STAT353: ENGINEERING STATISTICS

STAT353: ENGINEERING STATISTICS

This booklet contains the lecture notes relating to the module. Throughout the notes there are several solved examples and some unsolved problems, which will be solved in the class. The distance learning version has all gaps filled in.

AIMS OF THE MODULE

· To provide an appreciation of the role of statistics in engineering design, testing and manufacturing;

· To provide a basic grounding in probability and statistics and their application in engineering.

TEACHING METHODS

Teaching methods will consist of two hours per week of lectures and one hour per week of lab session/tutorials, which will be based on practical examples taken from engineering applications. Minitab is the statistical package used in the lab sessions where appropriate.

ASSESSMENT

100% Coursework consisting of one piece of take-away work and one in-class test.

RECOMMENDED TEXTS

Any book on statistical analysis intended for engineers will be useful. A list of examples is given below:

Hubele M R (2000). Engineering Statistics. New York: John Wiley.

Metcalfe A V (1994). Statistics in Engineering. London: Chapman and Hall.

Montgomery D C and Runger G C (1999). Applied Statistics and Probability for Engineers. New York: John Wiley.

Ross S M (1987). Introduction to Probability and Statistics for Engineers and Scientists. New York: John Wiley.

Vardeman S B (1994). Statistics for Engineering Problem Solving. Boston: PWS Publishing Company.

MODULE AUTHOR

MODULE LEADER 2003-04

Dr Graham Crocker

Department of Mathematics and Statistics

Dr Alex Kovner

Department of Mathematics and Statistics

CONTENTS

			Page
Section 1	Descriptive Statistics		1
1.1		Introduction	1
	1.1.1	The Role of Statistics	1
	1.1.2.	Populations and Samples	2
	1.1.3	Structure of Module	3
1.2		Types of data	4
	1.2.1	Some Definitions	4
	1.2.2	Quantitative Data	5
	1.2.3	Qualitative Data	5
1.3		Tabular Representation of Data	9
	1.3.1	Ungrouped Distributions	9
	1.3.2	Grouped Distributions	10
1.4		Graphical Representation of Data	12
	1.4.1	Basic Charts	13
	1.4.2	Histograms	17
	1.4.3	Shapes of Distributions	20
	1.4.4	Frequencies and Probabilities	22
	1.4.5	Other Graphs	24
1.5		Numerical Representation of Data	29
	1.5.1	Measures of Location	29
	1.5.2	Measures of Variation	33
	1.5.3	Choice of Measures	42
	1.5.4	Parameters and Statistics	43
1.6		Stratification	44
1.7		Comparison of Data Sets	46
	1.7.1	Guidelines for comparison	46
	1.7.2	Boxplots	50
1.8		Review	52

Section 2	Probability and Probability Distributions		53
2.1		Introduction	53
2.2		Probability	55
	2.2.1	Definitions	56
	2.2.2	Probability Rules	56
	2.2.3	Other Ways of Estimating Probabilities	57
	2.2.4	Conditional Probabilities	58
2.3		Probability Distributions	62
	2.3.1	Discrete Distributions	62
	2.3.2	Continuous Distributions	63
	2.3.3	Common Shapes and Specific Distributions	66
2.4		Fitting Distributions to Data	68
	2.4.1	Probability Plots	68
	2.4.2	Estimating Probabilities	71
	2.4.3	Testing Goodness-of-Fit	71


2.5		The Normal Distribution	72
	2.5.1	Parameters and Functions	72
	2.5.2	Mechanism	75
	2.5.3	Applications	75
2.6		The Lognormal Distribution	81
	2.6.1	Parameters and Functions	81
	2.6.2	Mechanism	81
	2.6.3	Applications	82
2.7		The Exponential Distribution	83
	2.7.1	Parameters and Functions	83
	2.7.2	Mechanism: The Poison Process	83
	2.7.3	Applications	88
2.8		The Weibull Distribution	90
	2.8.1	Parameters and Functions	90
	2.8.2	Applications	91
2.9		Other Continuous Distributions	92
	2.9.1	Other Named Distributions	92
	2.9.2	Using Calculus	93
2.10		Discrete Probability Distributions	98
	2.10.1	The Poisson Distribution	98
	2.10.2	The Binomial Distribution	103
2.11		Review	107

Section 3	Reliability		109
3.1		Introduction	109
3.2		Fundamental Concepts Associated with Reliability	110
	3.2.1	Some Important Functions	110
	3.2.2	Summary of Reliability Formulae	113
3.3		Lifetime Following an Exponential Distribution	114
	3.3.1	Associated Functions	114
	3.3.2	Constant Hazard Function	117
	3.3.3	Summary	117
3.4		Lifetime Following a Weibull Distribution	118
	3.4.1	Associated Functions	119
	3.4.2	Time-dependant Hazard Function	120
	3.4.3	Summary	121
	3.4.4	Bathtub Curve	122
3.5		Lifetime Following Normal or Lognormal distributions	123
3.6		Using the Functions: An Application	123
3.7		System Reliability	127
	3.7.1	Series System	127
	3.7.2	Parallel System	128
	3.7.3	Mixed system	129

Section 4	Estimation		131
4.1		Introduction	131
4.2		Sampling Distributions	132
4.3		Confidence Intervals for a Mean	134
	4.3.1	s known	134
	4.3.2	s not known	136
	4.3.3	Which Interval to Use?	138
		Comparing Means	139
4.4		Confidence Intervals for a Proportion	139
4.5		Confidence Intervals and Sample Size	141
	4.5.1	Estimating Means	141
	4.5.2	Estimating Proportions	141
	4.5.3	Preliminary Information	143

Section 5	Regression ands Correlation		145
5.1		Introduction	145
5.2		Types of Relationship	146
5.3		Correlation	146
	5.3.1	The Correlation Coefficient r	146
	5.3.2	Calculation of r	148
	5.3.3	Interpretation of r	148
	5.3.4	Testing the Significance of r	149
5.4		Regression	150
	5.4.1	The Dependent Variable and the Explanatory Variable	150
	5.4.2	Finding The Line of Best Fit	150
	5.4.3	Interpretation of a and b	152
	5.4.4	Predictions	152
5.5		A Full Regression Analysis	153
	5.5.1	Checklist of Stages	153
	5.5.2	Worked Example Using Excel	155
5.6		Using the Computational Formulae	160
	5.6.1	Correlation	160
	5.6.2	Regression	162
5.7		Non-linear Regression	164

	Appendices and Tables		165