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Notions of probability theory applied to reliability calculation and quality control
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Publisher: Editura Universitară
Author: Tudor Cătălin Apostolescu, Ioana Udrea, Despina Paula Duminică, Sorin Ionuț Badea, Florentina Badea
Edition: I
Pages: 138
Publisher year: 2025
ISBN: 978-606-28-2042-8
DOI: 10.5682/9786062820428
Product Code:
9786062820428
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This work provides a rigorous and applied synthesis of probabilistic methods used in engineering, with an emphasis on the analysis of the reliability of technical systems and the quality control of manufacturing processes. The integrated approach supports progressive learning and understanding of the relationship between the random behavior of systems and their performance over time.
Essential topics are addressed such as:
- probabilistic spaces, random variables and relevant distributions (exponential, Weibull, normal, binomial);
- reliability functions, densities, failure rates and system models (series, parallel, redundancy);
- risk analysis and product life expectancy estimation;
- Monte Carlo simulations and interpretation of experimental data;
- modern statistical methods of quality control, control charts and sampling plans.
The work is structured in such a way as to facilitate both individual study and applied teaching or research activity. The solved examples, case studies, self-assessment exercises and seminar sections contribute to the development of a clear perspective, applicable in industrial and academic environments alike.
This book reflects a solid teaching and professional experience and is specifically addressed to students, master's students, doctoral students and specialists in engineering and economic fields, concerned with quality, performance and sustainability.
Essential topics are addressed such as:
- probabilistic spaces, random variables and relevant distributions (exponential, Weibull, normal, binomial);
- reliability functions, densities, failure rates and system models (series, parallel, redundancy);
- risk analysis and product life expectancy estimation;
- Monte Carlo simulations and interpretation of experimental data;
- modern statistical methods of quality control, control charts and sampling plans.
The work is structured in such a way as to facilitate both individual study and applied teaching or research activity. The solved examples, case studies, self-assessment exercises and seminar sections contribute to the development of a clear perspective, applicable in industrial and academic environments alike.
This book reflects a solid teaching and professional experience and is specifically addressed to students, master's students, doctoral students and specialists in engineering and economic fields, concerned with quality, performance and sustainability.
-
Notions of probability theory applied to reliability calculation and quality control
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A SINCERE THOUGHT FOR THE AUTHORS/5
Chapter 1. INTRODUCTION/11
1.1 What is reliability?/11
1.2 The importance of reliability in engineering and industry/12
1.3 The role of probability theory in reliability analysis/13
Chapter 2. RELIABILITY AND QUALITY CONTROL – A COMMON PURPOSE /15
2.1 Applications of probability theory in quality control/15
2.2 Common methods based on probabilities/16
2.3 Reliability as part of quality/17
2.4 Accelerated testing and statistical control/17
2.5 Synthesized theory and exercises/21
Chapter 3. FUNDAMENTALS OF PROBABILITY THEORY/24
3.1 Probability space/24
3.2 Events and operations with events/24
3.3 Conditional probability and independence of events/25
3.4 Random variables (V.A.)/25
3.5 Distribution function and probability density/25
3.6 Parameters of a distribution/26
3.7 Theoretical support explained/27
Chapter 4. PROBABILITY DISTRIBUTIONS USED IN RELIABILITY CALCULATION/31
4.1 Exponential distribution/31
4.2 Weibull distribution/32
4.3 Other useful distributions in reliability/33
Chapter 5. FUNDAMENTAL CONCEPTS IN RELIABILITY/ 35
5.1 Time to failure (T)/35
5.2 Function reliability R(t)R(t)R(t)/35
5.3 Failure function (CDF) F(t)F(t)F(t)/35
5.4 Probability density f(t)f(t)f(t)/36
5.5 Failure rate (hazard function) h(t)h(t)h(t)/36
5.6 Mean time to failure (MTTF)/36
5.7 System availability (Availability)/37
5.8 Explanatory graph/37
Chapter 6. SYSTEM MODELS – SERIES/PARALLEL/MIXED/38
6.1 Series Systems/38
6.2 Parallel Systems/39
6.3 Mixed Systems (Series-Parallel)/39
6.4 Redundancy and Fault Tolerance/40
Chapter 7. PRACTICAL APPLICATIONS OF RELIABILITY/41
7.1 Reliability Estimation of Electronic Components/41
7.2 Reliability in Transportation and Automation/41
7.3 Software Reliability/42
7.4 Monte Carlo Simulations in Reliability/42
Chapter 8. CASE STUDY: CALCULATION OF RELIABILITY OF A REAL SYSTEM/43
8.1 System Description/43
8.2 System Modeling/43
8.3 Step-by-Step Calculation/44
8.4 Interpretation of the Result/44
8.5 CASE STUDY 1 – Calculating the Reliability of a System/47
8.6 CASE STUDY 2 – Reliability of a parallel system (with redundancy)/48
8.7 CASE STUDY 3 – Reliability of an assisted ventilation system (hospital)/50
Chapter 9. SELF-ASSESSMENT TEST AND EXERCISES
RECAPITULATIONS/52
9.1 Section A – Theoretical questions (grid)/52
9.2 Section B – Applied problems/53
Chapter 10. DEVICE RELIABILITY/55
10.1 What does “device” mean in the context of reliability?/56
10.2 Classification of devices by reliability/56
10.3 Factors influencing device reliability/57
10.4 Modeling the reliability of a device/57
10.5 Example: laboratory device/58
10.6 Reliability increase measures/58
10.7 Performance indicators/59
10.8 Real applications/59
Chapter 11. PROBABILITY THEORY NOTIONS APPLIED IN RELIABILITY CALCULATION AND ANALYSIS RISK/61
Chapter 12. SEMINAR APPLICATIONS/103
12.1 Seminar 1 Dependent events. Conditional probability/103
12.2 Seminar 2 Total probability theorem. Bayes' theorem /106
12.3 Seminar 3/111
12.4 Seminar 4 Binomial distribution/113
12.5 Seminar 5 Continuous uniform distribution/117
12.6 Seminar 6/122
12.7 Seminar 7/126
12.8 Seminar 8/128
12.9 Seminar 9/130
12.10 Seminar 10 Example/133
BIBLIOGRAPHY/134
Chapter 1. INTRODUCTION/11
1.1 What is reliability?/11
1.2 The importance of reliability in engineering and industry/12
1.3 The role of probability theory in reliability analysis/13
Chapter 2. RELIABILITY AND QUALITY CONTROL – A COMMON PURPOSE /15
2.1 Applications of probability theory in quality control/15
2.2 Common methods based on probabilities/16
2.3 Reliability as part of quality/17
2.4 Accelerated testing and statistical control/17
2.5 Synthesized theory and exercises/21
Chapter 3. FUNDAMENTALS OF PROBABILITY THEORY/24
3.1 Probability space/24
3.2 Events and operations with events/24
3.3 Conditional probability and independence of events/25
3.4 Random variables (V.A.)/25
3.5 Distribution function and probability density/25
3.6 Parameters of a distribution/26
3.7 Theoretical support explained/27
Chapter 4. PROBABILITY DISTRIBUTIONS USED IN RELIABILITY CALCULATION/31
4.1 Exponential distribution/31
4.2 Weibull distribution/32
4.3 Other useful distributions in reliability/33
Chapter 5. FUNDAMENTAL CONCEPTS IN RELIABILITY/ 35
5.1 Time to failure (T)/35
5.2 Function reliability R(t)R(t)R(t)/35
5.3 Failure function (CDF) F(t)F(t)F(t)/35
5.4 Probability density f(t)f(t)f(t)/36
5.5 Failure rate (hazard function) h(t)h(t)h(t)/36
5.6 Mean time to failure (MTTF)/36
5.7 System availability (Availability)/37
5.8 Explanatory graph/37
Chapter 6. SYSTEM MODELS – SERIES/PARALLEL/MIXED/38
6.1 Series Systems/38
6.2 Parallel Systems/39
6.3 Mixed Systems (Series-Parallel)/39
6.4 Redundancy and Fault Tolerance/40
Chapter 7. PRACTICAL APPLICATIONS OF RELIABILITY/41
7.1 Reliability Estimation of Electronic Components/41
7.2 Reliability in Transportation and Automation/41
7.3 Software Reliability/42
7.4 Monte Carlo Simulations in Reliability/42
Chapter 8. CASE STUDY: CALCULATION OF RELIABILITY OF A REAL SYSTEM/43
8.1 System Description/43
8.2 System Modeling/43
8.3 Step-by-Step Calculation/44
8.4 Interpretation of the Result/44
8.5 CASE STUDY 1 – Calculating the Reliability of a System/47
8.6 CASE STUDY 2 – Reliability of a parallel system (with redundancy)/48
8.7 CASE STUDY 3 – Reliability of an assisted ventilation system (hospital)/50
Chapter 9. SELF-ASSESSMENT TEST AND EXERCISES
RECAPITULATIONS/52
9.1 Section A – Theoretical questions (grid)/52
9.2 Section B – Applied problems/53
Chapter 10. DEVICE RELIABILITY/55
10.1 What does “device” mean in the context of reliability?/56
10.2 Classification of devices by reliability/56
10.3 Factors influencing device reliability/57
10.4 Modeling the reliability of a device/57
10.5 Example: laboratory device/58
10.6 Reliability increase measures/58
10.7 Performance indicators/59
10.8 Real applications/59
Chapter 11. PROBABILITY THEORY NOTIONS APPLIED IN RELIABILITY CALCULATION AND ANALYSIS RISK/61
Chapter 12. SEMINAR APPLICATIONS/103
12.1 Seminar 1 Dependent events. Conditional probability/103
12.2 Seminar 2 Total probability theorem. Bayes' theorem /106
12.3 Seminar 3/111
12.4 Seminar 4 Binomial distribution/113
12.5 Seminar 5 Continuous uniform distribution/117
12.6 Seminar 6/122
12.7 Seminar 7/126
12.8 Seminar 8/128
12.9 Seminar 9/130
12.10 Seminar 10 Example/133
BIBLIOGRAPHY/134
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