525201Statistics and Numerical Method

Part I: StatisticsWeek 1I: Data Presentation

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somsaksi@sut.ac.th

2

Data type Attribute data

–Discrete, proportion and count of defects are the most common

–We can count Variable data

–Continuous data–We can measure variables

Variable data ให้�ข้�อม�ลที่��ดิ์�กว�� และต้�องก�รจำ�นวนข้�อม�ลน�อยกว��

Sources of Engineering Data A retrospective study

◦Historical dataAn observational study

◦Data from processes or existing operation

A designed experiment◦Data from an experiment set for group of interested factors

4

Parameters

Population Sample

Mean µ

Variance S2 or SD2

Standard Deviation S or SD

Standard score Z

n

Xn

i i 1

Ex: The data of the first yield strength (kN) from experiment of circular tubes with cap welded to the end. Calculate the sample average and standard deviation.

96 102 104 126 140 160

96 102 108 128 156 164

102 104 126 128 160 170

EXCEL and Minitab’s results

mean 126.2Var 683.2SD 26.1 Welcome to Minitab, press F1 for

help. Mean of C8

Mean of C8 = 126.222

Standard Deviation of C8

Standard deviation of C8 = 26.1389

Ex: Calculate the sample mean and SD of compressive strength (psi) of 80 Al-Li alloy specimens.

105 221 183 186 121 181 180 14397 154 153 174 120 168 167 141

245 228 174 199 181 158 176 110163 131 154 115 160 208 158 133207 180 190 193 194 133 156 123134 178 76 167 184 135 229 146218 157 101 171 165 172 158 169199 151 142 163 145 171 148 158160 175 149 87 160 237 150 135196 201 200 176 150 170 118 149

EXCEL and Minitab’s results

Results for: Worksheet 2 Mean of C10

Mean of C10 = 162.662

Standard Deviation of C10

Standard deviation of C10 = 33.7732

Mean 162.7Var 1140.6SD 33.8

Graphing

Univariate DataDot plotStem and Leaf

DiagramHistogramBox PlotTime Series PlotIndividual Value

PlotInterval PlotPareto

Multivariate Data

Scatter PlotMatrix Plot

Dot Plot

Stem and Leaf DiagramStem-and-Leaf Display: Compressive Strength

Stem-and-leaf of Compressive Strength N = 80Leaf Unit = 1.0

1 7 6 2 8 7 3 9 7 5 10 15 8 11 058 11 12 013 17 13 133455 25 14 12356899 37 15 001344678888(10) 16 0003357789 33 17 0112445668 23 18 0011346 16 19 034699 10 20 0178 6 21 8 5 22 189 2 23 7 1 24 5

Histogram

Box Plot

IQR 1.5 IQR1.5 IQR 1.5 IQR 1.5 IQR

Interquartile Range (IQR) = Q3 – Q1

Outliers

Extreme Outliers

OutliersQ1

Q2Median

Q3Whisker Whisker

Box Plot

Box Plot

Time Series Plot

Individual Value Plot

Interval Plot

Pareto

Ex: The wire bond data was shown between Pull strength, Wire length and Die height

Observed Number

Pull Strength Wire Length Die Height

Observed Number

Pull Strength Wire Length Die Height

1 9.95 2 50 14 11.66 2 3602 24.45 8 110 15 21.65 4 2053 31.75 11 120 16 17.89 4 4004 35.00 10 550 17 69.00 20 6005 25.02 8 295 18 10.30 1 5856 16.86 4 200 19 34.93 10 5407 14.38 3 375 20 46.59 15 2508 9.60 3 52 21 44.88 15 2909 24.35 9 100 22 54.12 16 510

10 27.50 8 300 23 56.63 17 59011 17.08 4 412 24 22.13 6 10012 37.00 11 400 25 21.15 5 40013 41.95 12 500

Scatter Plot

Correlations: Pull Strength, Wire Length

Pearson correlation of Pull Strength and Wire Length = 0.982P-Value = 0.000

Correlations: Pull Strength, Die Height

Pearson correlation of Pull Strength and Die Height = 0.493P-Value = 0.012

Correlation

A measure of linear association between two variables.  

The correlation coefficient- which describes both the strength and direction of the relationship.

The correlation coefficient ranges from

-1 to 1

Correlation Coefficient; r

yyxx

xy

iyy

ixx

iixy

SS

Sr

yyS

xxS

yyxxS

2

2

)(

)(

))((r=1

r=0

r=0.92

r=-0.92

r=-1

r=0

Scatter Plot

Matrix Plot

Q & A