## Engineering Statistics

Engineers are vital to the success and effectiveness of many businesses in the 21st century. The successful solution of engineering problems must be based on an understanding of variability and how to apply the principles of mathematical statistics to real world problems. Descriptive statistics are used to reduce large amounts of data and describe them in ways that are easily comprehendible. Inferential statistics are used to test hypotheses to determine if the results of a study occur at a rate that is unlikely to be due to chance. Statistics offer a wide range of methods to test hypotheses, each of which is appropriate to a different type of experimental design. A good research design depends in part on two factors: controlling the situation so that the research is only measuring what it is supposed to measure and including as many of the relevant factors as possible so that the research fairly emulates the real world experience. Statistical techniques can be applied to the gamut of engineering problems including new product design, process development, and quality control.

Engineers are vital to the success and effectiveness of many businesses in the 21st century. Most of the products used by society and the processes used to produce them are designed by engineers. Engineers are also involved in developing solutions to many problems faced by modern society, such as climate change, and are widely valued for their skill at problem solving.

### The Steps of Problem Solving

As shown in Figure, 1, the engineering approach to problem solving comprises multiple steps.

- First, the engineer must develop a clear and concise description of the problem. Engineering is an applied scientific discipline, and engineering problems are typically quantified so that they can be better analyzed. A clear description of the problem helps in this endeavor.
- After the problem has been clearly defined, the engineer next identifies the important factors that bind the problem or play a role in the solution. This is often a tentative list and is revisited and revised as new data are compiled.
- After the important factors have been tentatively identified, the engineer next proposes a model based on scientific or engineering knowledge of the problem. This model is a representation of a situation, system, or subsystem. At this point in the process, a conceptual model that describes the situation or system under investigation is articulated. The conceptual model may also be used in the development of a later mathematical or computer model that mathematically represents the system or situation being studied. As part of the model-building process, the engineer articulates the assumptions used in building the model and any limits within which it applies.
- After the model is developed, experimental research is designed and data is collected to test how well the model reflects the real-world situation. The model is then refined on the basis of this data and manipulated to better assist in developing a solution to the problem. Further empirical research is then conducted to confirm that tine proposed solution to the problem is both effective and efficient.
- Based on the results of this study, the engineer draw s conclusions and makes recommendations on the best way to proceed in order to solve the; problem.

The successful solution of engineering problems must be based on an understanding of variability and how to apply the principles of mathematical statistics to real-world problems. Mathematical statistics is a branch of mathematics that deals with the analysis and interpretation of data. Mathematical statistics provides the theoretical underpinnings for various applied statistical disciplines, including engineering statistics, in which data is analyzed to find answers to quantifiable questions. Engineering statistics is the application of these tools and techniques to the analysis of real-world problems. The discipline of engineering statistics is concerned with the collection, presentation, analysis, and use of data in order to make practical decisions. Statistical methods are useful in helping the engineer understand the underlying variability that can be observed in systems and phenomena. For example, in manufacturing, some percentage of products always has defects, no matter how standardized or efficient the process. Statistics can help quality-control engineers better understand why this occurs and design processes or equipment that will help reduce the number of defective products produced.

### Classes of Statistics

There are two general classes of statistics: descriptive and inferential statistics.

### Descriptive Statistics

Descriptive statistics are used to describe and summarize large amounts of data in ways that are easily comprehensible. Descriptive statistics include various graphing techniques, measures of central tendency, and measures of variability.

- Graphing techniques are used to help the engineer aggregate and visually portray data so that it can be better understood. Some of the graphing techniques used by engineers include histograms, frequency distributions, stem-and-leaf plots, and time-series plots.
- Measures of central tendency, sometimes referred to less accurately as "averages," are used to estimate the midpoint of a distribution. The three types of measures of central tendency are the median (the number in the middle: of the distribution), the mode (the number occurring most often in the distribution), and tire mean (a mathematically derived measure in which the sum of all data in the distribution is divided by the number of data points in the distribution).
- Measure s of variability show how widely dispersed the values are over the distribution. The standard deviation the derived index of the degree to which scores differ from the mean of the distribution.

### Inferential Statistics

Although descriptive statistics can be useful in describing data, they do not allow engineers to draw conclusions or inferences from the data. Inferential statistics are used to test hypotheses to determine if the results of a study have statistical significance, meaning that they occur at a rate that is unlikely to be due to chance. A hypothesis is an empirically testable declarative statement about the relationship between the independent and dependent variables and their corresponding measures. The independent variable is the variable that is...

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