Error analysis with applications in engineering:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Rochester, NY
Lastran Corp.
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 235 S. graph. Darst. |
| ISBN: | 1893000028 |
Staff View
MARC
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| 245 | 1 | 0 | |a Error analysis with applications in engineering |c Wojciech Szczepiński and Zbigniew Kotulski |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Basic characteristics of error distribution; histograms 1
1.1 Introductory remarks; histograms 1
1.2 The average of a sample of measurements 4
1.3 Dispersion measures in error analysis 5
1.4 Cumulative frequency distribution 7
1.5 Examples of empirical distributions 8
1.6 Parameters obtained from the measured data
and their theoretical values 12
1.7 Problems 13
2 Sample points, random variables, and probability 17
2.1 * Probability and random variables1 17
2.2 The cumulative distribution function;
the probability density function 22
2.3 Moments 26
2.4 The normal probability distribution 30
2.5 * The characteristic function of a distribution 41
2.6 * Constants characterizing the random variables 44
2.7 * Deterministic functions of random variables 49
2.8 Some other one dimensional distributions 51
2.8.1 Discrete probability distributions 51
1 Sections marked with an asterisk may be omitted by readers who are mainly inter¬
ested in practical applications of error calculus.
viii Contents
2.8.1.1 The binomial distribution 52
2.8.1.2 The multinomial distribution 52
2.8.1.3 The Poisson distribution 53
2.8.2 Continuous probability distributions 53
2.8.2.1 The rectangular (uniform) distribution . . 53
2.8.2.2 The lognormal distribution 56
2.8.2.3 The exponential distribution 60
2.8.2.4 The chi squared distribution 62
2.8.2.5 The Weibull distribution 64
2.8.2.6 The Student t distribution 65
2.8.3 Remarks on other probability distributions 65
2.8.4 Measures of deviation from the normal distribution . 68
2.9 * Approximate methods for constructing
a probability density function 69
2.10 Multi dimensional probability distributions 72
2.11 Problems 79
3 Functions of independent random variables 85
3.1 Basic relations 85
3.2 Simple examples of applications 89
3.3 Examples of applications in non direct measurements .... 91
3.4 Remarks on the applications in the calculus
of tolerance limits 93
3.5 Statical analogy in the analysis of complex dimension nets . 96
3.6 Problems 101
4 Two dimensional distributions 105
4.1 Introductory remarks 105
4.2 Linear regression of experimental observations 112
4.2.1 The method of least squares for determining the lin¬
ear regression line 113
4.2.2 The method of moments for determining the linear
regression line 116
4.3 Linear correlation between experimentally
determined quantities 119
4.4 Two dimensional continuous random variables 122
4.5 The two dimensional normal distribution 126
4.5.1 The case of independent random variables 126
4.5.2 The circular normal distribution 128
4.5.3 The case of dependent random variables 132
4.6 Problems 135
5 Two dimensional functions
of independent random variables 141
5.1 Basic relations 141
Contents ix
5.2 The rectangular distribution of independent random variables 145
5.2.1 Analytical method for determining two dimensional
tolerance limits polygons 146
5.2.2 Statical analogy method for determining
two dimensional tolerance limit polygons 150
5.2.3 Graphical method for determining two dimensional
tolerance limits polygon. Williot s diagram 155
5.3 The normal distribution of independent random variables . 159
5.4 Indirect determination of the ellipses
of probability concentration 164
5.5 Problems 167
6 Three dimensional distributions 173
6.1 General remarks 173
6.2 Continuous three dimensional random variables 175
6.3 The three dimensional normal distribution 178
6.3.1 Independent random variables 178
6.3.2 The spherical normal distribution 179
6.3.3 The case of dependent random variables 181
6.4 Problems 183
7 Three dimensional functions
of independent random variables 189
7.1 Basic relations 189
7.2 The rectangular distribution of independent random variables 194
7.3 The normal distribution of independent random variables . 202
7.4 Indirect determination of the ellipsoids
of probability concentration 208
7.5 Problems 211
8 Appendix. Some useful definitions
and facts of probability theory 213
8.1 * Statistical linearization 213
8.2 * Limit theorems of probability theory 216
8.2.1 Concepts of the probabilistic convergence 216
8.2.2 The law of large numbers 218
8.2.3 The central limit theorems 218
8.3 * Elements of mathematical statistics 220
8.3.1 Estimators 220
8.3.2 Testing statistical hypotheses 221
8.3.3 Confidence intervals 223
8.4 * Bibliographical notes for future studies 223
References 225
x Contents
Index 232
|
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| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:51:23Z |
| institution | BVB |
| isbn | 1893000028 |
| language | English |
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| physical | X, 235 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Lastran Corp. |
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| spelling | Szczepinski, Wojciech Verfasser aut Error analysis with applications in engineering Wojciech Szczepiński and Zbigniew Kotulski Rochester, NY Lastran Corp. 2000 X, 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering mathematics Error analysis (Mathematics) Machine design Fehleranalyse (DE-588)4016608-9 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Fehleranalyse (DE-588)4016608-9 s Ingenieurwissenschaften (DE-588)4137304-2 s DE-604 Kotulski, Zbigniew Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009401552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Szczepinski, Wojciech Kotulski, Zbigniew Error analysis with applications in engineering Engineering mathematics Error analysis (Mathematics) Machine design Fehleranalyse (DE-588)4016608-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4016608-9 (DE-588)4137304-2 |
| title | Error analysis with applications in engineering |
| title_auth | Error analysis with applications in engineering |
| title_exact_search | Error analysis with applications in engineering |
| title_full | Error analysis with applications in engineering Wojciech Szczepiński and Zbigniew Kotulski |
| title_fullStr | Error analysis with applications in engineering Wojciech Szczepiński and Zbigniew Kotulski |
| title_full_unstemmed | Error analysis with applications in engineering Wojciech Szczepiński and Zbigniew Kotulski |
| title_short | Error analysis with applications in engineering |
| title_sort | error analysis with applications in engineering |
| topic | Engineering mathematics Error analysis (Mathematics) Machine design Fehleranalyse (DE-588)4016608-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Engineering mathematics Error analysis (Mathematics) Machine design Fehleranalyse Ingenieurwissenschaften |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009401552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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