Module
1
EMath 2 - Engineering Data Analysis
The Role of Statistics in Engineering
OUTLINE
1-1. The Engineering Method and Statistical Thinking
1-2. Collecting Engineering Data
1-3. Mechanistic and Empirical Models
1-4. Probability and Probability Models
Learning Goals
At the end of the module, you are expected to have learned the following:
 Explain engineering problem solving process.
 Describe the application of statistics in the engineering problem solving process.
 Distinguish between enumerative and analytic studies.
 Explain three methods of data collection: retrospective study, observational study, and
designed experiment.
 Explain the difference between mechanistic and empirical models.
 Describe the application of probability in the engineering problem solving process.
1-1 The Engineering Method and Statistical Thinking
Engineering Problem Solving Process
Engineers develop practical solutions and techniques for engineering problems by applying
scientific principles and methodologies. Existing systems are improved and/or new systems are
introduced by the engineering approach for better harmony between humans, systems, and
environments.
In general, the engineering problem solving process includes the following steps:
1. Problem definition: Describe the problem to solve.
2. Factor identification: Identify primary factors which cause the problem.
3. Model (hypothesis) suggestion: Propose a model (hypothesis) that explains the
relationship between the problem and factors.
4. Experiment: Design and run an experiment to test the tentative model.
5. Analysis: Analyze data collected in the experiment.
6. Model modification: Refine the tentative model.
7. Model validation: Validate the engineering model by a follow-up experiment.
8. Conclusion (recommendation): Draw conclusions or make recommendations based on the
analysis results.
(Note) Some of these steps may be iterated as necessary.
Application of Statistics
Statistical methods are applied to interpret data with variability. Throughout the engineering
problem solving process, engineers often encounter data showing variability. Statistics provides
essential tools to deal with the observed variability. Examples of the application of statistics in the
engineering problem solving process include, but are not limited to, the following:
1. Summarizing and presenting data: numerical summary and visualization in descriptive
statistics.
2. Inferring the characteristics (mean, median, proportion, and variance) of single/two
populations: z, t, x2, and F tests in parametric statistics; signed, signed-rank, and rank-sum tests in
nonparametric statistics.
3. Testing the relationship between variables: correlation analysis; categorical data analysis.
4. Modeling the causal relationship between the response and independent variables: regression
analysis; analysis of variance.
5. Identifying the sources of variability in response: analysis of variance.
6. Evaluating the relative importance of factors for the response variable: regression analysis;
analysis of variance.
7. Designing an efficient, effective experiment: design of experiment.
These applications would lead to development of general laws and principles such as Ohm's law and
design guidelines.
Enumerative vs. Analytic Studies
Two types of studies are defined depending on the use of a sample in statistical inference:
1. Enumerative study: Makes an inference to the well-defined population from which the
sample is selected. (e.g.) defective rate of products in a lot
2. Analytic study: Makes an inference to a future (conceptual) population. (e.g.) defective
rate of products at a production line
1-2 Collecting Engineering Data
Data Collection Methods
Three methods are available for data collection:
1. Retrospective study: Use existing records of the population. Some crucial information
may be unavailable and the validity of data be questioned.
2. Observational study: Collect data by observing the population with as minimal
interference as possible. Information of the population for some conditions of interest may be
unavailable and some observations be contaminated by extraneous variables.
3. Designed experiment: Collect data by observing the population while controlling
conditions on the experiment plan. The findings would obtain scientific rigorousness through
deliberate control of extraneous variables.
1-3 Mechanistic and Empirical Models
Mechanistic vs. Empirical Models
Models (explaining the relationship between variables) can be divided into two categories:
1. Mechanistic model: Established based on the underlying theory, principle, or law of a
physical mechanism.
where: I = current, E = voltage, R= resistance, and ɛ = random error
2. Empirical model: Established based on the experience, observation, or experiment of a
system (population) under study.
(e.g.) y = β0 + β1x + ɛ
where: y = sitting height, x = stature, and ɛ = random error
1-4 Probability and Probability Models
Application of Probability
Along with statistics, the concepts and models of probability are applied in the engineering
problem solving process for the following:
1. Modeling the stochastic behavior of the system: discrete and continuous probability
distributions.
2. Quantifying the risks involved in statistical inference: error probabilities in hypothesis testing.
3. Determining the sample size of an experiment for a designated test condition: sample size
selection
Reference:
Montgomery D. C. and Runger G.C., 2018, Applied Statistics and Probability for Engineers, 7th Edition,
111 River Street, Hoboken, NJ: John Wiley & Sons, Inc.