Statistics in Engineering1.1 OverviewAn engineer is someone who solves problems of interest to society by the efficient application of scientific principles by:Refining existing products
Trang 1MAS291 – Chapter 01 Summarize
The Role of Statistics in Engineering
Course: MAS291
Class: SE1731
Lecturer: Lê Đình Thắng
Student: Đặng Ngọc Minh Trí – SE173705
Trang 2TABLE OF CONTENTS
1 Statistics in Engineering 3
1.1 Overview 3
1.2 Example 3
2 Collecting Engineering Data 5
2.1 Basic Principles 5
2.2 Retrospective Study 5
2.3 Observational Study 6
2.4 Designed Experiments 6
2.5 Observing Processes Over Time 7
3 Mechanistic and Empirical Models 9
4 Probability and Probability Models 11
5 Summary 12
Trang 31 Statistics in Engineering
1.1 Overview
An engineer is someone who solves problems of interest to society by the efficient application of scientific principles by:
Refining existing products
Designing new products or processes
The field of Statistics deals with the collection, presentation, analysis, and use of data to
Make decisions
Solve problems
Design products and processes
Statistical techniques are useful for describing and understanding variability
By variability, we mean successive observations of a system or phenomenon
do not produce exactly the same result
Statistics gives us a framework for describing this variability and for learning about potential sources of variability
1.2 Example
Quality Control: Engineers often use statistical process control (SPC) techniques to monitor and control the quality of products and processes SPC involves using statistical methods to analyze data from production processes, identify trends and patterns, and make adjustments to improve quality and efficiency
Figure 1.1 Statistical Process Control (SPC)
Trang 4Reliability Analysis: Engineers use statistical methods to analyze data
on the performance of systems and components, such as electronic devices or mechanical equipment They can use statistical models to predict the probability of failure, estimate the lifetime of a product, or optimize maintenance schedules
Figure 1.2 Reliability Analysis Table
Design of Experiments: Engineers use statistical methods to design and analyze experiments that test the performance of new products or processes By varying input factors and measuring the resulting output, engineers can determine the optimal settings for a system and identify factors that affect performance
Decision Making: Engineers often use statistical techniques to support decision-making processes, such as risk analysis, cost-benefit analysis, and simulation modeling Statistical analysis can help engineers evaluate the potential outcomes of different decisions and identify the most cost-effective or efficient solution
Regression Analysis: Engineers use regression analysis to identify the relationship between different variables, such as temperature and pressure, or flow rate and energy consumption Regression analysis can help engineers predict how changes in one variable will affect others, and identify the most important factors that affect performance or quality
Trang 52 Collecting Engineering Data
Collecting engineering data is an essential step in the engineering method There are several methods for collecting data, including retrospective studies, observational studies, designed experiments
2.1 Basic Principles
The basic principles of collecting engineering data include defining the problem, identifying the variables, selecting the sample size and sampling method, collecting the data, and ensuring the data is accurate and reliable
2.2 Retrospective Study
A retrospective study using historical data would use either all or a sample
of the historical process data archived over some period of time
Retrospective studies involve analyzing past data to identify patterns and relationships This method is useful for studying the effects of historical events or changes in processes over time
Figure 2.1 Retrospective Study
Trang 62.3 Observational Study
An observational study: the engineer observes the process or population, disturbing it
Observational studies involve observing and measuring variables without manipulating them This method is useful for studying complex systems or processes that cannot be controlled
Figure 2.2 Observational Study
2.4 Designed Experiments
A designed experiment: the engineer makes deliberate in the controlable variables of the system, observes the resulting system output data
Designed experiments involve manipulating variables and observing the effects on the outcome variable This method is useful for identifying cause-and-effect relationships and optimizing processes
Trang 7Figure 2.3 Designed Experiments
2.5 Observing Processes Over Time
Observing processes over time involves monitoring variables over a period
of time to identify trends and patterns This method is useful for studying processes that change over time, such as manufacturing processes or environmental systems
Whenever data are collected over time it is important to plot the data over time Phenomena that might affect the system or process often become more visible in a time-oriented plot and the concept of stability can be better judged
Figure 2.4 The dot diagram illustrates variation but does not identify the
problem
Trang 8Figure 2.5 A time series plot of concentration provides more information
than a dot diagram
Figure 2.6 Enumerative versus analytic study
Trang 93 Mechanistic and Empirical Models
A mechanistic model is built from our underlying knowledge of the basic physical mechanism that relates several variables
Example: Ohm’s Law
Current = voltage/resistance
I = E/R
I = E/R +
An empirical model is built from our engineering and scientific knowledge of the phenomenon, but is not directly developed from our theoretical or first-principles understanding of the underlying mechanism
Example:
Suppose we are interested in the number average molecular weight (Mn) of a polymer Now we know that Mn is related to the viscosity of the material (V), and it also depends on the amount of catalyst ( ) and the temperature ( ) in C T the polymerization reactor when the material is manufactured The
relationship between Mnand these variables is
Mn = f(V,C,T)
say, where the form of the function is unknown.f
where the b’s are unknown parameters
Trang 10Example: Calculate the regression line with given wire bond pull strength
data table
Figure 3.1 Wire Bond Pull Strength Data Table
In general, this type of empirical model is called a regression model.
The estimated regression line is given by
Trang 11Figure 3.2 Three-dimensional plot of the wire and pull strength data.
Figure 3.3 Plot of the predicted values of pull strength from the empirical
model
4 Probability and Probability Models
• Probability models help quantify the risks involved in statistical inference, that is, risks involved in decisions made every day
• Probability provides the framework for the study and application of statistics
Trang 135 Summary
The engineering method is a systematic approach used by engineers to solve complex problems It involves defining the problem, researching and gathering data, developing a hypothesis, testing the hypothesis, and refining the solution until the desired outcome is achieved Statistical thinking is an important part of the engineering method because it enables engineers to make data-driven decisions and analyze the reliability and variability of their results By using statistical methods, engineers can make decisions based on data rather than intuition, which can lead to more accurate and efficient solutions to complex problems Collecting engineering data is an essential step in the engineering method There are several methods for collecting data, including retrospective studies, observational studies, designed experiments, and observing processes over time The basic principles of collecting engineering data include defining the problem, identifying the variables, selecting the sample size and sampling method, collecting the data, and ensuring the data is accurate and reliable
Mechanistic and empirical models are two types of models used in engineering Mechanistic models are based on physical laws and principles, while empirical models are based on observations and data Mechanistic models are useful for understanding the fundamental principles behind a system or process and predicting how it will behave under different conditions Empirical models are useful for predicting outcomes based on data and observations
In conclusion, Statistics plays a crucial role in engineering by providing tools and techniques for analyzing and interpreting data to inform decision-making and improve system performance Engineers use statistical methods in a wide range of applications, such as quality control, reliability analysis, design of experiments, decision making, and regression analysis By applying statistical techniques, engineers can identify patterns, predict outcomes, optimize processes, and improve the quality and efficiency of products and systems Overall, statistics is an essential tool for engineers to design, develop, and optimize complex systems and products in an efficient and effective way