Chap 11 Chap 11

Engineering StatisticsEngineering Statistics

PREP004 – Introduction to Applied Engineering

College of Engineering - University of Hail

Fall 2009

StatisticsStatistics

Statistics is the area of science that deals with Statistics is the area of science that deals with collection, organization, analysis, and collection, organization, analysis, and interpretation of data.interpretation of data.

It also deals with methods and techniques that It also deals with methods and techniques that can be used to draw conclusions about the can be used to draw conclusions about the characteristics of a large number of data points--characteristics of a large number of data points--commonly called a commonly called a populationpopulation– –

By using a smaller subset of the entire data.By using a smaller subset of the entire data.

For Example…For Example… You work in a cell phone factory and are asked to You work in a cell phone factory and are asked to

remove cell phones at random off of the assembly remove cell phones at random off of the assembly line and turn it on and off. line and turn it on and off.

Each time you remove a cell phone and turn it on Each time you remove a cell phone and turn it on and off, you are conducting a and off, you are conducting a random experiment.random experiment.

Each time you pick up a phone is a Each time you pick up a phone is a trialtrial and the and the result is called an result is called an outcomeoutcome..

If you check 200 phones, and you find 5 bad If you check 200 phones, and you find 5 bad phones, thenphones, then

relative frequencyrelative frequency of failure = 5/200 = 0.025=2.5% of failure = 5/200 = 0.025=2.5%

Statistics in EngineeringStatistics in Engineering Engineers apply physical Engineers apply physical

and chemical laws and and chemical laws and mathematics to design, mathematics to design, develop, test, and develop, test, and supervise various supervise various products and services. products and services.

Engineers perform tests Engineers perform tests to learn how things to learn how things behave under stress, and behave under stress, and at what point they might at what point they might fail.fail.

Statistics in EngineeringStatistics in Engineering

As engineers perform experiments, they As engineers perform experiments, they collect data that can be used to explain collect data that can be used to explain relationships better and to reveal relationships better and to reveal information about the quality of products information about the quality of products and services they provide.and services they provide.

Statistics : Major Engineering AreasStatistics : Major Engineering Areas

Quality control and process control use statistics as a tool to manage Quality control and process control use statistics as a tool to manage conformance to specifications of manufacturing processes and their conformance to specifications of manufacturing processes and their products. products.

Design of Experiments (DOE) uses statistical techniques to test and Design of Experiments (DOE) uses statistical techniques to test and construct models of engineering components and systems. construct models of engineering components and systems.

Time and methods engineering use statistics to study repetitive Time and methods engineering use statistics to study repetitive operations in manufacturing in order to set standards and find operations in manufacturing in order to set standards and find optimum procedures. optimum procedures.

Reliability engineering which measures the ability of a system to Reliability engineering which measures the ability of a system to perform for its intended function (and time) and has tools for improving perform for its intended function (and time) and has tools for improving performance. performance.

Probabilistic design involving the use of probability in product and Probabilistic design involving the use of probability in product and system design system design

Frequency Distribution: Frequency Distribution: Scores for an engineering class are as follows: 58, 95, 80, Scores for an engineering class are as follows: 58, 95, 80,

75, 68, 97, 60, 85, 75, 88, 90, 78, 62, 83, 73, 70, 70, 85, 75, 68, 97, 60, 85, 75, 88, 90, 78, 62, 83, 73, 70, 70, 85, 65, 75, 53, 62, 56, 72, 7965, 75, 53, 62, 56, 72, 79

To better assess the success of the class, we make a To better assess the success of the class, we make a frequency chart or a Histogram:frequency chart or a Histogram:

With Statistics the information can be better With Statistics the information can be better analyzed. analyzed.

The data are presented in a frequency The data are presented in a frequency distribution or histogram.distribution or histogram.

Divide each no. by 26

Analysis of HistogramsAnalysis of Histograms

Graph A is class distribution of numbers 1-10Graph A is class distribution of numbers 1-10Graph B is class distribution of semester creditsGraph B is class distribution of semester credits

Data for A = 5.64 Data for A = 5.64 +/-+/- 2.6 (much greater spread than B) 2.6 (much greater spread than B)Data for B = 15.7 Data for B = 15.7 +/-+/- 1.96 (smaller spread) 1.96 (smaller spread)Skew of A = -0.16 and Skew B = 0.146Skew of A = -0.16 and Skew B = 0.146CV of A = 0.461 and CV of B = 0.125 (CV = SD/Mean)CV of A = 0.461 and CV of B = 0.125 (CV = SD/Mean)

Frequency A

0

1

2

3

4

5

6

7

2 3 4 5 6 7 8 9 10

Frequency B

0123456789

12 13 14 15 16 17 18 19 20

Measures of Central Tendency & Measures of Central Tendency & VariationVariation

Central Tendency Measures:Central Tendency Measures:

Mean (Average) Mean (Average) , and Median, Mode, and Median, Mode

Variation and Dispersion Measures:Variation and Dispersion Measures:

Range RRange R, Standard Deviation and Variance, Standard Deviation and Variance R = Xmax - XminR = Xmax - Xmin

x 1

nx i

i1

n

s i1

n

(x i x )2

n 1

Normal Distribution Normal Distribution

Any probability distribution with a bell-shaped Any probability distribution with a bell-shaped curve is called a curve is called a normal distributionnormal distribution. .

The detailed shape of a normal distribution The detailed shape of a normal distribution curve is determined by its mean and standard curve is determined by its mean and standard deviation values. deviation values.

THE NORMAL CURVETHE NORMAL CURVE

approx. 68% of the data will fall in the interval of approx. 68% of the data will fall in the interval of -s-s to to ss, one std deviation , one std deviation

~ 95% of the data falls between -2~ 95% of the data falls between -2ss to 2 to 2ss, and , and approx all of the data points lie between -3approx all of the data points lie between -3ss to 3 to 3ss

Normal Curve has many applications in Normal Curve has many applications in Engineering : Product design, Quality, Reliability, Engineering : Product design, Quality, Reliability,

zi = (xi - x) / s

Engineering Statistical Engineering Statistical Software : Microsoft ExcelSoftware : Microsoft Excel

Business Statistics: A Decision-Business Statistics: A Decision-Making Approach, 6e © 2005 Making Approach, 6e © 2005 Prentice-Hall, Inc.Prentice-Hall, Inc.

Chap 2-Chap 2-1414

Statistics in ExcelStatistics in Excel

SelectSelect

Tools/Data AnalysisTools/Data Analysis

1

Business Statistics: A Decision-Business Statistics: A Decision-Making Approach, 6e © 2005 Making Approach, 6e © 2005 Prentice-Hall, Inc.Prentice-Hall, Inc.

Chap 2-Chap 2-1515

Choose HistogramChoose Histogram

2

3

Input data and bin ranges

Select Chart Output

Histograms in Excel(continued)

Engineering Statistical Engineering Statistical Software : MinitabSoftware : Minitab

Home Work 7Home Work 7

Use Excel to determine the Use Excel to determine the averageaverage, the , the rangerange and the and the standard deviation standard deviation of the of the

following set of numbers:following set of numbers:

(a)(a)24, 35, 17, 21, 24, 37, 2624, 35, 17, 21, 24, 37, 26

(b)(b)59.4, 51.3, 84.15 , 96.3 ,71.1 , 95.4 59.4, 51.3, 84.15 , 96.3 ,71.1 , 95.4 78.75 , 66.15 ,77.85 78.75 , 66.15 ,77.85

Chapter SummaryChapter Summary

Data in raw form are usually not easy to use for Data in raw form are usually not easy to use for decision making -- Some type of organization is decision making -- Some type of organization is needed:needed:

TableTable Graph Graph

Techniques reviewed in this chapter:Techniques reviewed in this chapter: Frequency Distributions, HistogramsFrequency Distributions, HistogramsMany Other Tools are available (Scatter Diagrams Many Other Tools are available (Scatter Diagrams

and Control Charts, Pareto diagram etc…)and Control Charts, Pareto diagram etc…)

Engineer use computer software to perform Engineer use computer software to perform statistical calculations and data analysis.statistical calculations and data analysis.