Statistics has been applied in various fields since ancient times to have control over things, in health, economics, social sciences and of course in engineering.
There are many statistical tools to work with data from a sample, in order to analyze the results and make decisions based on it. In the field of engineering it is applied for quality control, process improvements, forecasting, personnel control, industrial security, among many other uses. Despite being an exact science, mistakes can also be made (Outliers) so it is important to know how to apply the techniques and tools.
Key words: Statistics, apply, analysis, tools, infer.
applications-statistics-engineeringStatistics is a science that helps to collect and analyze data for subsequent interpretation for a specific purpose, it can be used for different purposes in different branches.
In this work, the topic of applied statistics in engineering is developed, touching on statistical subtopics that are fundamental to processes and that are the most widely used in the industrial sector, as well as examples of how these are used from the antiquity to the present day.
The theoretical framework is based on various sources such as books, magazines, databases and web pages from which its reliability was previously evaluated.
objective
Investigate the most common applications of statistics in engineering, mainly in industry, to see it from a practical point of view, that is, where statistical tools and techniques can be used to achieve some optimization, improvement or control.
1. Statistics
Statistics studies the scientific methods to collect, organize, summarize and analyze data, allow to obtain valid conclusions and make reasonable decisions based on the previous analysis. Statistics is, therefore, the science that collects, classifies and analyzes the information that is usually presented using aggregated data that allows observations to be quantified, measured, estimated and compared using measures of central tendency, distribution measures, graphical methods, etc.
HG Wells (1954) points out that "The day will come when statistical reasoning will be as necessary for the citizen as now is the ability to read and write."
Statistics has emerged as an indispensable discipline today, it serves to guide initiatives and achieve better results, which are indispensable factors in achieving the objectives that are set.
The role of Statistics in Science and Engineering today is crucial, fundamentally because when analyzing data collected in experiments of any kind, it is observed in most cases that said data is subject to some type of uncertainty. The researcher or the professional must make decisions regarding their object of analysis based on these data, for which they must have adequate tools.
Descriptive statistics summarize the information contained in the collected data and inferential statistics demonstrate associations and allow comparisons between observed characteristics.
1.1 Background
The word statistic originates from the techniques of collecting, organizing, preserving, and treating the state's own data, with which the ancient rulers controlled their subjects and economic domains. These techniques evolved along with the development of mathematics, using its tools in the process of analysis and interpretation of information.
By the middle of the 17th century in Europe, gambling was frequent, De Mèré, a gambler consulted the famous mathematician and philosopher Blaise Pascal to reveal to him the laws that control the game of craps, who, interested in the subject, and together with Pierre de Fermat they gave rise to the theory of probability, which has been developing and constituting itself as the fundamental basis of statistics.
Currently the importance of applied statistics in the development of research in various fields is recognized; More and more professionals from different disciplines require statistical methods such as sampling, simulation, design of experiments, statistical and inferential modeling, to carry out data analysis and interpretation.
1.2 Analysis
The technological advance in informatics has contributed enormously to the development of statistics, especially in the manipulation of information. Statistics, then, ceased to be an exclusive technique of scientists, to become an essential tool of all sciences.
The objective of statistical analysis is to identify trends, collect and scrutinize each individual data sample from which samples can be drawn.
When looking for a certain result in a problem or decision, statistical methods applied in a whimsical way can give any result, so a conscious and prudent analysis must be done, avoiding misinterpretations. AND.
Ezcurra is of the opinion that "To the extent that you torture your data long enough, they will say what you want to hear."
In probability, an experiment is considered before it is carried out, in statistics, we have to infer things about the values of the parameters from the observed results of an experiment already carried out, so that they complement each other.
Every problem comes down, at some point, to the verification of a statement through the testing of a hypothesis that can be rejected with a certain risk of error or provisionally accepted.
1.3 Application
From the business and industrial perspective, statistics is one of the most used tools, for example: In a company it is suspected that there are time zones where work accidents are more frequent. To study this phenomenon, they count work accidents that workers suffer according to time bands, for a year.
With that information, the company's safety managers must decide if there are time zones where accidents are more likely or, on the contrary, they occur absolutely randomly, using statistical tools and methods, parameterizing and then interpreting the result not only in numbers, but also in reality.
The previous example shows how statistics can be applied in different areas, not only in production or quality.
Other examples of what can be calculated and measured with statistics in the industry and the reason for doing so are:
- Assemblies per minute of an average worker: To have control and see what can be improved to reduce time Age of operators: To know that operators could already retire and consider the need to hire new personnel Average number of children of workers: Data such as these are necessary when insuring them or for certain benefits. Work experience or schooling of employees. Maintenance expenses per month: To see if there can be savings. Work absences and causes: To seek to lower the rate of absences.Consumption of a resource during the manufacture of a batch: To control and seek improvements or reduction of waste.
2. Parameterization
To parameterize is to declare parameters, in quantitative statistics, to work with any system. To design a mathematical model in inferential statistics, we can organize the operations in five steps:
- Objectives statement. Design, modeling and parameterization. Analysis. Design improvement. Design description.
After modeling, statistics come into play, since parameters, constants or variables are designed, thus making the parameterization. For any given value in the design of parameters, these will represent an object, which when applied statistical tools and processes will adjust to the most satisfactory and admissible design.
3. Statistical quality control
Statistical quality control is a collection of tools applied to industrial processes (labor, measured raw materials, machines and the environment), administrative processes and / or services in order to verify whether each and every part of the process and service meet certain quality requirements and helping to meet them are essential in quality improvement activities. Quality improvement means the systematic elimination of waste.
The quality of products and services has nowadays become one of the most important decision factors in most companies. Consequently, quality improvement has become an important aspect in many corporations.
3.1 Statistical process control
Statistical process control (CEP) is a very powerful tool to achieve process stability and improve process capacity. It can be considered as a set of tools for solving problems that can be applied in any process.
Continuous improvement of processes must be within the strategic objectives of a company, in order to increase its performance, efficiency and effectiveness, as well as favor an improvement in customer satisfaction, both internal and external. This requires a culture of improvement, organizational structures, resources and statistical tools so that change becomes part of daily activity. To guarantee continuous improvement in a company that has designed the processes of its Quality Management System, and their performance indicators, techniques and tools are used for the analysis, control, monitoring and improvement of said processes.
3.1.1 Tools
Currently, there are a series of methodologies, techniques and tools that can be developed in an organization, to support the design of the Quality Management System, the implementation of the principles of Total Quality, and / or to carry out the process. Continuous Improvement. Examples of these are:
- Pareto diagram. Cause-effect diagram (Ishikawa). Defect-concentration diagram. Control chart. Scatter diagram. Verification sheet. Correlation diagram. 5S methodology. 6 sigma methodology. Control charts and process capacity.
By using them, it is possible to increase the culture in the use of techniques for data processing and analysis in the company; improve data-driven decision making; it allows to know the behavior of the process indicators; facilitates the interpretation of results for all managers; illustrates the usefulness of the tools and encourages the use of other techniques in the future.
3.2 Applications of statistical quality control
Statistical methods play an important role in improving quality, some of their applications are:
- In the design and development of products to compare materials or ingredients and to determine the tolerances of the system and its components. This significantly reduces costs and time. To determine the capability of a manufacturing process, leading to higher yields and lower manufacturing costs. In durability testing, it helps by providing reliability and performance data, leading to new or long-lasting products. higher and less maintenance costs.
3.3 Scatterplots
Scatter diagrams are a very useful tool in predictions, either to make a decision or to contemplate some expense. It is done by plotting the points and drawing a regression line, none can go through all the points, so look for the one that passes as close to them vertically as possible.
Example of application of statistics in economic forecasts to forecast expenses in greenhouses:
A scatter diagram shows that there is a strong linear relationship between the average outdoor temperature for a month's days and the average daily gas consumption during that month in a greenhouse. You want to use this ratio to predict your gas consumption. If a month averages 10 degrees-day per day, how much gas will be used in that month?
After making a prediction using the scatter diagrams, it can be inferred that the gas consumption will be approx. 12.5 m 3.
4. Regression models
Regression Analysis is the most frequently used statistical technique to investigate and model the relationship between variables. Its attractiveness and usefulness are generally the result of using an equation to express the relationship between a variable of interest (the response) and a set of related predictive variables.
4.1 Linear regression
The simple linear regression forecast is an optimal model for trend patterns of demand (increasing or decreasing), that is, patterns that present a linear relationship between demand and time.
An example of a forecasting application is as follows:
The toy store Gaby wishes to estimate, by means of simple linear regression, the sales for the month of July of its new children's cart "Mate". The information on the sales behavior of all its chain stores is presented in the following table.
The relevant calculations are made:
And finally we can determine that the sales forecast for period 7 is equivalent to 13067 units. This helps us to make relevant and advance decisions on production, raw materials and distribution.
4.2 Nonlinear regression
Nonlinear regression models aim to build exact models, using functional equations that allow predicting, controlling or optimizing nonlinear problems, which is known as Functional Data Analysis.
5. Curve Adjustment
Curve fitting is a process by which, given a set of N pairs of points (X, Y), a mathematical function f (x) is determined such that the sum of the squares of the difference between the actual image and the corresponding obtained by means of the adjusted function in each point is minimal.
Curve fitting can be used to solve a variety of industry problems, for example:
A Sausage factory produces 5000 packages of sausages daily. Machine A produces 3,000 packages, of which 2% are badly stuffed (defective) and machine B produces the remaining 2,000 of which 4% are known to be defective. Determine the probability that a randomly chosen package is defective and that it comes from machine A or machine B.
- Probability that the defective packaging is from Machine A p (A / D) = p (A∩D) / p (D) = 0.012 / 0.028 = 0.4286
Corresponds to approximately 4.2%.
- Probability that the defective packaging is from Machine B p (B / D) = p (B∩D) / p (D) = 0.016 / 0.028 = 0.5714
Corresponds to approximately 5.7%.
To improve the estimations in decision-making, it is necessary to apply the Bayes' Theorem where the statistics that are made consist of observing the analysis of the data, which allows the researcher to make inferences or make exclusions or personal opinions on the subject. study.
5.1 Uncertainty
In our days, different statistical techniques are in daily use that, based on historical or sample observations, create logical-mathematical models that "venture" to describe or forecast a certain phenomenon with a certain degree of measurable certainty.
Statistics play an important role in issues where variability intervenes, giving rise to uncertainty. Beyond the data, statistics is essentially the study of uncertainty, which leads to the need to investigate a phenomenon from a scientific perspective.
Statistics is not the only branch of knowledge that has dealt with the study of uncertainty; probability examines how randomness in one part of a system affects another, providing through the model a random variable or a stochastic process, estimates and / or predictions about the data to be produced, that is, it describes the uncertainty of the phenomenon.
5.1.1 Outliers and errors
An Outliers (outlier) is an observation or set of observations that appears to be inconsistent with the rest of the data set, the presence of outliers in a data set can lead to errors in attempting to make inferences about the population of which they come from, hence the presence of these poses a fundamental problem in data analysis.
Statistical uncertainty is the randomness or error from various sources when using statistical methodology, the probability of something bad happening, in terms of decision theory, the average losses or the predicted losses when something bad happens.
When studying relationships between variables, statistics show statistical relationships and not causal relationships. In general, if we are not careful, we can reach the most absurd or biased conclusions, so we must do the analysis carefully and know the variables, so that when interpreting it, we do not make decisions that may be harmful.
6. Applications in other areas
Statistics serves to explore and exploit information in the social, biological, economic, and physical sciences, so it is important to "sell" statistics as something necessary for current and future generations.
Applied statistics deals with how and when to use mathematical procedures and how to interpret the results obtained, and can be used in many fields, such as:
- In the natural sciences: for the description of complex thermodynamic models, in quantum physics, in fluid mechanics or in the kinetic theory of gases, among many others. In the social and economic sciences: in the development of demography and sociology applied.In economics: to analyze macro and microeconomic parameters.In medical sciences: study the evolution of diseases and patients, death rates, the degree of effectiveness of a drug, etc.In engineering: For planning, budgets, process and quality control, industrial safety, production calculations, among others.
conclusion
After researching, reading and writing about statistics, parameterization, tools, methods and even examples, I can have a more general overview of the use of statistics in engineering, I know more about how it can be used to solve common problems of a company or in making decisions. However, it is not the only area that can be used, since it has various applications in the social, medical, economic and other sciences.
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