

for the normally distributed Ln(g) variable and conversion to the lognormally

distributed g variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Table 12.10 Simulation outcomes for the coefficients of –10 log base 10 of the simulated

population variances and 10 log base 10 of the simulated population means. 203

Figure 12.2 Results of the Monte Carlo simulation for the ξ

(–10Log(σ

(q))

coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

Figure 12.3 Results of the Monte Carlo simulation for the λ

(10Log(µ(q)) coefficients. . 204

Table 12.11 Simulation of the CIQ and its lambda coefficients. . . . . . . . . . . . . . . . . . . . . 205

Figure 12.4 Normal probability plot of the value difference between that for the

combination 0, 22, 32 and that for the baseline. . . . . . . . . . . . . . . . . . . . . . . . 206

Table 12.12 The L

) design and solution matrices used to explore the influence of

the factors on reducing the number of bad parts exhibiting dimples. The

outcomes BP of bad parts based upon a sample size of 1000 are also shown.

Computations were taken from the Design and Outcomes worksheet of the

modified L8(2^7) SDW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Table 12.13 The outcomes Y expressed as the natural log of the fraction of bad parts p.

The default models for Y and p are also shown along with R2 for the model

for p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Figure 12.5 The variance of p as a function of p according to the binomial distribution. . 209

Table 12.14 Computation of the lambda coefficients for Ln(p) and their EWE using the

estimated values for the variance of Ln(p) from Equation (12.8). Results

were taken from the Lambda Coefficients worksheet of the modified

L8(2^7) SDW for the binomial distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Figure 12.6 Comparison of computed cumulative distributions for trials 1 and 6. . . . . . . 211

Table 12.15 Design matrix, X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Table 12.16 Solution matrix, XS, having elements equal to ± 1/6. . . . . . . . . . . . . . . . . . . 213

Table 12.17 Outcomes for the 16 trials. The name array YPOP lists the population means

for the defects from which the samples were randomly selected. . . . . . . . . . 214

Figures and Tables xix

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Table 12.18 Computation of the phi coefficients and their EWE using the Taylor

expansion approximation of 1/Y for the sample variances for Ln(Y). The

coefficients for the population statistics are shown in the last column,

PHIPOP for comparison with PHI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Table 13.1 The L

) design matrix and cost per bit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Table 13.2 The L

) solution matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Figure 13.1 Cost per unit versus bit life for each of the four bits tested. . . . . . . . . . . . . . . 220

Table 13.3 Simulated replications of the bit lifetimes for each trial. SVAR is the list of

sample variance and Y is the list of sample means. Neither SVAR nor Y is

used in the subsequent computations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Table 13.4 Population statistics for the Weibull distributions. . . . . . . . . . . . . . . . . . . . . . 221

Table 13.5 Computation of slopes and intercepts for the inverse plots. . . . . . . . . . . . . . . 222

Figure 13.2 Weibull plot for trial 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Figure 13.3 Weibull plot for trial 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Figure 13.4 Weibull plot for trial 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

Figure 13.5 Weibull plot for trial 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

Table 13.6 Simulation of lifetimes and reciprocal lifetimes. . . . . . . . . . . . . . . . . . . . . . . 225

Table 13.7 Computed bit costs and average costs over 10 bits. . . . . . . . . . . . . . . . . . . . . 226

Table 13.8 Lambda coefficients for the –10 log average of 10 bit costs and a computation

of the overall cost savings in replacing the baseline bit with factor 11. . . . . . 226

Figure 13.6 Simulated distributions for the overall cost savings as computed by the

Weibull simulation method and by the lognormal approximation. . . . . . . . . . 227

Figure 13.7 Three types of regions for censoring: left, interval, and right. . . . . . . . . . . . . 228

Table 13.9 Comparison of regression and ML estimates for the shape (EALPHA) and

location (EBETA) parameters for the four trials. The population values are

also shown for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Table 13.10 Computations for ML estimates for the shape and location parameters using

Solver. The lifetimes shown are for trial 4, divided by 1000. The suspended

test expression shown at the bottom of the page for cell AC38 is for right

censored lifetimes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

Figure 14.1 The objective is to discover control factors that modify the response so that

it becomes linear with the signal having minimal variance. . . . . . . . . . . . . . . 234

Table 14.1 Linear and quadratic OPs for levels 3 to 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

Table 14.2 Seven control factors considered by DeMates in his injection molding case

study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Table 14.3 The values for P

) for i equal to 0, 1, and 2 versus the levels of the signal

factor taken from the OP8 SDW. The 8 × 3 array named XOP8 is used in the

computations that follow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Figure 14.2 The functions P

) and P

) as a function of the eight discrete levels

of the signal factor, M

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Table 14.4 The solution matrix X

S,OP

(XSOP8) for computing the OP coefficients for

fitting the part weights to the signal factor taken from the OP8 SDW. . . . . . . 241

Table 14.5 Average part weights versus the signal factor for each experimental trial of

the L

) OA taken from the Data worksheet in the OP8SDW. . . . . . . . . . . . 241

Table 14.6 Sample variances s

( j, q) of part weight versus the signal factor for each

experimental trial of the L

) OA taken from the Data worksheet in the

OP8SDW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

xx Figures and Tables

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