Page 24 - Applied statistics and probability for engineers

2 Chapter 1/The Role of Statistics in Engineering

important question is: What proportion of patients LWOT from the ED? These questions can be
solved by employing probability models to describe the ED, and from these models very precise
estimates of waiting times and the number of patients who LWOT can be obtained. 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 will encounter many examples of
these applications in this book.

Learning Objectives
After careful study of this chapter, you should be able to do the following:

1. Identify the role that statistics can play in the engineering problem-solving process
2. Discuss how variability affects the data collected and used for making engineering decisions
3. Explain the difference between enumerative and analytical studies
4. Discuss the different methods that engineers use to collect data
5. Identify the advantages that designed experiments have in comparison to other methods of collecting
engineering data
6. Explain the differences between mechanistic models and empirical models
7. Discuss how probability and probability models are used in engineering and science

1-1 The Engineering Method and Statistical Thinking

An engineer is someone who solves problems of interest to society by the eficient application of
scientiic principles. Engineers accomplish this by either reining an existing product or process
or by designing a new product or process that meets customers’ needs. The engineering, or
scientiic, 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 scientiic or engineering knowledge of the
phenomenon 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. Reine the model on the basis of the observed data.
6. Manipulate the model to assist in developing a solution to the problem.
7. Conduct an appropriate experiment to conirm that the proposed solution to the problem is
both effective and eficient.
8. Draw conclusions or make recommendations based on the problem solution.
The steps in the engineering method are shown in Fig. 1-1. Many engineering sciences
employ the engineering method: the mechanical sciences (statics, dynamics), luid science,
thermal science, electrical science, and the science of materials. Notice that the engineer-
ing method features a strong interplay among the problem, the factors that may inluence
its solution, a model of the phenomenon, and experimentation to verify the adequacy of
the model and the proposed solution to the problem. Steps 2–4 in Fig. 1-1 are enclosed in
a box, indicating that several cycles or iterations of these steps may be required to obtain
the inal solution. Consequently, engineers must know how to eficiently plan experiments,
collect data, analyze and interpret the data, and understand how the observed data relate to
the model they have proposed for the problem under study.