minitab_introduction

Six Sigma Certification

1

Minitab Introduction Black Belt DMAICDD M A I C

Introduction to Minitab

MinitabMinitab Is an Application Software

For Studying Statistical Tools and

Applying Them for Business Needs.

It Complements Six Sigma for its Features and Ease of

Implementation.


2


Objectives

At the end of this this topic, Introduction to Minitab, you

will be able to:

• Describe the basics of Minitab.

• Derive statistical parameters for a given set of data using Minitab and otherwise.

• Analyze the given data graphically and statistically using Minitab.


3


Minitab Basics

In Minitab, there are projects (Minitab Project, *.mpj) in which

• Data is stored in Minitab Worksheet, *.mtw

• Graphs are stored in Minitab Graphs, *.mgf

• Results in Minitab Session, *.txt

• Reports in Minitab Project Report: *.rtf

To Start a New Project

• Choose File > New.

• Choose Project, then click OK.

To save a project, you save all your work at once: all the data, all the output in the Session window, and all the open Graph windows. When you reopen the project, all that information appears for you.


4


Minitab BasicsTo Save a Project:

• Choose File > Save Project As.

• In Save in, navigate to the location where you'd like to keep your project.

• In File name, enter a name for your project, and click Save.

After this, simply choose File > Save Project to save all of your work.

Output or data can be used in another application or project by saving Session window output, data, and graphs as separate files.

To Open a Worksheet

• Data in an empty project is written in the available worksheet.

• It can be copied from a different worksheet by opening it in the project.


5


Minitab BasicsTo use the file <Pressure.mtw> available in the Data subdirectory or folder.

– Choose File > Open Worksheet

– Move to the Data subdirectory and select the worksheet Pressure.mtw.

– Click Open.

Graphs allow you to display patterns, relationships, and distributions in your data that are difficult to evaluate simply by looking at a worksheet. We will study few graphs useful for data analysis.

Selecting Graph Items for Editing Cosmetic changes like the font of or color, or structural changes like increasing the range of a scale can be done.

• For making selection, there are three methods:– Click the item.

– Choose Editor > Select Item, then choose the item from the list.

– Select the item from the list in the graph editing toolbar.


6


Minitab Basics

• After selecting the intended item, editing can be done by either of the ways:

– Double-click the item.

– Choose Editor > Edit.

– Right-click and choose Edit.

– Click, the Edit button, on the Graph Editing toolbar.

Graphs in Other Applications

• Graph may be added in Report Pad in Minitab or to Word or

PowerPoint. – With the layout active, choose Edit > Copy Graph.

– In the Word document, place the cursor where you want to insert the graph.

– Choose Edit > Paste Special.


7


Minitab Basics– In As, choose Mtb Graph Object. This ensures that the graph can be edited

in the Word document. With other options (picture or bitmap, for example), the resulting image cannot be edited with Minitab graph editing tools.

– Click OK.

– Double-click the graph in the Word document. Minitab's graph annotation toolbar appears, and you can double-click any graph item to edit it as you would in Minitab.

Save and Exit

– Choose File > Save Project.

– Exit Minitab by choosing File > Exit.

– It also saves the Report Pad which can be referred for presentations.


8


Minitab Basics : Window

Menu BarMenu BarSession Window:

• Analytical OutputSession Window:

• Analytical Output

Data Window:• A Worksheet different from a Spreadsheet• Column names are above first row

3 data types of Columns: Text/ Numeric/ Date• Everything in a column is considered to be the same

variable

Data Window:• A Worksheet different from a Spreadsheet• Column names are above first row

3 data types of Columns: Text/ Numeric/ Date• Everything in a column is considered to be the same

variableInfo Window:• Synopsis of worksheetInfo Window:• Synopsis of worksheet

History Window:• Stores CommandsHistory Window:• Stores Commands

• Multiple (max Four) Interactive Windows.

• Only one can open at a time.• Windows can be saved

separately.

Tool BarTool Bar


9


Minitab Basics : Toolbar

Open File

Save File

Print Window

Cut

Copy

Paste

Undo

Previous Command

Next CommandFind

Find Next

Last Dialog Box

Session Window

Data Window

Manage Graphs

Close Graphs

Cancel

Help

Session Window ToolbarSession Window Toolbar


10


Minitab Basics : Toolbar

Open File

Save File

Print Window

Cut

Copy

Paste

Undo

Insert Cells

Insert Rows

Insert Columns

Move Columns

Clear Cells

Last Dialog Box

Session Window

Previous Brushed Row

Next Brushed Row

Data Window

Manage Graphs

Cancel

Help

Close Graphs

Data Window Toolbar Data Window Toolbar

Commands can also be accessed from drop down menus or Hot keys.


11


Minitab BasicsTo Transfer Data from Worksheet to Session Window:

Go to Data > Display DataData > Display Data


12


Minitab Basics

Change Data Type:

Manip > Change Data Type >

Numeric to TextManip > Change Data Type >

Text to NumericManip > Change Data Type >

Date/Time to TextManip > Change Data Type >

Date/Time to Numeric


Numeric to Date/Time


Text to Date/Time

To Change Data type:Go to Data > Change Data TypeData > Change Data Type

Numeric to Text


13


Minitab BasicsTo Code Data type:Go to Data > CodeData > Code

Text to Numeric Code


14


Minitab BasicsTo Extract data: Go to Data > Extract from Date/ Time > Text Data > Extract from Date/ Time > Text

Data > Extract from Date/ Time > NumericData > Extract from Date/ Time > Numeric

Month extracted from Date


15


Basic Statistics

Statistics is the collection, organization, analysis, interpretation and

presentation of data. The most common ones are:

Count Average

Minimum Maximum

Sum Percent Defects

We would be studying a few of the important Statistics such as:

• Statistics which defines the location:

Mean Median

Mode

• Statistics which defines the dispersion:

Range Variance

Standard Deviation Quartile

Rec

all


16


Basic Statistics : DispersionTurn-Around-Time (TAT) of service calls for two brands of TVs ‘A’ and ‘B’ are shown. As a customer, which one would you prefer to buy?

Turn-around-time A Turn-around-time A

Turn-around-time BTurn-around-time B

AB

Turn-around-time A Turn-around-time A

Turn-around-time BTurn-around-time B

AB

I

II

Deb

ate


17


Basic Statistics : Dispersion

Only central - tendency of data cannot be the deciding factor for judging performance. The variation-

tendency (spread) of data also needs to be known.

RangeA value obtained by finding the difference between maximum and minimum values of a data set = Maximum – Minimum

Variance and Standard DeviationDeviation is the distance of data from its mean, showing how much data is distributed. If these deviations are summed up, it gives zero. In order to find the data deviation, the individual differences from the mean are squared. The sum of the values gives variance and when the square root is taken, its gives the standard deviation.


18


Population and Sample Statistics

Population StatisticsPopulation Statistics Sample StatisticsSample Statistics

Nxi

Population mean (µ)

1

)( 22

n

xxs i

Estimate for variance (s2)

Estimate for Std Deviation(s)

)( 2ss

N

xi2

2 )(

Population variance (σ2)

n

XiX

Sample mean (X-bar)

Population Std Deviation(σ)

)( 2


19


Basic Statistics : Dispersion

QuartileData is put in order and each quartile holds 25% of the total data components. Quartile gives some idea of the dispersion of data. There are three quartiles designated as Q1, Q2 and Q3 First quartile, Q1 = a value corresponding to 25%Second Quartile (median), Q2 = a value corresponding to 50%Third Quartile, Q3 = a value corresponding to 75%Inter quartile Range, IQR = Q3-Q1

Example - Calculate quartile and IQR for the data:1, 10, 20, 4, 9, 5, 4, 3

Q1 = 3.25Q1 = 3.25

Q2 (Median) = 4.5Q2 (Median) = 4.5

Q3 = 10.75Q3 = 10.75

1 3 4 4 5 10 9 20 IQR = 7.5IQR = 7.5


20


Exercise

Find mean, median, mode, range, variance, and standard

deviation (sigma) for the sample data given below:

2, -2, 0, 1, 5, 4, 3, 1, 0, -2, -4, -3 ,-2, -2, 0


21


Solution

For the data set below, the values for various parameters is

2, -2, 0, 1, 5, 4, 3, 1, 0, -2, -4, -3 ,-2, -2, 0.

The sorted data is -4, -3, -2, -2, -2, -2, 0, 0, 0, 1, 1, 2, 3, 4, 5.

1. Mean = 0.0667

2. Median = 0

3. Mode = -2

4. Range = 9-5 = 4

5. Variance = 6.92

6. Standard Deviation (sigma) = 2.63

Q1 Q2 Q3

IQR = Q3 – Q1 = 0


22


Solving Using Minitab• Open a new Worksheet (in the existing or a new Project)

• Type in the numbers vertically in a column

• Name the column as DATA• Go to StatStat Basic Basic

StatisticsStatistics Display Display

Descriptive StatisticsDescriptive Statistics. Double- click C1 to be chosen as “Variables”

• Go to Statistics to select the required values and click OK

• Find the answers displayed in the Session window.


23


Solving Using Minitab


24


Graphical Analysis

We have seen that Minitab can be used for statistical analysis

of data. Now let us study how we can analyze data

graphically using the tools listed below:

– Pareto Chart

– Histogram

– Dot Plot

– Box Plot

– Scatter Plot

– Matrix Plot

– Marginal Plot

– Time-Series Plot

– Run Chart

– Normality Test


25


Pareto AnalysisPareto chart is named after an Italian economist

Vilfredo Pareto whose theory states that 80% of wealth is owned by 20% of the population. Based on this theory, the chart is used to visually depict the significance level of categories plotted.

• The theory that 80% of the problems come from 20% of the causes is called Pareto’s principle. While the percentages may not be always exactly 80/20, there usually are “the vital few and the trivial many.”

• Generally, Pareto chart is used to plot a measurement that reflects cost to the organization.

Vilfredo Pareto1848 - 1923

Example – Draw a Pareto chart for Customer Complaints received from eight different zones of India – 54,25,75,12,65,42,12,41

<Pareto_complaints.mtw>


26


Pareto Analysis

To draw a Pareto chart, follow the path – Minitab> Stats > Quality Tools > Pareto ChartMinitab> Stats > Quality Tools > Pareto Chart

Count

Perc

ent

ZoneCount

Percent 32.4 25.0 12.7 10.0 7.8 6.1 2.9 2.9Cum %

132

32.4 57.4 70.1 80.1 88.0 94.1 97.1 100.0

102 52 41 32 25 12 12OtherFourTwoSixEightFiveThreeOne

400

300

200

100

0

100

80

60

40

20

0

Pareto Chart of Zone


27


Pareto Analysis

Conclusion:

The chart shows One, Three and Five as the major sources of customer

complaints. The improvements should be initially concentrated on these

major contributors.

Pareto Chart is used when:

• Trying to focus on the most significant problem or cause

• Relating cause and effect, by comparing a Pareto chart classified by causes with one classified by effects

• Analyzing data by groups, to reveal unnoticed patterns

• Communicating with others about your data

• Evaluating improvement, by comparing before and after data


28


ExerciseDraw a Pareto Chart for the following travel expenses for six months. As the approving authority for travel expenses, which departments should you monitor first for controlling the expenses:

Deptt Travel Expenses

E 5200

E 4500

A 4000

E 3500

D 5800

B 3200

B 3000

C 400

D 7500

A 6200


C 700

E 4600

E 2500

B 2200

D 7500

C 200

A 5400

E 2800

B 1200

C 500


A 5000

C 1000

B 2500

B 2700

D 8000

A 1700

C 300

D 6500

A 8000

D 7000

<Pareto_dept.mtw>


29


SolutionPareto Chart depicts (visually) the total expenses for six months for each

of the five departments.Tr

avel E

xpense

s

Perc

ent

DepartmentCount

20.3 13.0 2.7Cum % 37.2 63.9 84.2 97.3 100.0

42300 30300 23100 14800 3100Percent 37.2 26.7

OtherBEAD

120000

100000

80000

60000

40000

20000

0

100

80

60

40

20

0

Pareto Chart of Deptt

Maximum Contributors


30


ExerciseReena is a quality personnel whose job involves inspecting TVs for sound output on the scale 1 to 5, (1 being the lowest wattage and 5 the highest). Following is the data for 20 TVs. Calculate the percentage of TVs that Reena should reject. (Criterion for reject is that the sound output is between 1 – 3).

Sound OutputSound Output Sound OutputSound Output Sound OutputSound Output

1 4 2

1 2 5

2 3 4

2 5 4

4 5 3

5 4 1

2 4

<Pareto_TV.mtw>


31


Solution


32


Solution

Frequency

Perc

ent

Sound Output ScaleCount

20.0 15.0 10.0Cum % 30.0 55.0 75.0 90.0 100.0

6 5 4 3 2Percent 30.0 25.0

31524

20

15

10

5

0

100

80

60

40

20

0

Pareto Chart of Sound OutputMaximum Contributors

The percentage of rejected TVs = 25 + 15 + 10 = 50%


33


Histogram

• Is a chart that displays distribution, center location, and variation of data by categorizing data.

• Unlike bar graph (commonly used in Excel), it can show distribution of continuous data.

From the given data, draw a Histogram for the number of

working days (production) in a month for a three year period.

Month Jan-02 Feb-02 Mar-02 Apr-02 May-02 Jun-02 Jul-02 Aug-02 Sep-02 Oct-02 Nov-02 Dec-02Working_days 22 22 24 23 24 21 17 23 23 24 19 23



<histogram.mtw>


34


Histogram


35


Histogram

W_days

Frequency

2624222018

7

6

5

4

3

2

1

0

3

4

77

4

22

3

22

Histogram of W_days

Data labels may be defined


36


Histogram

W_days

Frequency

282624222018

7

6

5

4

3

2

1

0

Mean 22.33StDev 2.586N 36

Histogram of W_daysNormal

Shows distribution in comparison to normal curve of same mean and standard deviation Other options may be tried


37


Dot Plot

• Is a chart that plots dots on a number line depicting frequency and spread of the data. If the data size is large, each dot on the chart represents more than one value.

Considering the same data used for plotting Histogram, let us

now draw a Dot Plot

• Go to

Minitab > Graph > DotplotMinitab > Graph > Dotplot

• Choose the option “ SimpleSimple”

<histogram.mtw>


38


Dot PlotTo find the corresponding values for dots, • Right- click on the graph and choose BrushBrush.• Right-click again and select the columns required to be displayed in “Set “Set ID Values”ID Values”..• Choose the area and find the display.Choose the area and find the display.


39


Box Plot• Boxplot is used to obtain information about the shape, dispersion, and mid-value of a

given data.

• Spots outliers

• Used to assess the symmetry of the data

Draw a Boxplot the same working days example. (Change the working

days for Jun-2003 as 10 and Dec-2003 as 31).

• Go to

Minitab > Graph > BoxplotMinitab > Graph > Boxplot

• Choose the option “ SimpleSimple”

• Select the data column

<boxplot.mtw>


40


W_days

30

25

20

15

10

Boxplot of W_days

Box Plot

MEDIANMEDIAN

3rd Quartile Q33rd Quartile Q3

1st Quartile Q11st Quartile Q1LOWER LIMIT= Q1 - 1.5 (Q3- Q1)LOWER LIMIT= Q1 - 1.5 (Q3- Q1)

UPPER LIMIT= Q3 + 1.5 (Q3- Q1)UPPER LIMIT= Q3 + 1.5 (Q3- Q1)

OUTLIEROUTLIER OUTLIEROUTLIER

OUTLIEROUTLIER OUTLIEROUTLIER


41


Box Plot : Analysis

• The line drawn through the box represents the median of the data.

• The edge above the median represents the first quartile (Q1), while the edge below represents the third quartile (Q3). Thus the box portion of the plot represents the interquartile range (IQR = Q3-Q1), or the middle 50% of the observations.

• The lines extending from the box are called whiskers. The whiskers extend outward to indicate the lowest and highest values in the data set (they exclude outliers).

• Extreme values, or outliers, are represented by dots. A value is considered an outlier if it is outside of the box (greater than Q3 or less than Q1) by more than 1.5 times the IQR.

• Brush may be used on the graph to find the values of outliers.


42


Scatter Plot• The Scatter Plot illustrates the relationship between two variables.

• Though the variation in one variable with respect to the other is graphically shown, the graph cannot be relied on making judgments on the same. Example- Relationship between population in India to Growth rate of China.

Draw the Scatter Plot for the data

<Scatterplot.mtw>

Year Month Sales Adv Exp AdAgency2000 January 210 30 Wise2000 February 205 25 Wise2000 March 202 55 Wise2000 April 245 43 Wise2000 May 237 60 Wise2000 June 290 50 Wise2000 July 299 60 Wise2000 August 345 43 Wise2000 September 326 34 Wise2000 October 355 36 Wise2000 November 359 38 Wise2000 December 371 34 Wise

Year Month Sales Adv Exp AdAgency2001 January 368 30 Smart2001 February 358 25 Smart2001 March 345 36 Smart2001 April 380 36 Smart2001 May 391 30 Smart2001 June 403 35 Smart2001 July 410 45 Smart2001 August 430 29 Smart2001 September 410 33 Smart2001 October 415 35 Smart2001 November 435 37 Smart2001 December 450 40 Smart


43


Scatter Plot

• For the given data, we may find the relationship of Sales w.r.t. the expenses on Advertisement cost, its variation with month/ Ad agency

• Go to Graph > Scatterplot > SimpleGraph > Scatterplot > Simple

• All three plots can be made together by choosing Sales Exp as y and Adv Exp, month, and Ad agency as x(s)


44


Sale

s

6050403020 3800037900378003770037600

400

300

200

2001.002000.752000.502000.252000.00

400

300

200

Adv Exp Month

Year

Scatterplot of Sales vs Adv Exp, Month, Year

Scatter Plot

No relation

Positive relation, but groups

High sales expenses in the year 2001


45


Scatter Plot (With Group)

Adv Exp

Sale

s

6050403020

450

400

350

300

250

200

AdAgencySmartWise

Scatterplot of Sales vs Adv Exp

Plot suggests Sales are more for Smart Agency


46


Matrix Plot• Matrix Plot is used to find relationship between multiple variables

• Let us create a Matrix Plot for the Sales data discussed in Scatter Plot

• Go to Graph > Matrix Plot > With GroupsGraph > Matrix Plot > With Groups and enter data as:


47


Matrix Plot

Sales

604020 2001.02000.52000.0

400

300

20060

40

20

Adv Exp

Month

38000

37800

37600

400300200

2001.0

2000.5

2000.0

380003780037600

Year

AdAgencySmartWise

Matrix Plot of Sales, Adv Exp, Month, Year

Mir

ror

Imag

e

Mirror Image• Same result can be drawn from the plot


48


Marginal Plot• A marginal plot is a Scatter plot with graphs at the margins of the

x- and/or y-axes, which depict the distribution of the points in each direction, or the sample marginal distributions.

Let us create a Marginal Plot for

the given data:

Failing_students Rich_students School_Code3 130 12 55 21 35 35 205 44 162 51 24 64 160 72 65 83 100 95 210 101 30 112 60 121 12 134 175 142 75 153 125 16<Marginal_students.mtw>


49


Marginal Plot

• Go to Graph > Marginal Plot > With HistogramsGraph > Marginal Plot > With Histograms


50


Marginal Plot

Rich_students

Failing_st

udents

200150100500

5

4

3

2

1

Marginal Plot of Failing_students vs Rich_students

Shows positive relationship

Expert Tip: The Marginal plot only indicates the relationship between entities. The method of finding the exact equation between entities will be learnt later.


51


Time Series Plot

• The Time Series Plot is used to:

– Detect seasonality in data

– Detect trends in data over time

– Compare trends across groups

• The time series data is plotted on the vertical y-axis versus time on the horizontal x-axis.

• A Scatter plot can be used instead, if:

– the data is not in chronological order, or

– the data collection intervals are irregular, you may want to create a Scatter plot instead.


52


Time Series Plot

• Example – A toy manufacturer in America has four production lines working on all days. The data shows number of defects in each line for the month of January, 2005. Find the stability of the data.

• Go to

Stat > Time Series > Time Stat > Time Series > Time

Series PlotSeries Plot

Date Owl Cat Tortoise Mouse1/1/05 22 23 22 221/2/05 23 23 21 211/3/05 24 24 24 241/4/05 23 25 22 201/5/05 25 19 21 241/6/05 23 18 20 211/7/05 24 19 22 171/8/05 22 17 23 221/9/05 23 23 21 23

1/10/05 21 24 20 241/11/05 19 26 22 181/12/05 20 23 24 231/13/05 19 19 22 191/14/05 21 18 20 181/15/05 19 17 21 261/16/05 20 20 22 201/17/05 24 17 23 171/18/05 22 25 22 221/19/05 25 25 21 251/20/05 22 26 20 181/21/05 23 23 21 231/22/05 20 17 23 201/23/05 25 19 23 251/24/05 24 18 22 191/25/05 19 19 22 191/26/05 22 23 22 221/27/05 24 19 22 171/28/05 22 17 23 221/29/05 23 23 21 211/30/05 23 23 21 231/31/05 21 24 20 24<Run.mtw>


53


Time Series Plot : Multiple


54


Time Series Plot : Multiple

Date

Data

01/30/

2005

01/27/

2005

01/2

4/20

05

01/2

1/20

05

01/1

8/20

05

01/15/

2005

01/12/

2005

01/09/

2005

01/0

6/20

05

01/0

3/20

05

26

24

22

20

18

16

Variable

TortoiseMouse

OwlCat

Time Series Plot of Owl, Cat, Tortoise, Mouse


55


Time Series Plot : Simple

Date

Mouse

01/30/

2005

01/2

7/20

05

01/24/

2005

01/21/

2005

01/1

8/20

05

01/15/

2005

01/12/

2005

01/0

9/20

05

01/0

6/20

05

01/03/

2005

26

24

22

20

18

16

Time Series Plot of Mouse

Date

Tort

ois

e

01/30/

2005

01/2

7/20

05

01/24/

2005

01/21/

2005

01/1

8/20

05

01/15/

2005

01/12/

2005

01/0

9/20

05

01/0

6/20

05

01/03/

2005

24

23

22

21

20

Time Series Plot of Tortoise

Date

Cat

01/30/

2005

01/2

7/20

05

01/24/

2005

01/21/

2005

01/1

8/20

05

01/15/

2005

01/12/

2005

01/0

9/20

05

01/0

6/20

05

01/03/

2005

26

24

22

20

18

16

Time Series Plot of Cat

Date

Ow

l

01/30/

2005

01/2

7/20

05

01/24/

2005

01/21/

2005

01/1

8/20

05

01/15/

2005

01/12/

2005

01/0

9/20

05

01/0

6/20

05

01/03/

2005

25

24

23

22

21

20

19

Time Series Plot of Owl


56


Time Series Plot : Result Analysis

• The time series plot consists of– Time scale (index, calendar, clock, or stamp column) on the x-axis

– Data scale on the y-axis

– Lines displaying each time series

• For the data, four sets of data, one for each line are plotted the same time series plot.

• The time series plot suggests no grouping or seasonal effect in data. Though it gives some indication but primarily suggests no trends/ some oscillations.

• The plot is not a good way to judge. To statistically show the evidence of non- randomness, Run chart is used.


57


Run Chart

• Run charts are used to monitor process changes associated with characteristic of interest over time.

• It is used to find patterns in process data or randomness or stability on the basis of – – Test for number of runs about the median

• Clusters

• Oscillations

– Test for number of runs up and down

• Trends

• Mixtures

• Consider the same example of toys.

• Go to Stat > Quality Tools > Run ChartStat > Quality Tools > Run Chart<Run.mtw>


58


Run Chart

If the data is in

single column If the data is in

multiple columns


59


Run Chart

Sample

Ow

l, ..., M

ouse

30282624222018161412108642

26

24

22

20

18

16

Number of runs about median:

0.40593

17Expected number of runs: 16.35484Longest run about median: 5Approx P-Value for Clustering: 0.59407Approx P-Value for Mixtures:

Number of runs up or down:

0.72084

19Expected number of runs: 20.33333Longest run up or down: 4Approx P-Value for Trends: 0.27916Approx P-Value for Oscillation:

Run Chart of Owl, ..., Mouse

17>16.35

19<20.33

Run about the median


60


Run Chart : Graph Analysis

Run about the median• A run about the median is one or more consecutive

points on the same side of the median. When the points are connected by a line, a run ends when the line crosses the median. A new run begins with the next plotted point.

• In the example, 17 runs about the median were observed. The blue circles marked show the runs about the median.


61



Test for number of runs about the median• The test checks two types of non-random behavior - mixtures and

clusters.

• Mixtures are characterized by an absence of points near the median.

• Clusters are groups of points that have similar values.

• When the observed number of runs is – statistically greater than the expected number of runs, then mixtures are

suggested. (In the example, 17>16.35, therefore mixtures).

– statistically less than the expected number of runs, then clusters are suggested.

• In this example, though Mixtures are more than Clusters, the p-values for clustering (0.594) and mixtures (0.405) are greater than the alpha-level of 0.05. Therefore, you can conclude that the data does not indicate mixtures or clusters.


62


Run Chart

Sample

Ow

l, ..., M

ouse

30282624222018161412108642

26

24

22

20

18

16


0.40593



0.72084


Run Chart of Owl, ..., Mouse

17>16.35

19<20.33

Run up or down


63



Run up or down• A run up or down is one or more consecutive points in

the same direction. A new run begins each time there is a change in direction (either ascending or descending) in the sequence of data.

• For example, when the preceding value is smaller, a run up begins and continues until the proceeding value is larger than the next point, then a run down begins.

• In the example below, 19 runs up or down were observed. The blue lines marked show the runs up or down.


64



Test for number of runs up and down• This test is based on the number of runs up or down -

increasing or decreasing - and is sensitive to two types of non-random behavior - oscillation and trends.

• When the observed number of runs is– statistically greater than the expected number of runs, then

oscillation is suggested.

– statistically less than the expected number of runs, then a trend is suggested. (In the example, 19<20.33, therefore trends).

• In this example, the p-values for trends (0. 279) and oscillation (0. 720) are greater than the alpha-level of 0.05. Therefore, you can conclude that the data does not indicate a trend or oscillation.


65


Normality Test

• A normality test is used to check if the given data is normally distributed.

• It is important to check for normality because most of the tools (tests of means and variances) to be discussed, assume the data to be normal. The data, therefore should first be checked because taking it through the tools.

• Though most of the data collected is normal (Central Limit Theorem), as soon as the data is collected, it should be checked for normality before it is treated by a statistical tool. Normality may also be checked for any data at any point of project cycle, which is relevant to the project.


66


Normality Test

There are various methods to check for

Normality. We will discuss the three most

commonly used methods:

Probability Plot• Follow the path in Minitab:

– Minitab> Graph > Probability PlotMinitab> Graph > Probability Plot

• Example – Given is the data of the number of accidents in an year on a highly accident – prone highway. Check if the data is normal.

MONTH #ACCIDENTS

JAN 3

FEB 4

MAR 0

APRIL 1

MAY 2

JUNE 4

JULY 3

AUGUST 5

SEPTEMBER 1

OCTOBER 4

NOVEMBER 2

DECEMBER 0

How to Check for Normality?


67


Normality Test: Probability Plot


68




69



ACCIDENTS

Perc

ent

76543210-1-2

99

95

90

80

70

605040

30

20

10

5

1

Mean

0.436

2.417StDev 1.676N 12AD 0.339P-Value

Normality test for accidentsNormal

0.05 is the alpha value (alpha risk/ type – I error or the significance level). Generally, the value assigned is 5% unless stated otherwise or demanded by the process.

Conclusion:P – value = 0.436. Since p – value is greater than 0.05, the given data is normal.


70


Normality Test: Graphical Summary• Minitab> Stat > Basic Statistics > Graphical SummaryMinitab> Stat > Basic Statistics > Graphical Summary

Default is 95% unless stated otherwise


71


Confidence Level

• Confidence Interval gives you a range of likely values based on the

sample.Confidence Level is how sure you want to be that the population mean or std. deviation falls in the confidence interval you are going to calculate based on the sample!

• Six Sigma and industry typically use a 95% Confidence Level which means:

– 95% chance that the population mean or std. deviation lies within the confidence interval.

– 5% chance (alpha risk) that population mean is outside the confidence interval.

– For highly sensitive processes which are working at a high sigma level, this value of alpha risk may be reduced from 5% to ensure less alpha error. Similarly, vice – versa also holds true.


72


Normality Test: Graphical Summary

Conclusion:

Since p – value is greater than 0.05, the given data is normal.

Confidence interval for Mean


73


Normality TestMinitab> Stat > Normality TestMinitab> Stat > Normality Test


74


Normality Test

Conclusion:P – value = 0.436. Since p – value is greater than 0.05, the given data is

normal.

ACCIDENTS

Perc

ent

7.55.02.50.0-2.5-5.0

99

95

90

80

70

605040

30

20

10

5

1

Mean

0.436


Probability Plot of ACCIDENTSNormal - 95% CIThe PPrediction rediction

IIntervalnterval is the range in which the new response value is expected to fall. That is, it provides an interval of possible response values given a combination of predictor levels.


75


ExerciseFor the given data, check if it is normal. If so, analyze your data using all/

few of the following charts:

– Pareto Chart

– Histogram

– Dot Plot

– Box Plot

– Scatter Plot

– Matrix Plot

– Marginal Plot

– Time-Series Plot

– Run Chart

<Charts_Exercise.mtw>

Durability Carpet_type Composition Brand Plastic_fibre Colour Porosity_Inv App_temp

18.95 1 A Strength 10 White 42.9 2512.62 1 B Strength 7 Red 30.2 3011.94 1 A Strength 7 Red 28.9 3014.42 1 B Strength 8 Red 33.8 3010.06 2 A Strength 6 Red 25.1 307.19 2 B Strength 5 Black 19.4 357.03 2 A Strength 5 Black 19.1 35

14.66 2 B Strength 8 Red 34.3 3010.92 3 A Power 6 Red 26.8 3013.28 3 B Power 8 Red 31.6 3014.52 3 A Power 8 Red 34 3012.51 3 B Power 7 Red 30 3010.46 4 A Power 6 Red 25.9 3021.4 4 B Power 12 White 47.8 2018.1 4 A Power 10 White 41.2 2522.5 4 B Power 12 White 50 20


76


Solution

• Here the response is Durability and rest are the input variables. Let us do Normality Test to find if the data is Normal.

Durability

Perc

ent

252015105

99

95

90

80

70

605040

30

20

10

5

1

Mean

0.458


Probability Plot of DurabilityNormal

Since p > 0.05, Data is Normal

<Charts_Exercise.mpj


77


Solution• Though not mentioned, the most desired value for

Durability would be the highest value

• Let us draw a dot plot to see the response.

As seen using Brush, the lower values occur for the

combinations below.


78


Solution

• Let us see if a Box plot can give some information

Brand

Dura

bility

StrengthPower

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Boxplot of Durability vs Brand

Carpet_type

Dura

bility

4321

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Boxplot of Durability vs Carpet_ type

Strength brand gives lower Durability (also seen from Dot plot)

Brand 4 gives more variation but also

higher values

Brand 2 gives lower Durability values


79


Solution

• We would code the text variables so that we can treat them as Numeric – Composition (A=1,B=2) and Colour (White=1, Red=2, Black =3)


80


Solution

• Data > Code > Text to NumericData > Code > Text to Numeric


81


Solution

• In this case, we are interested only in the relationship of Xs with y, Durability, we are using a Scatter plot


82


SolutionDura

bili

ty

3.52.51.5 10.07.55.0 453525

20

15

10

5

363024

20

15

10

52.01.51.0 321

Carpet_type Plastic_fibre Porosity

App_temp NComp NColour

BrandPowerStrength

Scatterplot of Durability vs Carpet_ type, Plastic_ fibr, Porosity, ...

Note: Matrix Plot can also be drawn instead of Scatter plot.


83


Solution

ConclusionsConclusions

Durability is undesirable if:

• There is less plastic fiber

• Less porosity_inv

• High temperature (beyond 30)

• High Ncolour (Black)

• Strength brand

• Carpet type 2

• Both compositions give mixed values.


84


Self- Practice Exercise

Analyze the data for the defect causes Analyze the data for the defect causes

given by <Charts_Exercise2.mtw>, given by <Charts_Exercise2.mtw>,

using the discussed tools. using the discussed tools.

Discuss the answers Discuss the answers

amongst your amongst your

teams.teams.


85


SolutionCount

Perc

ent

Defect type

Count 364 261Percent 31.9 13.8 11.0 7.7 6.8 6.5 6.3

20686.3 5.6 4.0

Cum % 31.9 45.6 56.7 64.4 71.2 77.7

895

84.0 90.4 96.0 100.0

716 499 443 422 412 411

Othe

r

Missing

Parts

Power

Plug

Broke

n

Part

Brok

en

Missing

Har

dware

Pack

aging

dam

aged

Miss

ing ass

embly

tool

Damag

ed H

ardw

are

Low Br

ightnes

s

Manua

l Miss

ing

7000

6000

5000

4000

3000

2000

1000

0

100

80

60

40

20

0

Pareto Chart of Defect type

Sample

No. of Defe

cts

240220200180160140120100806040201

100

80

60

40

20

0


0.20194



0.50000


Run Chart of No. of Defects

p>0.05, Random data

Major Contributors


86


Minitab : Ready ReckonerMinitab : Ready Reckoner

<Minitab_Shortcut_Guide>

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Documents

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