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2024 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control

verfasst von: Dharmaraja Selvamuthu, Dipayan Das

Verlag: Springer Nature Singapore

Buchreihe : University Texts in the Mathematical Sciences

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This revised book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. It is shaped by the experience of the two teachers teaching statistical methods and concepts to engineering students. Practical examples and end-of-chapter exercises are the highlights of the text, as they are purposely selected from different fields. Statistical principles discussed in the book have a great relevance in several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles to mention a few.

Organised into 16 chapters, the revised book discusses four major topics—probability theory, statistical methods, the design of experiments, and statistical quality control. A large number of students with varied disciplinary backgrounds need a course in basics of statistics, the design of experiments and statistical quality control at an introductory level to pursue their discipline of interest. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The whole book also serves as a master level introductory course in all the three topics, as required in textile engineering or industrial engineering.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Probability and statistics are two branches of mathematics while probability deals with the laws governing random events, statistics encompasses collection, analysis, interpretation and display of numerical data. Probability has its origin in the study of gambling and insurance in the seventeenth century, and it is now an indispensable tool of both social and natural sciences. Statistics may be said to have its origin in census counts taken thousands of years ago; as a distinct scientific discipline, however, it was developed in the early nineteenth century as the study of populations and economics, and as the mathematical tool for analyzing such numbers.
Dharmaraja Selvamuthu, Dipayan Das

Probability

Frontmatter
Chapter 2. Basic Concepts of Probability
Abstract
If mathematics is the queen of sciences, then probability is the queen of applied mathematics. The concept of probability originated in the seventeenth century and can be traced to games of chance and gambling. Games of chance include actions like drawing a card, tossing a coin, selecting people at random and noting number of females, number of calls on a telephone, frequency of accidents, and position of a particle under diffusion. Today, probability theory is a well-established branch of mathematics that finds applications from weather predictions to share market investments. Mathematical models for random phenomena are studied using probability theory.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 3. Random Variables and Expectations
Abstract
Random experiments have sample spaces may not consist of numbers. For instance, in a coin-tossing experiment, the sample space consists of the outcomes “head" and “tail”, i.e.,
$$\varOmega =\{\text {head, tail}\}.$$
Since statistical methods primarily rely on numerical data, it becomes necessary to represent the outcomes of the sample space mathematically.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 4. Standard Distributions
Abstract
This chapter delves into some discrete and continuous distributions that are frequently encountered, while also examining their key characteristics.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 5. Multiple Random Variables and Joint Distributions
Abstract
Multiple r.v.s are often involved in various random experiments. For instance, an educator might examine the joint behavior of study time and grades, while a physician may investigate the joint behavior of blood pressure and weight. Similarly, an economist could study the joint behavior of business volume and profit. Indeed, most practical problems entail multiple underlying r.v.s of interest. In some scenarios, more than one r.v. will be of interest. Therefore, the joint probability distributions for two discrete and two continuous r.v.s will be discussed and finally generalized for more than two variables.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 6. Limiting Distributions
Abstract
In statistics, the capability to infer information about a population from a sample and assess the validity of those inferences is essential. Because of this, it is crucial to research the asymptotic behavior of r.v. sequences. The weak law of large numbers, the strong law of large numbers, and the central limit theorem (CLT), are some of the most significant results within the theory of limit theorems that are covered in this chapter.
Dharmaraja Selvamuthu, Dipayan Das

Statistical Methods

Frontmatter
Chapter 7. Descriptive Statistics
Abstract
Statistics is an art of learning from data. One of the tasks to be performed after collecting data from any observed situation, phenomena, or interested variable is to analyze that data to extract some useful information. Statistical analysis is one of the most applied tools in the industry, decision-making, planning, public policy, etc. Many practical applications start from analyzing data, which is the main information source. Given this data, the analyst should be able to use this data to have an idea of what the collected data has to say, either by providing a report of his/her findings or making decisions.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 8. Sampling Distributions
Abstract
Now, we are ready to discuss the relationship between probability and statistical inference. The two key facts to statistical inference are (a) the population parameters are fixed numbers that are usually unknown and (b) sample statistics are known for any sample. For different samples, we get different values of the statistics and hence this variability is accounted for identifying distributions called sampling distributions. In this chapter, we will discuss certain distributions that arise in sampling from normal distribution.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 9. Estimation
Abstract
In many real-life problems, the population parameter(s) is (are) unknown and someone is interested to obtain the value(s) of parameter(s). But, if the whole population is too large to study or the units of the population are destructive in nature or there is limited resources and manpower available then it is not practically convenient to examine each and every unit of the population to find the value(s) of parameter(s). In such situations, one can draw sample from the population under study and utilize sample observations to estimate the parameter(s).
Dharmaraja Selvamuthu, Dipayan Das
Chapter 10. Testing of Hypothesis
Abstract
In this chapter, we will discuss another way to deal with the problem of making a statement about an unknown parameter associated with a probability distribution, based on a random sample. Instead of finding an estimate for the parameter, we shall often find it convenient to hypothesize a value for it and then use the information from the sample to confirm or refute the hypothesized value.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 11. Analysis of Correlation and Regression
Abstract
It is quite often that one is interested to quantify the dependence (positive or negative) between two or more random variables. The basic role of covariance is to identify the nature of dependence. However, the covariance is not an appropriate measure of dependence since it is dependent on the scale of observations. Hence, a measure is required which is unaffected by such scale changes. This leads to a new measure known as the correlation coefficient. Correlation analysis is the study of analyzing the strength of such dependence between the two random variables using the correlation coefficient. For instance, if X represents the age of a used mobile phone and Y represents the retail book value of the mobile phone, we would expect smaller values of X to correspond to larger values of Y and vice versa.
Dharmaraja Selvamuthu, Dipayan Das

Design of Experiments

Frontmatter
Chapter 12. Single-Factor Experimental Design
Abstract
Often, we wish to investigate the effect of a factor (independent variable) on a response (dependent variable). We then carry out an experiment where the levels of the factor are varied. Such experiments are known as single-factor experiment. There are many designs available to carry out such experiment. The most popular ones are completely randomized design, randomized block design, Latin square design, and balanced incomplete block design.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 13. Multifactor Experimental Designs
Abstract
In order to study the effects of two or more factors on a response variable, factorial designs are usually used. By following these designs, all possible combinations of the levels of the factors are investigated. The factorial designs are ideal designs for studying the interaction effect between factors. By interaction effect, we mean that a factor behaves differently in the presence of other factors such that its trend of influence changes when the levels of other factors change. This has already been discussed in Chap. 1. In this chapter, we will learn more about factorial design and analysis of experimental data obtained by following such designs.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 14. Response Surface Methodology
Abstract
Response surface methodology or in short RSM is a collection of mathematical and statistical tools and techniques that are useful in developing, understanding, and optimizing processes and products. Using this methodology, the responses that are influenced by several variables can be modeled, analyzed, and optimized.
Dharmaraja Selvamuthu, Dipayan Das

Statistical Quality Control

Frontmatter
Chapter 15. Acceptance Sampling
Abstract
Statistical quality control means application of statistical techniques for checking the quality of products. The products include manufactured goods such as computers, mobile phones, automobiles, clothing and services such as health care, banking, and public transportation. The word “quality” is defined in many ways. To some people, quality means fitness for use. To others, quality is inversely proportional to variability. Some people also think that quality means degree of conformance to specifications of products. One can read Montgomery (2001) for a detailed discussion on the meaning of quality. Whatsoever be the definition of quality, there are many statistical methods available for checking the quality of products. In this chapter, we will focus on one of the two important methods, namely, acceptance sampling. In the next chapter, we will discuss the other method-quality control chart.
Dharmaraja Selvamuthu, Dipayan Das
Chapter 16. Control Charts
Abstract
In the subject of statistical quality control, the word control bears a special technical meaning. A manufacturing process is said to be in control when a stable system of chance causes seems to be operating. However, this word is often misinterpreted by saying that a process is in control only when it has no variation.
Dharmaraja Selvamuthu, Dipayan Das
Backmatter
Metadaten
Titel
Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control
verfasst von
Dharmaraja Selvamuthu
Dipayan Das
Copyright-Jahr
2024
Verlag
Springer Nature Singapore
Electronic ISBN
978-981-9993-63-5
Print ISBN
978-981-9993-62-8
DOI
https://doi.org/10.1007/978-981-99-9363-5

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