Practical Statistics for Engineers and Scientists

Nicholas P. Cheremisinoff, Louise Ferrante

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780877625056
• eBook ISBN: 9781000159936
• Edition: 1
• Topic: Tecnologia e ingegneria
• Subtopic: Design industriale

This book provides direction in constructing regression routines that can be used with worksheet software on personal computers. The book lists useful references for those readers who desire more in-depth understanding of the mathematical bases, and is helpful for science and engineering students.

CHAPTER 1

Notations and Definitions

USE OF SUBSCRIPTS

Subscripts are used to denote the number of an observation in a set. For Example: x_i is the ith observation in a set. x_(i) is the ith ordered observation in a set. Let us review Illustration 1.

Illustration 1

Consider the following data set {5, 10, 6, 2}. The observations are:

$\begin{array}{c}{x}_1=5,x_2=10,x_3=6,x_4=2\\ x_{\left(1\right)}=2,x_{\left(2\right)}=5,x_{\left(3\right)}=6,x_{\left(4\right)}=10\end{array}$

Summations are denoted by the symbol of capital Sigma (Σ) and the operation is performed over the limits of the observation.

Illustration 2

${\displaystyle \sum _{i=1}^4{x}_i=x_1+x_2+x_3+x_4}$

${\displaystyle \sum _{i=1}^n{x}_1=x_1+x_2+x_3+\&+x_n}$

${\displaystyle \sum _{i=1}^n{x}_1^2=x_1^2+x_2^2+x_3^2+\&+x_n^2}$

${\displaystyle \sum _{i=1}^{n}c{x}_i=c{\displaystyle \sum _{i=1}^n{x}_1}=c\left(x_1+x_2+\&+x_n\right),\text{where}}c=\text{constant}$

${\displaystyle \sum _{i=1}^{n}c=nc}$

${\displaystyle \sum _{i=1}^n\left(x_i\pm y_i\right)={\displaystyle \sum _{i=1}^n{x}_i\pm {\displaystyle \sum _{i=1}^n{y}_i}}}$

${\displaystyle \sum _{i=1}^3{\displaystyle \sum _{j=1}^2{x}_{ij}={\displaystyle \sum _{i=1}^3\left(x_{i\text{1}}+x_{i2}\right)=x_{11}+x_{21}+x_{31}+x_{12}+x_{22}+x_{32}}}}$

DEFINITIONS OF DISTRIBUTIONS

An important step in analyzing the statistical significance of data and in regression is the layout and tabulation of data values. Frequency distributions are a useful format for scanning and reviewing the important features of large bodies of data. In preparing frequency distributions one must select data groups. Important rules-of-thumb to apply when choosing data groups are:

• Find the minimum and maximum values in the set.

• Do not use fewer than 6 or more than 15 groups.

• Select unambiguous grouping criteria.

• Group intervals should be of equal length.

• Select a convenient group midpoint.

An example of preparing frequency distributions using the above rules is shown below.

Illustration 3

Bales of rubber are checked in a warehouse for brown spots. These brown spots ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• About the Author
• Chapter 1 Notations and Definitions
• Chapter 2 Confidence Limits and Sample Size
• Chapter 3 Data Scatter and the Use of Control Charts
• Chapter 4 Analysis of Variance
• Chapter 5 The Correlation Coefficient and Introduction to Spectral Density Analysis
• Chapter 6 Linear Regression and Interactive Models
• Chapter 7 Experimental Design and Parameter Estimation
• Appendix A “DATA-FIT” Program User’s Guide
• Appendix B General Definitions and Miscellaneous Statistical Methods
• Bibliography
• Suggested Readings
• Index