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 |  موضوع: كتاب Textile Processes - Quality Control and Design of Experiments الخميس 07 أكتوبر 2021, 12:35 am | |
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أخواني في الله
أحضرت لكم كتاب
Textile Processes - Quality Control and Design of Experiments
First Edition
Professor D.Sc. Georgi Borisov Damyanov
Associate Professor PhD Diana Stoyanova
Germanova Krasteva
Department of Textile Engineering
Technical University of Sofia
و المحتوى كما يلي :
CONTENTS
PREFACE xi
ABOUT THE AUTHORS xiii
LIST OF FIGURES xv
LIST OF TABLES xvii
PART I: INTRODUCTION TO MATHEMATICAL STATISTICS 1
I.1. GENERAL TERMS AND DEFINITIONS 3
Parameters and numerical characteristics of the random variable 6
Characteristics for location 6
Dispersion characteristics 7
Moments 9
Properties of numerical characteristics 11
I.2. LAWS OF RANDOM VARIABLES DISTRIBUTION 13
Continuous distributions 13
Discrete distributions 16
I.3. STATISTICAL ESTIMATES 21
Conducting the test 21
Point estimates 24
Interval estimates 25
Confidence intervals 28
Confidence intervals of the estimates in cases of normal distribution 28
Confidence interval of the l parameter for Poisson distribution 30
Confidence interval of the parameter p for binomial distribution 31
I.4. STATISTICAL PROCESS CONTROL AND CONTROL CHARTS 33
Statistical process control 33
Control charts 36
Design of statistical control charts 37
Types of control charts 38VI • CONTENTS
I.5. CORRELATION ANALYSIS 65
Coefficient of linear correlation 66
Coefficient of determination, anticorrelation, and indeterminate coefficients 66
Correlation in case of alternative indicators—the four-field method 68
Multiple and partial correlation 70
I.6. ANALYSIS OF VARIANCE 73
Single-factor analysis of variance 73
Multifactor ANOVA 75
PART II: DESIGN OF AN EXPERIMENT 79
II.1. MAIN CONCEPTS IN MATHEMATICAL MODELING AND OPTIMIZATION 81
II.2. CHOICE OF PARAMETERS OF OPTIMIZATION 85
II.3. CHOICE OF INPUT FACTORS 89
Methods of rank correlation 93
Coefficient of rank correlation 94
Coefficient of concordance 98
Random balance method 103
Design of the experiment 103
Construction of a diagram of dispersion 104
Separation of essential factors 107
II.4. MAIN STAGES OF EXPERIMENTAL MODELING 109
II.5. REGRESSION ANALYSIS 113
II.6. FULL FACTORIAL EXPERIMENT 123
Properties of the extended matrix of FFE 124
Types of matrices 125
Stages of derivation of the model 125
Calculation of coefficients 129
Verification of reproducibility of the process 129
Calculation of the test variance 130
Determination of the variance of regression coefficients 130
Verification of the significance of regression coefficients 130
Registration of the derived model 130
Calculation of the values of the output variable on the model 130
Verification of the model adequacy 130
II.7. FRACTIONAL FACTORIAL EXPERIMENT 133
Stages of construction of a fractional factorial experiment 134
Determination of the minimum number of tests for deriving a linear model 135
Choice of main and additional factors 135CONTENTS • VII
Composing the design of the experiment 135
Setting the determining contrasts 136
Setting the generalized determining contrast 136
Mixing the coefficients 137
II.8. STATISTICAL METHODS FOR MOVEMENT TO AN OPTIMAL AREA 139
Box–Wilson method 139
Condition for application of the method 140
Method principle 140
Method application conditions 141
Disadvantages of the method 141
Application 141
Simplex method 147
Simplex property 147
Criterion for reaching the optimal area 148
Specifying the optimal area 148
Construction of the initial simplex 148
Calculating the values of the coordinate points 150
Calculating the coordinates of the mirrored point apex 150
Determining the coordinates of the starting points 151
Filling in the simplex table 151
Determining the coordinates of an additional point 152
Formation of a new simplex 152
II.9. INVESTIGATION OF THE OPTIMUM AREA: COMPOSITE DESIGNS OF SECOND ORDER 153
Orthogonal central composite experiment 154
Number of tests 154
Design of the experiment 154
Determination of regression coefficients 155
Determination of regression coefficients’ variances 156
Significance of coefficients of regression equation 156
Recording of regression equation 157
Verification of adequacy of the model 157
Determination of the number of tests 158
Determination of the size of the star arm, a, and the value, k 158
Plan of the experiment 158
Determination of the regression coefficients 158
Determination of the variances of the regression coefficients 160
Significance of the coefficients of the regression equation 161
Record of the regression equation 162
Verification of the model adequacy 162
Rotatable central composite experiment 163
Number of tests 163
Design of the experiment 164
Determination of regression coefficients 165VIII • CONTENTS
Variance of regression coefficients 165
Significance of coefficients of regression equation 166
Verification of adequacy of the model 166
Determination of regression coefficients 167
Determination of variance of reproducibility 169
Determination of variances of regression coefficients 169
Verification of significance of regression coefficients 170
Recording of the model 171
Verification of model adequacy 171
Optimal composite experiment 171
Number of tests 171
Design of the experiment 172
Determination of regression coefficients 172
Variance of regression coefficients 173
Significance of coefficients of regression equation 173
Verification of adequacy 173
Determination of the regression coefficients 174
Determination of the variances of the regression coefficients 176
Verification of the significance of the coefficients of the regression equation 176
Record of the model 177
Verification of the model adequacy 177
II.10. OPTIMIZATION OF TARGET FUNCTION 179
Canonical analysis 180
Algorithm for reduction to a canonical form 180
Determination of the surface type 181
Differentiation of target function 184
Solving the system of linear equations 185
Determination of the extreme value of output parameter 185
Determination of the rotation angle 185
Determination of regression coefficients in canonical equation 185
Additional verification of calculation correctness 186
Determination of surface type 186
Determination of the optimal parameters of the cylinder drawing device 187
II.11. TAGUCHI METHODS 189
Innovations in the sphere of the designed experiment 189
Off-line methods of control 190
System design 190
Parameter design 195
Design of the parameter tolerances (tolerance plan) 202
Loss function 202
Application of the function 204CONTENTS • IX
APPENDIX 1: STUDENT’S T-DISTRIBUTION 209
APPENDIX 2: CHI-SQUARED χ2-DISTRIBUTION 211
APPENDIX 3: FISHER’S F-DISTRIBUTION a = 0.05 213
APPENDIX 4: FISHER’S F-DISTRIBUTION a = 0.01 217
APPENDIX 5: COCHRAN’S CRITICAL VALUES 221
APPENDIX 6: DENSITY OF NORMAL DISTRIBUTION N(0, 1) 225
APPENDIX 7: PROBABILITY P FOR S
d ≤ Sdo 227
APPENDIX 8: RANDOM NUMBERS 229
BIBLIOGRAPHY 231
INDEX 23
235
A
Absolute frequency, 22
Acceptable quality level (AQL), 37–38
Active experiment, 82, 89
Adjusted coefficient of multiple
correlation, 118
Algorithmic system design methods, 193
Analysis of variance (ANOVA)
multifactor, 75–77
single-factor, 73–74
Analytically experimental models, 82
Analytical models, 81
ANOVA. See Analysis of variance
AQL. See Acceptable quality level
Area of response, 91
Arithmetic mean, 24–25
Arranged range, 21
Asymmetry of distribution, 9–10
B
Binomial distribution
confidence intervals of parameter, 31
discrete distributions, 16–17
Box–Wilson method
applications, 141–143
condition for application of method, 140
disadvantages, 141
method application conditions, 141
principle, 140
work algorithm, 143–147
Bulgarian State Standard BDS 11319:1990, 38
C
Canonical analysis
algorithm for canonical form reduction,
180–181
elliptic paraboloid surface, 182–183
hyperbolic paraboloid surface, 183–184
surface type determination, 181–182
c-charts, 57
Centered random variable, 13
Center of the experiment, 91
Central moments, 9
Characteristic measures, 198–199
Characteristics
dispersion, 7–9
location, 6–7
moments, 9–11
Chi-squared distribution, 30, 211–212
Choice of factors, 90–91
Classical method of function analysis, 179
Cochran’s critical values, 221–223
Coefficient for linear correlation, 66
Coefficient of adjustment, 33–35
Coefficient of anticorrelation, 67
Coefficient of concordance
assessment of significance, 99–100
determination, 98–99
Coefficient of determination, 66
Coefficient of double correlation, 70
Coefficient of multiple correlation, 118
Coefficient of process stability, 33
Coefficient of rank correlation
assessment of significance, 97–98
determination, 94–96
Coefficient of variation, 8, 27–28
Coefficients of regression equation, 113
Compatibility of the factors, 89–90
Composite designs of second order, 153
Concentrated parameters, 82
Conducting the test, 21–24
Confidence intervals of estimates, 28–30
INDEX236 • INDEX
Confidence intervals of parameter
binomial distribution, 31
Poisson distribution, 30–31
Confidence level, 3
Continuous distributions
normal distribution, 13–15
uniform distribution, 15–16
Continuous random variable, 4
Control charts
batches of similar products, 45–46
creating, 36
designing, 37–38
extreme values, 48–49
group values, 48–49
limits, 36–37
qualitative indicators, 54–61
quantitative indicators, 38–45
small batches with different distribution
characteristics, 47–48
Control parameters, 196
Correlation dependency factors, 65
Correlation moment, 10
Co-variation factor, 10
Cumulative curve, 24
Cumulative frequency, 22
D
DC. See Determining contrast
Degree of fractionality, 133
Density of normal distribution, 225–226
Density of probability distribution, 4
Design failure mode and effect
analysis, 193
Design of an experiment, 79
Determining contrast (DC), 134
Deviation control factors, 196
Diagram of dispersion, 104–106
Discrete distributions
binomial distribution, 16–17
Poisson distribution, 18–19
Discrete random variable, 4
Dispersion characteristics, 7–9
Distribution density law, 13
Distribution function, 4
Distribution parameters, 6
Distribution polygon, 23
Dynamic models, 82
Dynamic programming optimization
methods, 179
E
Elliptic paraboloid surface, 182–183
Errors from the choice, 110
Errors from the measurements, 110
Event, 3
Experimental modeling, 109–110
Experimental models, 81–82
Experimental research, 82
Extreme experiment, 79
Extreme values, 48–49
F
Failure mode and effect analysis (FMEA),
192–195
FFE. See Full factorial experiment
Fisher’s F-distribution, 213–215, 217–219
FMEA. See Failure mode and effect
analysis
Four-field method, 68–69
Fractional factorial experiment (FrFE)
construction stages, 134–137
definition, 133
Fractional replica
definition, 133
number of tests, 133–134
FrFE. See Fractional factorial experiment
Full factorial experiment (FFE)
calculation of coefficients, 125, 129
design of the experiment, 123–124
dispersion of regression coefficients,
126, 130
dispersion test, 126, 130
properties of extended matrix,
124–125
registration of derived model, 126, 130
types of matrices, 125
verification for reproducibility of process,
126, 129
verification of adequacy of model, 127,
130–131
verification of significance of regression
coefficients, 126, 130INDEX • 237
G
Gaussian distribution. See Normal
distribution
GC. See Generating correlation
GDC. See Generalized determining
contrast
Generalized determining contrast
(GDC), 134
Generalized target function, 86
Generating correlation (GC), 133
Gross errors, 110–111
Group values, 48–49
H
Histogram of frequency distribution, 23
House of quality, 193
Hyperbolic paraboloid surface, 183–184
Ii
-charts, 48–49
Impossible event, 3
Independence, 89
Indeterminate coefficient, 67
Initial moments, 9
Input factors, 89
Input parameters, 81
Integral system design methods, 193
Interval estimates, 21, 25–28
Intuitive system design methods, 193
Kk
-charts, 48–49
Kendall’s coefficient of rank correlation, 95
Kurtosis, 10
L
Linear correlation factor, 11
Linear deviation, 8
Linear irregularity coefficient, 27
Linear programming optimization
methods, 179
Location characteristics, 6–7
Loss function
application of function, 204–208
definition, 202
functional characteristics, 203
M
Manageable parameters, 196
Mathematical expectation, 6
Mathematical models, 81
Mean linear deviation, 26
Median, 7, 25
Method of Lagrange multipliers, 179
Method of least squares, 114
Modal value, 25
Mode, 7, 25
Models of dynamics, 82
Moment characteristics, 9–11
Morphological system design methods, 193
Multifactor analysis of variance, 75–77
N
Noncontrol parameters, 196
Nonlinear programming optimization
methods, 179
Normal distribution
confidence intervals of estimates, 28–30
continuous distributions, 13–15
np-charts, 56–57
NPM. See Nuisance performance measure
Nuisance parameters, 196
Nuisance performance measure (NPM), 198
Number of tests, fractional replica,
133–134
Numerical characteristics
definition, 6
properties, 11–12
O
OCCE. See Orthogonal central composite
experiment
Off-line methods of control
parameter design, 195–202
system design, 190–195
tolerance design, 202
Optimal composite designs, 153–154
Optimal composite experiment
adequacy model verification, 173, 177
coefficients of regression equation, 173,
176–177
design of the experiment, 172, 175
number of tests, 171, 174238 • INDEX
regression coefficients determination, 172,
174, 176
regression coefficients variances,
173, 176
Optimization methods, 179
Order of distribution, 5
Orthogonal central composite experiment
(OCCE)
adequacy model verification, 157,
162–163
coefficients of regression equation,
156–157, 161–162
design of the experiment, 154–155, 158
number of tests, 154, 158
recording of regression equation, 157, 162
regression coefficients determination,
155–156, 158–160
regression coefficients variances, 156,
160–161
Orthogonal table, 197
Output parameters, 81
P
Parameter design
characteristic measures, 198–199
division of factors, 196
interactions between factors, 199–202
reduction of effect of nuisance factors,
196–198
Partial coefficient of correlation, 70–71
Passive experiment, 82, 89
p-charts, 54–56
Point estimates, 21, 24–25
Poisson distribution
confidence intervals of parameter, 30–31
discrete distributions, 18–19
Polynomial equations, 113
Polynomial regression model, 113
Practically impossible event, 3
Practically valid event, 3
Price factors, 196
Primary range, 21
Probability of occurrence of a specific
event, 3
Process failure mode and effect analysis,
193–194
Q
QFD. See Quality function deployment
Quadruple table, 69
Qualitative indicators, control charts
number of defective products, 56–57
number of defects, 57
relative number of defective products,
54–56
relative number of defects, 57–58, 61
Quality function deployment (QFD),
191–192
Quantile, 6
Quantitative indicators, control charts
individual and absolute values, 45
practical limits, 43–44
x R / control chart, 42–43
x R / control chart, 39–42, 52–53
x S / control chart, 39, 50–52
R
Random balance method
concept, 103
construction of dispersion diagram,
104–106
design of the experiment, 103–104
separation of essential factors, 107
Random disturbances, 81
Random errors, 110
Random event, 3
Random numbers, 229–230
Random variable
continuous, 4
definition, 3
discrete, 4
Random variables distribution, 4
Range, 9, 25
Rank correlation
coefficient of concordance, 98–100
coefficient of rank correlation, 94–98
definition, 93
RCCE. See Rotatable central composite
experiment
Regression analysis, 113–119, 122
Regression equation, 113
Relative frequency, 22
Rotatable central composite designs, 153INDEX • 239
Rotatable central composite experiment
(RCCE)
adequacy model verification, 166, 171
coefficients of regression equation,
166, 170
design of the experiment, 164, 168
number of tests, 163, 167
regression coefficients determination, 165,
167, 169
regression coefficients variances,
165–166, 169–170
S
Saturated matrix, 125
Separating points, 106
Signal factors, 196
Significant level, 3
Simplex method
coordinate points, 150
criterion for reaching optimal area, 148
examples, 147
initial simplex, 148–150
mirrored point apex coordinates, 150–151
property, 147
specifying optimal area, 148
Single-factor analysis of variance, 73–74
Skewness, 9–10
SPC. See Statistical process control
Spearman’s coefficient of rank
correlation, 94
Standard deviation, 7, 26
Standardization of a random variable, 14
Statistical estimates, 21
Statistical population, 3
Statistical process control (SPC), 33–35
Student’s t-distribution, 29, 209–210
Supersaturated matrix, 125
Surface type determination, 181–182
Systematic errors, 110
System design
failure mode and effect analysis, 192–195
four groups, 190
quality function deployment, 191–192
System of normal equations, 115
T
Taguchi methods
designed experiment, 189–190
loss function, 202–208
off-line methods of control, 190–202
Target control factors, 196
Target functions, 85–88
Target performance measure (TPM), 198
Theory of experiment, 83
Tolerance design, 202
TPM. See Target performance measure
Uu
-charts, 57–58, 61
Uniform distribution, 15–16
Unsaturated matrix, 125
V
Valid event, 3
Variance, 7, 26
X
x R / control chart, 42–43
x R / control chart, 39–42, 52–53
x S / control chart, 39, 50–52
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