Technology & Engineering
Probability Engineering
Probability engineering is the application of probability theory to engineering problems. It involves the use of statistical methods to analyze and design systems that involve uncertainty and variability. The goal is to optimize the performance of systems while minimizing the risk of failure.
Written by Perlego with AI-assistance
Related key terms
1 of 5
5 Key excerpts on "Probability Engineering"
- Kuldip S. Rattan, Nathan W. Klingbeil, Craig M. Baudendistel(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Probability and Statistics in Engineering CHAPTER 11 11.1 INTRODUCTION There are a multitude of uses for probability and statistics in engineering. At the very least, the inherent nature of variability in engineering experimentation requires a working knowledge of statistics to help clearly and accurately describe the physical phenomena being tested. Applications of engineering statistics include quality con- trol, transportation, logistics, reliability, factorial experimentation, stochastic design, and probabilistic modeling, among others. While many of these applications are asso- ciated with the field of Industrial and Systems Engineering, virtually all engineering disciplines require a formal class in statistics. As such, the treatment here is simply a brief introduction to help motivate some of the foundational applications that engi- neering students will see as they move forward in their intended degree programs. 11.2 QUALITY CONTROL PROBABILITY IN MANUFACTURING An inspector examines a batch of 100 turbine engine blades. It is found that 2 have major defects, 5 have minor defects, and the rest have no defects at all. As such, the probabilities of randomly selecting a blade with major defects, minor defects, or no defects can be reasoned as follows: When randomly selecting a single blade, there are 100 equally likely selections that can result in 1 of 3 possible outcomes. The probability of selecting a blade with a major defect is 2 out of 100 or 2/100 = 0.02 = 2%. Similarly, the probability of selecting a blade with minor defects is 5 out of 100 or 5/100 = 0.05 = 5%. Lastly, the probability of selecting a single blade free from defects is 93 out of 100 or 93/100 = 0.93 = 93%. Note that the individual probabilities of all possible outcomes add up to 1 or 100%: P(major defects) + P(minor defects) + P(no defects) = 100% 0.02 + 0.05 + 0.93 = 1.00. In general, n ∑ i=1 P i = 1, (11.1) where P i are the individual probabilities of n possible outcomes.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- University Publications(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter- 4 Reliability Engineering Reliability engineering is an engineering field, that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is often reported as a probability. Overview A Reliability Block Diagram Reliability may be defined in several ways: • The idea that something is fit for a purpose with respect to time; • The capacity of a device or system to perform as designed; • The resistance to failure of a device or system; • The ability of a device or system to perform a required function under stated conditions for a specified period of time; • The probability that a functional unit will perform its required function for a specified interval under stated conditions. • The ability of something to fail well (fail without catastrophic consequences) ____________________ WORLD TECHNOLOGIES ____________________ Reliability engineers rely heavily on statistics, probability theory, and reliability theory. Many engineering techniques are used in reliability engineering, such as reliability prediction, Weibull analysis, thermal management, reliability testing and accelerated life testing. Because of the large number of reliability techniques, their expense, and the varying degrees of reliability required for different situations, most projects develop a reliability program plan to specify the reliability tasks that will be performed for that specific system. The function of reliability engineering is to develop the reliability requirements for the product, establish an adequate reliability program, and perform appropriate analyses and tasks to ensure the product will meet its requirements. These tasks are managed by a reliability engineer, who usually holds an accredited engineering degree and has additional reliability-specific education and training.
- Douglas C. Montgomery, George C. Runger(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Probability models that can be used to solve these types of problems are discussed in Chapters 2 through 5. The concepts of probability and statistics are powerful ones and contribute extensively to the solutions of many types of engineering problems. You encounter many examples of these applications in this book. 1.1 The Engineering Method and Statistical Thinking An engineer is someone who solves problems of interest to society by the efficient application of scientific principles. Engineers accomplish this by either refining an existing product or proc- ess or by designing a new product or process that meets customers’ needs. The engineering, or scientific, method is the approach to formulating and solving these problems. The steps in the engineering method are as follows: 1. Develop a clear and concise description of the problem. 2. Identify, at least tentatively, the important factors that affect this problem or that may play a role in its solution. 3. Propose a model for the problem, using scientific or engineering knowledge of the phe- nomenon being studied. State any limitations or assumptions of the model. 4. Conduct appropriate experiments and collect data to test or validate the tentative model or conclusions made in steps 2 and 3. 5. Refine the model on the basis of the observed data. 6. Manipulate the model to assist in developing a solution to the problem. 1.1 The Engineering Method and Statistical Thinking 3 Develop a clear description Identify the important factors Propose or refine a model Conduct experiments Manipulate the model Confirm the solution Conclusions and recommendations FIGURE 1.1 The engineering method. 7. Conduct an appropriate experiment to confirm that the proposed solution to the problem is both effective and efficient. 8. Draw conclusions or make recommendations based on the problem solution. The steps in the engineering method are shown in Figure 1.1.
eBook - PDFAnalytical Methods for Risk Management
A Systems Engineering Perspective
- Paul R. Garvey(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
Chapter 2 Elements of Probability Theory 2.1 Introduction Whether referring to a storm’s intensity, an arrival time, or the success of a decision, the word “probable,” or “likely,” has long been part of our language. Most people have an appreciation for the impact of chance on the occurrence of an event. In the last 350 years, the theory of probability has evolved to explain the nature of chance and how it can be studied. Probability theory is the formal study of events whose outcomes are uncertain. Its origins trace to 17th-century gambling problems. Games that involved playing cards, roulette wheels, and dice provided mathematicians with a host of interest-ing problems. The solutions to many of these problems yielded the first principles of modern probability theory. Today, probability theory is of fundamental impor-tance in science, engineering, and business. Engineering risk management aims to identify and manage events whose out-comes are uncertain. In particular, its focus is on events that, if they occur, have unwanted impacts or consequences to a project or program. The phrase “ if they occur ” means these events are probabilistic in nature. Thus, understanding them in the context of probability concepts is essential. This chapter presents an in-troduction to these concepts and illustrates how they apply to managing risks in engineering systems. 2.2 Interpretations and Axioms We begin this discussion with the traditional look at dice. If a six-sided die is tossed, there clearly are six possible outcomes for the number that appears on the upturned face. These outcomes can be listed as elements in a set { 1 , 2 , 3 , 4 , 5 , 6 } . 13 14 Elements of Probability Theory The set of all possible outcomes of an experiment, such as tossing a six-sided die, is called the sample space , which we will denote by . The individual outcomes of are called sample points, which we will denote by ω .
- Hugh L. Dryden, Theodore Von Karman, Kalinske Anton Adam(Authors)
- 2016(Publication Date)
SCIENCE OF ENGINEERING 99 he must be able to make things that have quality characteristics lying within previously specified tolerance ranges. Hence, a basic engineering problem is to devise an operation of using raw and fabricated materials that, if carried out, will give a thing wanted. The specified tolerance ranges for the quality characteristics of the thing wanted define a target for the engineer. He devises an operation and predicts that, if carried out, it will hit the target, but, since he does not have certain or perfect knowledge of facts and physical laws, he cannot be certain that a given operation will hit its target; in fact the best that he can hope to do is to know the probability of hitting the target. Here then is one fundamental way in which probability enters into everything that an engineer does. Furthermore, if the thing produced fails to meet tolerance re-quirements, the engineer is penalized in one way or another. For example, if the quality of any piecepart fails to meet its tolerance requirements, a loss is incurred through rejection or modification of the defective part; if the time-to-blow of a protective fuse fails to meet its tolerance range, loss of property and even loss of life may result; if the time-to-blow of a fuse in a shell fails to meet its tolerance range, the shell may burst prematurely and kill mem-bers of the gun crew and, in any case, the round of ammunition will fail to fulfill its function of destruction within the ranks of the enemy. This means that when the engineer undertakes to use probability theory it is essential that he thoroughly understand the conditions under which its use will lead to valid predictions. In what follows we introduce the term operation to include any experimental procedure designed to produce a previously specified result. In this sense, a production process is an operation, and a method of measuring is also an operation.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
