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Complete overview of the theory and fundamentals of Reliability Analysis applied with Minitab and Python tools
Reliability Analysis Using Minitab and Python expertly applies Minitab and Python programs to the field of reliability engineering, presenting basic concepts and explaining step-by-step how to implement statistical distributions and reliability analysis methods using the two programming languages. The textbook enables readers to effectively use software to efficiently process massive amounts of data while also reducing human error.
Examples and case studies as well as exercises and questions are included throughout to enable a smooth learning experience. Excel files containing the sample data and Minitab and Python example files are also provided.
Students who have basic knowledge of probability and statistics will find this textbook highly approachable. Nonetheless, it also covers material on basic statistics at the beginning, so students who are not familiar with statistics can follow the material as well.
Written by a highly qualified author in the field, sample topics covered in Reliability Analysis Using Minitab and Python include:
Reliability Analysis Using Minitab and Python serves as an excellent introductory level textbook on the topic for both undergraduate and graduate students. It presents information clearly and concisely and includes many helpful additional learning resources to aid in understanding of concepts, information retention, and practical application.
Jaejin Hwang is Associate Professor in the Industrial and Systems Engineering Department at Northern Illinois University, USA. He received his PhD in Industrial and Systems Engineering from Ohio State University, USA, in 2016 and has published two books with CRC Press and Mercury Learning & Information respectively. He has also been a guest editor for the International Journal of Environmental Research and Public Health.
About the Author ix
Preface xi
Acknowledgments xiii
About the Companion Website xv
1 Introduction 1
1.1 Reliability Concepts 1
1.1.1 Reliability in Our Lives 1
1.1.2 History of Reliability 2
1.1.3 Definition of Reliability 2
1.1.4 Quality and Reliability 3
1.1.5 The Importance of Reliability 4
1.2 Failure Concepts 5
1.2.1 Definition of Failure 5
1.2.2 Causes of Failure 5
1.2.3 Types of Failure Time 7
1.2.4 The Reliability Bathtub Curve 12
1.3 Summary 16
2 Basic Concepts of Probability 19
2.1 Probability 19
2.1.1 The Importance of Probability in Reliability 20
2.2 Joint Probability with Independence 20
2.3 Union Probability 21
2.4 Conditional Probability 22
2.5 Joint Probability with Dependence 22
2.6 Mutually Exclusive Events 23
2.7 Complement Rule 24
2.8 Total Probability 24
2.9 Bayes' Rule 25
2.10 Summary 26
3 Lifetime Distributions 29
3.1 Probability Distributions 29
3.1.1 Random Variables 29
3.2 Discrete Probability Distribution 30
3.3 Continuous Probability Distribution 32
3.3.1 Reliability Concepts 33
3.3.2 Failure Rate 35
3.4 Exponential Distribution 37
3.4.1 Exponential Lack of Memory Property 40
3.4.2 Excel Practice 41
3.4.3 Minitab Practice 41
3.4.4 Python Practice 43
3.5 Weibull Distribution 46
3.5.1 Excel Practice 52
3.5.2 Minitab Practice 52
3.5.3 Python Practice 53
3.6 Normal Distribution 54
3.6.1 Excel Practice 60
3.6.2 Minitab Practice 60
3.6.3 Python Practice 62
3.7 Lognormal Distribution 63
3.7.1 Excel Practice 66
3.7.2 Minitab Practice 66
3.7.3 Python Practice 68
3.8 Summary 70
4 Reliability Data Plotting 77
4.1 Straight Line Properties 77
4.2 Least Squares Fit 79
4.2.1 Excel Practice 81
4.2.2 Minitab Practice 82
4.2.3 Python Practice 82
4.3 Linear Rectification 84
4.4 Exponential Distribution Plotting 84
4.4.1 Excel Practice 92
4.4.2 Minitab Practice 92
4.4.3 Python Practice 94
4.5 Weibull Distribution Plotting 96
4.5.1 Minitab Practice 99
4.5.2 Python Practice 100
4.6 Normal Distribution Plotting 103
4.6.1 Minitab Practice 105
4.6.2 Python Practice 105
4.7 Lognormal Distribution Plotting 106
4.7.1 Minitab Practice 108
4.7.2 Python Practice 110
4.8 Summary 111
5 Accelerated Life Testing 115
5.1 Accelerated Testing Theory 115
5.2 Exponential Distribution Acceleration 117
5.3 Weibull Distribution Acceleration 118
5.3.1 Minitab Practice 119
5.3.2 Python Practice 120
5.4 Arrhenius Model 123
5.4.1 Minitab Practice 125
5.4.2 Python Practice 127
5.5 Summary 129
6 System Failure Modeling 131
6.1 Reliability Block Diagram 131
6.2 Series System Model 132
6.3 Parallel System Model 135
6.4 Combined Serial-Parallel System Model 138
6.5 k-out-of-n System Model 140
6.6 Minimal Paths and Minimal Cuts 142
6.7 Summary 148
7 Repairable Systems 151
7.1 Corrective Maintenance 151
7.2 Preventive Maintenance 152
7.3 Mean Time between Failures 152
7.4 Mean Time to Repair 153
7.5 Availability 153
7.5.1 Inherent Availability 153
7.5.2 Achieved Availability 154
7.5.3 Operational Availability 155
7.5.4 System Availability 156
7.6 Maintainability 156
7.7 Preventive Maintenance Scheduling 157
7.7.1 Python Practice 160
7.8 Summary 161
8 Case Studies 165
8.1 Parametric Reliability Analysis 165
8.1.1 Description of Case Study 166
8.1.2 Minitab Practice 166
8.1.3 Python Practice 177
8.2 Nonparametric Reliability Analysis 184
8.2.1 Description of Case Study 184
8.2.2 Minitab Practice 185
8.2.3 Python Practice 189
8.3 Driverless Car Failure Data Analysis 190
8.3.1 Description of Case Study 190
8.3.2 Minitab Practice 193
8.3.3 Python Practice 199
8.4 Warranty Analysis 202
8.4.1 Description of Case Study 202
8.4.2 Minitab Practice 204
8.5 Stress-Strength Interference Analysis 210
8.5.1 Description of Case Study 210
8.5.2 Minitab Practice 211
8.5.3 Python Practice 213
8.6 Summary 214
Index 219
In modern society, we rely on various complex and advanced devices and systems to enjoy convenience and enhance our lives. For example, autonomous vehicles allow drivers to engage in other activities while driving, and advances in space technology have ushered in an era in which civilians can also go to space.
However, advances in technology have some side effects. With the development of technology, the area in which humans can intervene is reduced, and when there is a problem in a system or device, humans can be adversely affected. For example, cars that are being produced these days are often electronic systems that systematically operate the overall functions of the car. If the central computer unit that controls the car breaks down, the driver will be limited in what they can do with it. Autonomous vehicle accidents due to system errors are also occasionally encountered, which can be viewed in a similar context.
With the development of these technologies, the necessity of the reliability field can be felt more acutely. A complex system may have thousands or tens of thousands of large and small parts interlocked. If the failure characteristics of such a system and the time it takes to failure can be predicted, very serious accidents can be prevented, and customer satisfaction can be increased.
When did the field of reliability begin to gain attention? The United States is one of the major countries that pioneered the field of reliability. The need for reliability was highlighted during World War II. Electronic military equipment was shipped immediately after development, but when it arrived at the destination (far east), the equipment underwent many failures. At the time of development, there was no defect when the quality inspection was conducted. After investigation, it was found that the place where the equipment was actually used was a high-temperature and high-humidity environment, which caused equipment (vacuum tube) failure. In other words, the environment in which the equipment was developed and the environment in which it was used were very different, causing failure. At this time, a professional reliability analysis team was founded, and efforts to reduce the occurrence of failures in the actual equipment-use environment began.
At the same time, Germany also began to actively consider using the reliability field to increase the mission success rate of missiles. In modern society, reliability-related fields are widely used in addition to their use in the military industry. Reliability is considered to be an extended concept of quality control, and it is not an exaggeration to say that reliability is considered in designing and manufacturing almost all equipment and products, from industrial equipment to household appliances.
According to the dictionary definition of the word reliability, it is as follows:
The quality of being trustworthy or of performing consistently well.
This definition can also be considered in connection with product or system failure. It can be said that minimizing failure is one of the important factors of reliability.
In addition, time is another very important factor in defining reliability, because reliability is dependent on time. For example, the failure rate within 1 year of buying a car and after 10 years will be very different. For this reason, the concept of time is an essential element in reliability.
Finally, reliability can be expressed as a probability. That is, it can be evaluated through a quantified method. For example, the probability that the purchased car will fail within 1 year could be 5%, and the probability that it will fail within 10 years could be 90%.
In summary, reliability can be defined as:
The probability that a system or product will perform the expected function in a specific environment over a specific period of time.
In other words, the defect in military equipment (vacuum tubes) in World War II previously mentioned can be seen as a result of the lack of consideration for the specific environment in which the equipment was used. In order to understand and predict reliability in such a case, the concept of probability and distribution of statistics can be applied, and it will be mainly covered in this book.
Case
In the US auto market, the warranty is usually 3 years or 36,000 miles. Automaker A is planning a 5-year or 60,000-mile warranty to give it an edge over its competitors. The automaker wants to know whether the parts they receive from their subcontractors are 99% or more reliable over 5 years. How can subcontractors prove the reliability of parts?
Quality and reliability are often considered together, but the difference between these two concepts needs to be explored, as shown in Table 1.1.
Table 1.1 Description of quality and reliability.
The American rating company J.D. Power and Associates considers the quality and reliability of automobiles as important metrics, and automotive customers are also interested in these metrics. The new car Initial Quality Index (IQS) is an index that quantifies the number of problems per 100 new cars within 90 days. The Vehicle Dependability Study Index (VDS) quantifies the number of problems per 100 vehicles that occurred in the previous year among vehicles older than 3 years. We can see by the stated time spans that the concept of reliability is implied.
As products and systems become more sophisticated and complex, reliability becomes more and more critical. In the case of a smartphone, more than 500 parts are normally included. Failure of certain parts can lead to serious failures that make the entire smartphone unusable. In addition, the complexity of products and systems can expose them to more human error in the design and the development stage.
Failure of products and systems has a substantial impact on safety and cost. According to the factor of 10 rule, the more delayed the response to the reliability problem is, the more the cost of tenfold or greater increases as it moves to the next stage, as seen in Figure 1.1.
Figure 1.1 The factor of 10 rule.
The development cycle of products is gradually shortening due to advances in technology, heated competition for products, and increased customer expectations. In the case of smartphones, development cycles often range from six months to less than a year. Such a tight schedule increases the risk of human errors and failures. The importance of reliability concepts throughout the entire product cycle could grow in these circumstances.
The dictionary definition of failure is as follows:
Lack of success.
The omission of expected or required action.
If we approach the definition of failure from an engineering perspective, it is as follows:
The inability of a system or component to perform its required functions within specified performance requirements.
In other words, the concept of failure is closely related to the definition of reliability mentioned previously. Failure can also be classified into hard and soft failures, as seen in Table 1.2.
Table 1.2 Description of hard and soft failures.
Adverse effects caused by failure can be divided into three stages according to the scale shown in Figure 1.2. A small failure can cause inconvenience in our daily life, such as an air conditioning malfunction. Intermediate failures can take a toll on our bodies, property, safety, and finances, such as with a vehicle's brake failure. In addition, large failures cause disasters in society. Examples include breakdowns or crashes of airplanes and spacecraft.
Figure 1.2 The adverse effects of...
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