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<b>MAS291 – Chapter 01 Summarize</b>

<b>The Role of Statistics in Engineering</b>

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2.5 Observing Processes Over Time...7

3. Mechanistic and Empirical Models...9

4. Probability and Probability Models...11

5. Summary...12

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<b>1. Statistics in Engineering</b>

<b>1.1 Overview</b>

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 phenomenondo not produce exactly the same result.

Statistics gives us a framework for describing this variability and for learning about potential sources of variability.

<b>1.2 Example</b>

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)

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Reliability 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 andanalyze 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.

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<b>2. Collecting Engineering Data</b>

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.

<b>2.1 Basic Principles</b>

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.

Figure 2.1. Retrospective Study

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Figure 2.2. Observational Study

<b>2.4 Designed Experiments</b>

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.

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Figure 2.3. Designed Experiments

<b>2.5 Observing Processes Over Time</b>

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 theproblem.

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Figure 2.5. A time series plot of concentration provides more informationthan a dot diagram.

Figure 2.6. Enumerative versus analytic study.

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<b>3. Mechanistic and Empirical Models</b>

A mechanistic model is built from our underlying knowledge of the basicphysical mechanism that relates several variables.

<b>Example: Ohm’s Law</b>

Current = voltage/resistanceI = E/R

I = E/R +

<b>An </b>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.

Suppose we are interested in the number average molecular weight (M<small>n</small>) of apolymer. Now we know that M<small>n</small> 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 M<small>n</small>and these variables is

M<small>n</small> = f(V,C,T)

say, where the form of the function is unknown.f

where the b’s are unknown parameters.

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<b>Example: Calculate the regression line with given wire bond pull strength </b>

data table

Figure 3.1. Wire Bond Pull Strength Data Table

<b>In general, this type of empirical model is called a regression model.</b>

The <b>estimated</b> regression line is given by

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Figure 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 empiricalmodel.

<b>4. Probability and Probability Models</b>

• 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.

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<b>5. Summary</b>

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.

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