Applied Statistics & Design of Experiment HW in MINITAB

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Meet Minitab

Minitab®, the Minitab logo®, Quality Companion by Minitab® and Quality Trainer by Minitab® are registered trademarks of Minitab, Inc. in the United States and other countries. Capability SixpackTM, Process Capability SixpaekTM, ReportPadTM, and StatCuideTM are all trademarks of Minitab, Inc.

Six Sigma@ is a registered trademark and service mark of Motorola, Inc. All other marks referenced remain the property of their respective owners.

Table of Contents

1 Getting Started .............................................. 1-1

Objectives ................................................... 1-1

Overview .................................................... 1-1

Typographical Conventions in this Book ............................. 1-2

The Story .................................................... 1-3

Starting Minitab ............................................... 1-3

Opening a Worksheet ........................................... 1-4

What's Next .................................................. 1-6

2 Graphing Data .............................................. 2-1

Objectives ................................................... 2-1

Overview .................................................... 2-1

Exploring the Data ............................................. 2-2

Examining Relationships Between Two Variables ....................... 2-8

Using Graph Layout and Printing ................................. 2-11

Saving Projects ............................................... 2-1 3

What's Next ................................................. 2-14

3 Analyzing Data .............................................. 3-1

Objectives ................................................... 3-1

Overview .................................................... 3-1

Displaying Descriptive Statistics ................................... 3-2

Performing an ANOVA .......................................... 3-4

Using Minitab's Project Manager .................................. 3-8

What's Next ................................................. 3-11

4 Assessing Quality ............................................. 4-1

Objectives ................................................... 4-1

Overview .................................................... 4-1

Evaluating Process Stability ....................................... 4-2

Evaluating Process Capability ..................................... 4-8

What's Next ................................................. 4-10

iii

Designing an Experiment ..................................... 5-1

Objectives ................................................... 5-1

Overview ................................................... 5-1

Creating an Experimental Design ................................. 5-2

Viewin9 the Design ............................................ 5-5

Enterin9 Data ................................................ 5-5

Analyzing the Design .......................................... 5-6

Drawing Conclusions .......................................... 5-9

What's Next ................................................ 5-12

6 Using Session Commands ..................................... 6-1

Objectives ................................................... 6-1

Overview ................................................... 6-1

Enablin9 and Typing Commands ................................. 6-2

Rerunnin9 a Series of Commands ................................. 6-5

Repeating Analyses with Execs ................................... 6-6

What's Next ................................................. 6-8

7 Generating a Report .......................................... 7-1

Objectives ................................................... 7-1

Overview ................................................... 7-1

Using the ReportPad ........................................... 7-2

Savin9 a Report ............................................... 7-6

Copyin9 a Report to a Word Processor ............................. 7-6

Using Embedded Graph Editin9 Tools .............................. 7-7

Sending Output to Microsoft PowerPoint ........................... 7-9

What's Next ................................................ 7-11

Preparing a Worksheet ........................................ 8-1

Objectives ................................................... 8-1

Overview ................................................... 8-1

Getting Data from Different Sources ............................... 8-2

Preparing the Worksheet for Analysis ............................... 8-4

What's Next ................................................ 8-11

9 Customizing Minitab ......................................... %1

Objectives ................................................... 9-1

Overview .................................................... 9-1

Settin9 Options ............................................... 9-2

Creatin9 a Custom Toolbar ...................................... 9-3

Assignin9 Shortcut Keys ......................................... 9-5

Restorin9 Minitab's Default Settings ................................ 9-6

What's Next .................................................. 9-7

10 Getting Help .............................................. 10-1

Objectives .................................................. 10-1

Overview ................................................... 10-1

Gettin9 Answers and Information ................................. ] 0-2

Minitab Help Overview ......................................... 10-4

Help ....................................................... 10-6

StatGuide ................................................... 10-8

Session Command Help ....................................... 10-1 0

What's Next ................................................ 10-11

11 Reference ................................................ 11-1

Objectives .................................................. 11-1

Overview ................................................... 11-1

The Minitab Environment ....................................... 11-2

Minitab Data ................................................ 11-5

Index ........................................................ 1-1

1 Getting Started

Objectives In this chapter, you:

[] Learn how to use Meet Minitah, page 1-1

n Start Minitab, page 1-3

u Open and examine a worksheet, page i-4

Overview Meet Minitah introduces you to the most commonly used features in Minitab. Throughout the book, you use functions, create graphs, and generate statistics. The contents of Meet Minitab relate to the actions you need to perform in your own Minitab sessions. You use a sampling of Minitab's features to see the range of features

and statistics that Minitab provides.

Most statistical analyses require a series of steps, often directed by background knowledge or by the subject area you are investigating. Chapters 2 through 5 illustrate the analysis steps in a typical Minitab session:

[] Exploring data with graphs

[] Conducting statistical analyses and procedures

I Assessing quality

[] Designing an experiment

Chapters 6 through 9 provide information on:

[] Using shortcuts to automate future analyses

[] Generating a report

[] Preparing worksheets

[] Customizing Minitab to fit your needs

Meet Minitab 1-1

Chapter 1 Typographical Conventions in this Book

Chapter 10, Getting Help, includes information on getting answers and using Minitab Help features. Chapter 11, Reference, provides an overview of the Minitab environment and a discussion about the types and forms of data that Minitab uses.

You can work through Meet Minitab in two ways:

[] From beginning to end, following the story of a fictional online bookstore through a common workflow

m By selecting a specific chapter to familiarize yourself with a particular area of Minitab

Meet Minitab introduces dialog boxes and windows when you need them to perform a step in the analysis. As you work, look for these icons for additional information:

Provides notes and tips

@ Suggests related topics in Minitab Help and StatGuide

Typographical Conventions in this Book [Enter]

[Alt]+[D]

Denotes a key, such as the [Enter] key.

Denotes holding down the first key and pressing the second key. For example, while holding down the [Alt] key, press the [D] key.

File ÿ Exit Denotes a menu command, in this ease choose Exit from the File menu. Here is another example: Stat * Tables ÿ Tally Individua! Variables means open the Stat menu, then open the Tables submenu, and finally choose Tally Individual Variables.

Click OK. Bold text clarifies dialog box items and buttons and Minitab commands.

Enter Pulsel. Italic text specifies text you need to enter.

1-2 Meet Minitab I

The Story Getting Started

The Story An online book retail company has three regional shipping centers that distribute orders to eonsumers. Each shipping center uses a different computer system to enter and process order information. To integrate all orders and use the most efficient

method company wide, the company wants to use the same computer system at all three shipping centers.

Throughout this book, you analyze data from the shipping centers as you learn to use Minitab. You create graphs and conduct statistical analyses to determine which computer system is the most efficient and results in the shortest delivery time.

After you identify the most efficient computer system, you focus on the data from this center. First, you create control charts to see whether the center's shipping process is in control, Then, you conduct a capability analysis to see whether the process is operating within specification limits. Finally, you conduct a designed experiment to further improve the shipping center's processes,

Additionally, you learn about session commands, generating a report, preparing a worksheet, and customizing Minitab.

Starting Minitab

Start Minitab

Before you begin your analysis, start Minitab and examine the layout of the windows.

1 From the Windows Taskbar, choose Start ÿ Programs * Minitab ÿ Minitab 16 Statistical Software.

Minitab opens with two main windows visible:

B The Session window displays the results of your analysis in text format. Also, in this window, you ean enter commands instead of using Minitab's menus.

m The Data window contains an open worksheet, which is similar in appearance to a spreadsheet. You can open multiple worksheets--each in a different Data window.

Meet Minitab 1-3

Chapter 1 Opening a Worksheet

Session windowÿ._..._

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'llcoll to ÿ[inltÿ, pÿels FI foÿ hllp.

Data window: - Columns -------------

- Rows

- Cells

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Iÿ [ For more information on the Minitab environment, see The Minitab Environment on page 11-2.

Opening a Worksheet You can open a new, empty worksheet at any time. You can also open one or more files that contain data. When you open a file, you copy the contents of the file into the current Minitab project. Any changes you make to the worksheet while in the project will not affect the original file.

The data for the three shipping centers are stored in the worksheet ShippingData.MTW.

I In some cases, you will need to prepare your worksheet before you begin an analysis. For I information on setting up a worksheet, see Chapter 8, Preparing a Worksheet.

1-4 Meet Minitab

Opening a Worksheet Getting Started

Open a worksheet

Choose File ÿ Open Worksheet.

Click Look in Minitab Sample Data folder, near the bottom of the dialog box. Deÿktcÿ iÿata'NTW

In the Sample Data folder, double-click Meet Minitab.

Choose ShippingData.MTW, then click Open. If you get a message box, check Do not

Examine worksheet

You can change the default folder for opening and saving Minitab files by choosing Tools ÿ Options ÿ General.

..u D ocan,,eras

MÿNÿ Piacÿ

[eÿk In ,ÿab ÿ Oat a f O, dez

display this message again, then click OK. To restore this message for every time you open a worksheet, return to Minitab's default settings. See Restoring Minitab's Default Settings on page 9-6.

The data are arranged in columns, which are also called variables. The column

number and name are at the top of each column. Each row in the worksheet represents a case, which is information on a single book order.

Column with Column with Column with date/time data numeric data text data

Column name

Row number

]C3-D C4 C6 C'-'7 Order ÿ Arrival Days sGi& oiÿaeÿ"l

1 ÿlEastern 3/3/2009 8:34 !3/7/2009 16:21 4.28264 On time , 285 iEastem 3/3/20098:3513/8/200917:05i 3.35417 Ontime 198

3 I Eastern 3/3/2009 8:38j *i * Back orderl 299 -- 2,1 i Eastern 13/3/2009 8:40'3/7/2009 15:52 ; 4.30000 ÿOn time 205

5 ]Eastern i3/3/2009 8:42 3/9/2009 14:48, 6.25417;Late 250 6 IEastern i3/3/2009 8:4313/8/2009 15 48ÿ 6.29308 On time 93: 7 IEastern i3/3/2009 8:50 '3/7/2009 10:02 4.05000 ion time I89 8 IEastern 13/3/20098:553/8/2009 16:30ÿ 5.31597 On time 335

Minitab accepts three types of data: numeric, text, and date/time. This worksheet contains each type.

The data include:

,, Shipping center name

,, Order date

[] Delivery date

Meet Minitab 1-5

Chapter 1 What's Next

[]

Number of delivery days

Delivery status ("On time" indicates that the book shipment was received on time; "Back order" indicates that the book is not currently in stock; "Late" indicates that the book shipment was received six or more days after ordered)

[] Distance from shipping center to delivery location

] For more information about data types, see Minitab Data on page 11-5.

What's Next Now that you have a worksheet open, you are ready to start using Minitab. In the next chapter, you use graphs to check the data for normality and examine the relationships between variables.

1-6 Meet Minitab

2 Graphing Data

Objectives In this chapter, you:

[] Create and interpret an individual value plot, page 2-2

[] Create a histogram with groups, page 2-4

[] Edit a histogram, page 2-5

[] Arrange multiple histograms on the same page, page 2-6

[] Access Help, page 2-8

[] Create and interpret scatterplots, page 2-9

[] Edit a scatterplot, page 2-10

[] Arrange multiple graphs on the same page, page 2-12

[] Print graphs, page 2-13

[] Save a projeet, page 2-13

Overview Before conducting a statistical analysis, you can use graphs to explore data and assess relationships among the variables. Also, graphs are useful to summarize findings and to ease interpretation of statistieal results.

You can access Minitab's graphs from the Graph and Stat menus. Built-in graphs, which help you to interpret results and assess the validity of statistieal assumptions, are a!so available with many statistical commands,

Graph features in Minitab include:

[] A pictorial gallery from which to choose a graph type

[] Flexibility in customizing graphs, from subsetting of data to specifying titles and footnotes

Meet Minitab 2-1

Chapter 2 Exploring the Data

-, Ability to change most graph elements, such as fonts, symbols, lines, placement of tick marks, and data display, after the graph is created

-, Ability to automatically update graphs

This chapter explores the shipping center data you opened in the previous chapter, using graphs to compare means, explore variability, check normality, and examine the relationship between variables.

For more information on Minitab graphs, go to Graphs in the Minitab Help index and then double-click the Overview entry for details on Minitab graphs. To access the Help index, choose Help • Help, then click the Index tab.

Exploring the Data Before conducting a statistical analysis, you should first create graphs that display important characteristics of the data.

For the shipping center data, you want to know the mean delivery time for each shipping center and how variable the data are within each shipping center. You also want to determine if the shipping center data follow a normal distribution so you that you can use standard statistical methods for testing the equality of means.

Create an individual value plot

You suspect that delivery time is different for the three shipping centers. Create an individual value plot to compare the shipping center data.

1 If not continuing from the previous chapter, choose File • Open Worksheet. If continuing from the previous chapter, go to step 4.

2 Click Look in Minitab Sample Data folder, near the bottom of the dialog box.

3 In the Sample Data folder, double-click Meet Minitab, then choose ShippingData.MTW. Click Open.

4 Choose Graph • Individual Value Plot.

For most graphs, Minitab displays a pictorial gallery. Your gallery choice determines the available graph creation options.

5 Under One Y, choose With Groups, then click OK.

Mÿ61>ÿo ÿs

J Caeÿd

2m2 Meet Minitab

Exploring the Data Graphing Data

In Graph variables, enter Days.

In Categorical variables for grouping (1-4, outermost first), enter Center.

To create a graph, you only need to complete the main

dialog box. However, you can cliek any button to open dialog boxes to customize your graph.

Cÿ Of dec Days C't Days

tarÿe ¢_ÿegÿcd vÿhÿNÿs fÿ€ ÿ (1-4, ÿreost ÿ,ÿ)ÿ

V I

The list box on the left shows the variables from the worksheet that are available for the analysis. The boxes on the right display the variables that you select for the analysis.

Click Data View. Check Mean connect line. ÿ,0ÿ,

D,ÿa I)b!ÿay Click OK in each dialog box. r- ÿ,ÿ

F !ÿaa syÿl

F Fÿ_ ccrÿect hno

C_ategaÿed va,ÿ for attdÿta aÿatr, eat:

__J [

..... " I To select variables in most Minitab dialog boxes, you can: double-click the variables in the variables list box; highlight the variables in the list box, then choose Select; or type theIvariables' names or column numbers.

Graph window output

Individual Value Plot of Days 8

i ÿ °t i

i ÿ : 1o ° t

Cÿn I:er

Meet Minitab 2-3

Chapter 2 Exploring the Data

Interpret results

The individual value plots show that each center has a different mean delivery time. The Western center has a lower shipping time than the Central and Eastern centers. The variation within each shipping center seems about the same.

Create a grouped

histogram

Another way to compare the three shipping centers is to create a grouped histogram, which displays the histograms for each center on the same graph. The grouped histogram will show how much the data from each shipping center overlap.

1 Choose Graph 1,- Histogram.

2 Choose With Ht And Groups, then click OK.

3 In Graph variables, enter Days.

4 In Categorical variables for grouping (0-3), enter Center.

5 Click OK.

Graph window output

Histogram of Days Non'nat

2 3 4 Days

5 6 7

2-4 Meet Minitab

Exploring the Data Graphing Data

Interpret results

As you saw in the individual value plot, the means for each center are different. The mean delivery times are:

Central-- 3,984 days

Eastern--4.452 days

Western- 2.981 days

The grouped histogram shows that the Central and Eastern centers are similar in mean delivery time and spread of delivery time. In contrast, the Western center

mean delivery time is shorter and less spread out. Chapter 3, Analyzing Data, shows how to detect stastistieally significant differences among means using analysis of variance.

I If your data change, Minitab can automatically update graphs. For more information, go to

I Updating graphs in the Minitab Help index. Edit

histogram Editing graphs in Minitab is easy. You can edit virtually any graph element. For the histogram you just created, you want to:

,, Make the header text in the legend (the table with the center information) bold

[] Modify the title

Change the legend table header font

1 Double-click thelegend.

2 Click the Header Font tab.

3 Under Style, cheek Bold.

4 Click OK.

es I Lÿaÿon He.ÿrr-ÿ IÿFoÿl

Change the title

1 Double-click the title (Histogram of Days).

2 In Text, type Histogram of Delivery Time.

3 Click OK.

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jr- bÿdÿo ] .-

o_g 1 carÿ:d

lTahÿaa

Temgÿ £ms ITC

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i St,d,ÿ _ÿe: 1,9 _ÿd lJÿ---- (

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Meet Minitab 2-5

Chapter 2 Exploring the Data

Graph window output 0.4ÿ

0,34

0,2ÿ

O,lq

Histogram of Delivery Time Normal

3 4 5 6 Days

Interpret results

The histogram now features a bold font for the legend heading and a more descriptive title.

In addition to editing individual graphs, you can change the default settings for future graphs.

[] To affect general graph settings, such as font attributes, graph size, and line types, choose Tools ÿ- Options ÿ- Graphics.

[] To affect graph-specific settings, such as the scale type on histograms or the method for calculating the plotted points on probability plots, choose Tools ÿ- Options ÿ Individual Graphs.

The next time you open an affected dialog box, your preferences are reflected.

Create a paneled

histogram

To determine if the shipping center data follow a normal distribution, create a paneled histogram of the time lapse between order and delivery date.

1 Choose Graph ÿ Histogram.

2 Choose With Fit, then click OK. I ÿ--' ÿ-------ÿ

.h O/the WTÿh Fa ÿd ad 6rÿlÿ ÿoups

2-6 Meet Minitab

Exploring the Data Graphing Data

3 In Graph variables, enter Days. C2 Order @aCh vÿaNÿs: C3 ArrÿJ [DaysC4 Oays C6 O;stm:e

5 In By variables with groups in separate panels, enter Center.

6 Click OK in each dialog box.

Click Multiple Graphs, then click the By Variables tab.

Graph window output

Histogram of Days Normal

Central

Wesfÿ-n

1 2 3 4 5 6 7 Easlÿrn 2O ÿ

2 3 4 5 6 7 Days

Panel variable: Center

Interpret results

The delivery times for each center are approximately normally distributed as shown by the distribution curves exhibiting the same pattern.

If you have fewer than 50 observations, you may want to use a normal probability plot (Graph - Probability Plot) to assess normality.

( Meet Minitab 2-7

Chapter 2 Examining Relationships Between Two Variables

Examining Relationships Between Two Variables Graphs can help identify whether associations are present among variables and the strength of any associations. Knowing the relationship among variables can help to guide further analyses and determine which variables are important to analyze.

Because each shipping center serves a small regional delivery area, you suspect that distance to delivery site does not greatly affect delivery time. To verify this suspicion and eliminate distance as a potentially important factor, examine the relationship between delivery time and delivery distance.

Access Help To find out which graph shows the relationship between two variables, use Minitab Help.

1 Choose Help )- Help.

2 Click the Index tab.

In Type in the key-word to find, type Graphs and then double-click the Overview entry to access the Help topic.

In the Help topic, under the heading Types of graphs, click Examine

relationships between pairs of variables.

raphing Data Overt'Jew e aÿse

F,lÿnÿa b provÿJe5 a fÿxÿ suÿ of grBphs to support a varmt), of anafysÿs neÿds, P,tany custormzatÿon options are avaÿbÿ when you crest8 a graph and many more arÿ avaÿabÿ after you creÿtÿ

Types of graphs U se the foÿo wing chart to seÿct a graph from |he Graph rrÿnÿ that fls your needs:

TO ,. Use.,

let sddtiort to thÿ graphs avai!lzÿ from th# Gralÿh rcÿnu, Ltln'ÿab errors an!zÿ,l;ÿ =pc oJfi¢ graphs on thÿ 5tlÿt nÿtz, such iIÿ ¢orttro/ohllrtÿ. l,ÿlrtÿlzb s(so hal; ÿ ÿ.ÿ ÿarÿ Of rcÿrÿy Iÿla!ÿlÿ:sl art a g/sÿ,r.. Charÿ arÿ tlvÿ,ÿ ÿ, bÿ do not apÿslzr On iz rrÿnÿl by dÿt (wPÿh the ÿx¢ÿ ptJorÿ of 5tÿrn-arÿd°Lrÿ f!. To add ohlÿrs¢|ÿr grÿphÿ to a rÿnÿ, tlÿo

2-8 Meet Minitab

Examining Relationships Between Two Variables Graphing Data

_ÿ, Ex?s!ning Rela,lon,hlp, Beÿeen Pÿiÿ o' Vadableÿ

Graph Uÿes

Mÿtrlx Plo!

Mÿrgÿnÿl Iÿot Use a ÿ to ÿsÿeÿs the dÿitrÿutÿnÿ of hvo varÿb'ÿl as weÿ ls the regtÿnshÿ beh'¢eÿ them. A ÿrgÿ7ÿl pÿol ÿ a ÿ¢alleNbt wlh ÿ. ÿ, or d0ÿD bÿa m ÿ mÿrgnÿ,

This Help topic suggests that a scatterplot is the best choice to see the relationship between delivery time and delivery distance.

Create a scatterplot

I or help on any Minitab dialog box, click Help in the lower left corner of the dialog box or press [FI]. For more information on Minitab Help, see Chapter 1 O, Getting Help.

1 Choose Graph ÿ Scatterplot.

2 Choose With Regression, then click OK.

V.rÿchConned. V,ÿbCorÿert Lÿ aÿd GroL,ÿ

C2 Oÿder c3 Arriÿaÿ C4 Days C6 ÿe

Under Y variables, enter Days. Under X variables, enter Distance.

; y varlableÿ i X variables I ÿ" I

Dÿa ÿ,ew., j

Meet Minitab 2-9

Chapter 2 Examining Relationships Between Two Variables

Click Multiple Graphs, then click the By Variables tab.

In By variables with groups in separate panels, enter Center.

6 Click OK in each dialog box.

Vÿbÿs 8yVuiabÿs I

C3ÿc4DaysOÿ'¢CeÿtÿAIrÿ'J [ Cenÿer ÿy vaxÿes ÿ ÿroups ÿ sepÿe pÿeÿs:

OK ] Cÿ,",ce]

Graph window output

OJ 0

Scatterplot of Days vs Distance

0 120 240 360 460

12D 240 360 480 Dklhlnco

Panel vadable: Center

Interpret results

The points on the scatterplot exhibit no apparent pattern at any of the three centers. The regression line for each center is relatively flat, suggesting that the proximity of a delivery location to a shipping center does not affect the delivery time.

Edit scatterplot

To help your colleagues quickly interpret the scatterp]ot, you want to add a footnote to the plot.

1 Click the scatterplot to make it active.

2 Choose Editor ÿ Add ÿ Footnote. [ ÿ,eÿ-ÿp lÿweea deÿ,eeÿ ÿrÿ ÿd ÿaÿo horn ÿ tearer.

3 In Footnote, type Relationship between deliveO, time and distance from shipping center.

4 Click OK.

] J

2-10 Meet Minitab

Using Graph Layout and Printing Graphing Data

Graph window output

Scatterplot of Days vs Distance

1;ÿ0 240 360 480 Cereal Eastern

120 240 360 480 Distance

RelaUonship beb,.,'een deliver/Lime and dlsLaÿe from shipping center. Panel variable: Center

Interpret results

The seatterplot now features a footnote that provides a brief interpretation of the results.

Using Graph Layout and Printing Use Minitab's graph layout tool to place nmltiple graphs on the same page. You can add annotations to the layout and edit the individual graphs within the layout.

To show your supervisor the preliminary results of the graphical anaIysis of the shipping data, display all four graphs on one page.

I"ÿ I When you issue a Minitab command that you previously used in the same session, Minitab iÿI remembers the dialog box settings. To set a dialog box back to its defaults, press IF3].

Meet Minitab 2-11

Chapter 2 Using Graph Layout and Printing

Create graph layout

1 With the scatterplot active, choose Editor ÿ Layout Tool. The active graph, the scatterplot, is already included in the layout.

A list of all open graphs

Buttons used to move graphs to and from the layout

The next graph -J to be moved to the layout

Scÿt t e*ÿot oÿ #dyÿ vs Iÿt ÿe

"'' ,'ÿ "a¢ÿ4 ÿ7o'

e4 ÿ ÿo a6 ÿ

2 Click the scatterplot and drag it to the bottom right corner of the layout,

3 Click [] to place the individual value plot in the upper-left corner of the layout.

4 Click [] to place the grouped histogram in the upper-right corner.

5 Cliek ÿ to place the paneled histogram in the lower-left corner.

6 Click Finish.

J Graph window output

IoÿxÿJÿ Wkÿ lÿt of Oÿ

hÿtaÿam ef Oays ÿa t te/ioÿt nf Days W 134st azÿe

If the worksheet data change after you create a layout, Minitab does not automatically update the graphs in the layout, You must re-create the layout with the updated individual graphs.

Meet Minitab

Saving Projects Graphing Data

Annotate the layout

You want to add a descriptive title to the layout.

1 Choose Editor ÿ Add I,- Title.

2 In Title, type Graphical Analysis of Shipping Center Data. Click OK.

Graph window output

Graphical Analysis of Shipping Center Data Indÿduÿ Vÿ! Rot of Days

iI " i : °

tÿstoÿ of ÿ Tÿe

i z ÿ 4 s ÿ 7oÿ'

cattapÿt of Da't; vs Iÿstance

Print graph layout

You can print an individual graph or a layout just as you would any other Minitab window.

1 Click the Graph window to make it active, then choose File * Print Graph.

2 Click OK.

Saving Projects Minitab data are saved in worksheets. You can also save Minitab projects which can

contain multiple worksheets. A Minitab project contains all your work, including the data, Session window output, graphs, history of your session, ReportPad contents, and dialog box settings. When you open a project, you can resume working where you left off.

It is a good practice to save your work to a location outside the Program Files folder. While working through this book, files are saved to a Meet Minitab folder in the My Documents folder. You can save files to a location of your choice (outside the

Program Files folder).

Meet Minitab 2-13

Chapter 2 What's Next

Save a Minitab project

Save all of your work in a Minitab project.

Choose File ÿ Save Project As.

Navigate to the folder in which you want to save your files.

My Recerÿ Docks

Deÿktop

In File name, type My_GraDhs.MPJ. Minitab automatically adds the extension .MPJ to the file name when you save the

project.

My Doÿs

Mÿ ÿu -Mu Grÿs MPJ

My Neiwÿk S ave aÿ ÿ FNiva& N e;ÿr.t ['.M PJ} ZJ Caned Piÿce=

Click Save. oeÿ9"llCSon,.

• ÿ l lf you close a project before saving it, Minitab prompts you to save the project,

What's Next The graphical output indicates that the three shipping centers have different delivery times for book orders. In the next chapter, you display descriptive statistics and perform an analysis of variance (ANOVA) to test whether the differences among the shipping centers are statistically significant.

2-14 Meet Minitab

3 Analyzing Data

Objectives In this chapter, you:

[] Display and interpret descriptive statistics, page 3-2

m Perform and interpret a one-way ANOVA, page 3-4

[] Display and interpret built-in graphs, page 3-4

-, Access the StatGuide, page 3-8

[] Use the Project Manager, page 3-8

Overview

The field of statistics provides principles and methodologies for collecting, summarizing, analyzing, and interpreting data, and for drawing conclusions from analysis results. Statistics can be used to describe data and to make inferences, both

of which can guide decisions and improve processes and products.

Minitab provides:

[] Many statistical methods organized by category, such as regression, ANOVA, quality tools, and time series

[] Built-in graphs to help you understand the data and validate results

E The ability to display and store statistics and diagnostic measures

This chapter introduces Minitab's statistical commands, built-in graphs, StatGuide, and Project Manager. You want to assess the number of late and back orders, and test whether the difference in delivery time among the three shipping centers is statistically significant.

For more information on Minitab's statistical features, go to Stat menu in the Minitab Help index.

( Meet Minitab 3-1

Chapter 3 Displaying Descriptive Statistics

Displaying Descriptive Statistics Descriptive statistics summarize and describe the prominent features of data.

Use Display Descriptive Statistics to find out how many book orders were delivered on time, how many were late, and the number that were initially back ordered for each shipping center.

Display descriptive

statistics 2

If continuing from the previous chapter, choose File • New, then choose Minitab Project. Click OK. Otherwise, just start Minitab.

Choose File • Open Worksheet.

Click Look in Minitab Sample Data folder, near the bottom of the dialog box.

In the Sample Data folder, double-click Meet Minitab, then choose ShippingData.MTW. Click Open. This worksheet is the same one you used in Chapter 2, Graphing Data.

Choose Stat ÿ Basic Statistics ÿ Display Descriptive Statistics.

In Variables, enter Days.

In By variables (optional), enter Center Status.

For most Minitab commands, you only need to complete the main dialog box to execute the command. But, you can often use subdialog boxes to modify the analysis or display additional output, like graphs.

C20rdeÿ Days C3 Arrivtd

C5 Status ¢6 DLÿt ÿ,ce

Center 5tÿus

8 Click Statistics.

9 Uncheck First quartile, Median, Third quartile, N nonmissing, and N missing.

10 Check N total.

11 Click OK in each dialog box.

ISeÿn F Trimmed mere F ÿnonrÿ ,ÿ ÿofrr, eÿ F ÿm F Nnÿ

F ÿariÿtÿe ÿ Fÿ_"arcan F £umÿalÿ N

F" CÿrcJÿve pÿceÿ

F Eÿ F 5umÿsquÿres Cfÿdÿstaÿs F Pÿn F Sÿrÿss a ÿefaÿ

i F ÿterÿ rÿaÿo F MSSO_ ¢- Fÿ

Changes made in the Statistics subdialog box affect the current session only. To change the default settings for future sessions, use Tools ÿ Options • Individual Commands • Display Descriptive Statistics. When you open the Statistics subdialog box again, it reflects your preferences.

3-2 Meet Minitab

Displaying Descriptive Statistics Analyzing Data

Session window output

Descriptive Statistics: Days

Results for Center = Central

Total Variable Status Count Mean SE Mean StDev Minimum Maximum Days Back order 6 * * * * *

Late 6 6.431 0.157 0.385 6.078 7.070 On time 93 3.826 0.119 1.149 1.267 5.983

Results for Center = Eastern

Total Variable Status Count Mean SE Mean StDev Minimum Maximum Days Back order 8 * * * * *

Late 9 6.678 0.180 0.541 6.254 7.748 On time 92 4.234 0.112 1.077 1.860 5.953

Results for Center = Western

Total Variable Status Count Mean SE Mean StDev Minimum Maximum Days Back order 3 * * * * *

On time 102 2.981 0.108 1,090 0.871 5.681

y Interpret

results

I The Session window displays text output, which you can edit, add to the ReportPad, and print. The ReportPad is discussed in Chapter 7, Generating a Report.

The Session window presents each center's results separately. Within each center, you can find the number of back, late, and on-time orders in the Total Count column.

[] The Eastern shipping center has the most back orders (8) and late orders (9).

[] The Central shipping center has the next greatest number of back orders (6) and late orders (6).

[] The Western shipping center has the smallest number of back orders (3) and no late orders.

You can also review the Session window output for the mean, standard error of the mean, standard deviation, minimum, and maximum of order status for each center. These statistics are not given for back orders because no delivery information exists for these orders.

Meet Minitab 3-3

Chapter 3 Performing an ANOVA

Performing an ANOVA One of the most commonly used methods in statistical decisions is hypothesis testing. Minitab offers many hypothesis testing options, including t-tests and analysis of variance. Generally, a hypothesis test assumes an initial claim to be true, then tests this claim using sample data.

Hypothesis tests include two hypotheses: the null hypothesis (denoted by H0) and the alternative hypothesis (denoted by HI). The null hypothesis is the initial claim and is often specified using previous research or common knowledge. The alternative

hypothesis is what you may believe to be true.

Based on the graphical analysis you performed in the previous chapter and the descriptive analysis above, you suspect that the difference in the average number of delivery days (response) across shipping centers (factor) is statistically significant. To verify this, perform a one-way ANOVA, which tests the equality of two or more means categorized by a single factor. Also, conduct a Tukey's multiple comparison test to see which shipping center means are different.

Perform an 1 ANOVA 2

Choose Stat ÿ ANOVA ÿ One-Way.

In Response, enter Days. In Factor, enter Center.

In many dialog boxes for statistical commands, you can choose frequently used or required options. Use the subdialog box buttons to choose other options.

ct center Reÿe: cz Order c3 arrS'al [ÿ:tor: ]ÿceat er C4 Days

Dÿtar, ce V ÿore re_#duaÿ F ÿ:ÿe ÿts

3 Click Comparisons.

4 Check Tukey's, family error rate, then click OK. tÿy's, fÿ9 ,ÿrÿ rato:l

F E-ÿr's, ÿ error rate;

F L2,u'ÿt's, fart, h'errÿ rate:

I- ÿ's tcKB, fÿ4rÿ error rate:

F--F--f-- f--

3-4 Meet Minitab

Performing an ANOVA Analyzing Data

5 Click Graphs.

For many statistical commands, Minitab includes built-in graphs that help you interpret the results and assess the validity of statistical assumptions.

6 Check Individual value plot and Boxplots of data.

7 Under Residual Plots, choose Four in one.

8 Click OK in each dialog box.

Eaxlÿets e' data

Reÿduÿ FÿY:$ rÿ Iÿ,idual Nÿs i-¸ , Fr,,,¸ : F-: ,,

Re_slduaÿ versus the variaNes:

Session window output

One-way ANOVA: Days versus Center

Source DF SS MS F P Center 2 114.63 57.32 39.19 0.000 Error 299 437.28 1.46 Total 301 551.92

S = 1.209 R-Sq = 20.77ÿ R-Sq(adj) = 20.24ÿ

Level N Mean StDev Central 99 3.984 1.280 Eastern 101 4.452 1.252 Western 102 2.981 1.090

Individual 95ÿ Cls For Mean Based on Pooled StDev ..... + ......... + ......... + ......... +_ -- _

( .... *___)

( .... , .... )

( .... .___)

..... + ......... + ......... + ......... + ....

3.00 3.50 4.00 4.50

Pooled StDev = 1.209

Grouping Information Using Tukey Method

Center N Mean Grouping Eastern 101 4.452 A Central 99 3.984 B Western 102 2.981 C

Means that do not share a letter are significantly different.

Meet Minitab 3-5

Chapter 3 Performing an ANOVA

Tukey 954 Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Center

Individual confidence level = 98.014

Center = Central subtracted from:

Center Lower Center Upper Eastern 0.068 0.468 0.868 Western -1.402 -1.003 -0.603

......... + ......... + ......... + ......... +

(.-..-..)

(---*---)

......... + ......... + ......... + ......... +

-1.0 0.0 1.0 2.0

Center = Eastern subtracted from:

Center Lower Center Upper ......... + ......... + ......... + ......... +

Western -1.868 -1.471 -1.073 (---*---) + ......... + ÷ 4-

-i.0 0.0 1.0 2.0

Interpret results

The decision-making process for a hypothesis test can be based on the probability value (p-value) for the given test.

If the p-value is less than or equal to a predetermined level of significance ((z-level), then you reject the null hypothesis and claim support for the alternative hypothesis.

If the p-value is greater than the (z-level, you fail to reject the null hypothesis and cannot claim support for the alternative hypothesis.

In the ANOVA table, the p-value (0.000) provides sufficient evidence that the average delivery time is different for at least one of the shipping centers from the others when (z is 0.05. In the individual 95% confidence intervals table, notice that none of the intervals overlap, which supports the theory that the means are statistically different. However, you need to interpret the multiple comparison results to see where the differences exist among the shipping center averages.

Tukey's test provides grouping information and two sets of multiple comparison intervals. In the grouping table, factor levels within the same group are not significantly different from each other. Each shipping center is in a different group. Therefore, all levels means have signifieanfly different average delivery times.

The Tukey confidence intervals show:

[] Central shipping center mean subtracted from Eastern and Western shipping center means

[] Eastern shipping center mean subtracted from Western center mean

3-6 Meet Minitab

Performing an ANOVA Analyzing Data

The first interval in the first set of the Tukey output is 0.068 to 0.868. That is, the mean delivery time of the Eastern center minus that of the Central center is somewhere between 0.068 and 0.868 days. The Eastern center's deliveries take longer than the Central center's deliveries. You similarly interpret the other Tukey test results. The means for all shipping centers differ significantly because all of the confidence intervals exclude zero. Therefore, all the shipping centers have

significantly different average delivery times. The Western shipping center has the fastest mean delivery time (2.981 days).

Graph window output

Individual Value Plot of Days vs Center 8ÿ

7 ÿ

aoxplot of Days 8

0 Cent3Cÿalral ÿ€ÿm WeCoera

Center Eaÿ Western Center

Residual Plots for Days

Normal probability Plot

,J , J ÿ - 2 3,0

Versus Rts

3r5 4 0 Fitted VeJue

4.5

Histogram

0 Rÿllfd, al

Versus Order

atlon Order

Interpret results

The individual value plots and boxplots indicate that the delivery time varies by shipping center, which is consistent with the graphs from the previous chapter. The boxplot for the Eastern shipping center indicates the presence of one outlier (indicated by *), which is an order with an unusually long delivery time.

Use residual plots, available with many statistical commands, to check statistical assumptions:

= Normal probability plot-- to detect nonnormality. An approximately straight line indicates that the residuals are normally distributed.

= Histogram of the residuals--to detect multiple peaks, oufliers, and nonnormality. The histogram should be approximately symmetric and bell-shaped.

Meet Minitab 3-7

Chapter 3 Using Minitab's Project Manager

Residuals versus the fitted values--to detect nonconstant variance, missing higher-order terms, and outliers. The residuals should be scattered randomly around zero.

Residuals versus order--to detect time-dependence of residuals. The residuals should exhibit no clear pattern.

For the shipping data, the four-in-one residual plots indicate no violations of statistical assumptions. The one-way ANOVA model fits the data reasonably well.

Y Save project

y Access

StatGuide

In Minitab, you can display each of the residual plots on a separate page. You can also create a plot of the residuals versus the variables.

You want more information on how to interpret a one-way ANOVA, particularly Tukey's multiple comparison test. Minitab StatGuide provides detailed information about the Session and Graph window output for most statistical commands.

1 Place your cursor anywhere in the one-way ANOVA Session window output.

2 Click [ÿ on the Standard toolbar.

You want to learn more about Tukey's multiple comparison method, In the Contents pane, click Tukey's method.

4 If you like, use [] [] to browse through the one-way ANOVA topics.

5 In the StatGuide window, click D to close it.

I For more information about using the StatGuide, see StatGuide on page 10-8.

Save all your work in a Minitab project.

1 Choose File ÿ Save ProjectAs.

2 Navigate to the folder in which you want to save your files.

3 In File name, type My_Stats.MPJ.

4 Click Save.

Using Minitab's Project Manager Now you have a Minitab project that contains a worksheet, several graphs, and

Session window output from your analyses. The Project Manager helps you navigate, view, and manipulate parts of your Minitab project.

Use the Pro)ect Manager to view the statistical analyses you just conducted.

3-8 Meet Minitab

Using Minitab's Project Manager Analyzing Data

Open Project Manager

1 To access the Project Manager, click [] on the Project Manager toolbar or press [Ctrl]+[I].

J My 5tatÿ.PÿJ Sesÿ tÿory

Rÿted Iÿcÿerÿ5

pphgOaÿa,HrW cÿkÿm

Lÿ3 ÿ'ÿes

Session j Wockÿheeÿ

Descrÿo Sÿaÿcs: Days ÿhÿppÿ'xÿDaÿa,HTW Reÿs for Center = Centÿaÿ ÿppÿOÿa.MTW Resÿs foÿ Ceÿer ÿ Eaÿem SI'ÿa,NTW

[] Resets for Cenÿ = Weÿern ÿa,MTW [] Oÿoÿw/ANOVA: Days vÿuÿ Cerÿeÿ ÿa,MIwV

In&iÿaaÿ vaho Fÿ oÿ Oayÿ vs cenÿ ÿpaÿDÿa ,Mÿ oÿ ÿ Days Slÿaÿa,Mÿ€:

[] Reÿ Moÿ fÿ Dayÿ ÿaÿa,MTW

You can easily view the Session window output and graphs by choosing from the list in the right pane. You can also use the icons on the Project Manager toolbar to access different output.

For more information, see Project Manager on page 11-3.

View Session window output

You want to review the one-way ANOVA output. To become familiar with the Project Manager toolbar, use the Show Session Folder icon [] on the toolbar, which opens the Session window.

1 Click [ÿ] on the Project Manager toolbar.

2 Double-click One-way ANOVA: Days versus Center in the left pane.

Meet Minitab 3-9

Chapter 3 Using Minitab's Project Manager

One-way ANOVA: Days versus Center

Source BF 33 HS F P Caner 2 114,03 57.32 39.19 0,000 Erroÿ 299 437.28 1.46 Total 301 351.92

S = 1,209 R-3K = 20.77% R-Sq(adj) = 20,24%

Individual 95% CIs For Hean Based on Pooled 3tPav

Level N Hean 3uOev ..... + ........ -+ ......... + ......... + .... Central 99 3.984 1,280 (----*---) Eastern i01 4,432 1.252 (----*----) Vest.eKn 102 2.981 1,090 (----1---)

..... + ......... + ......... + ......... + .... 3.00 3,ÿ0 4,00 4,30

Bÿouplng Information gsinÿ Tokey ¾eUhod

Centeÿ N Mean 0ÿouplng Eastern 101 4.452 A Central 09 3.904 B Vesrern 102 2.081 C

Means that do not share a letteÿ aÿe slgnificantly different.

Tukey 93% Siÿult.aneous Confidence Inr.ervals All Pairuise Comparisons among Levels of Center

The Project Manager displays the one-way ANOVA Session window output in the right pane.

View graphs You also want to view the boxplot again. Use the Show Graphs ieon ÿ] on the toolbar.

1 Click ÿ on the Project Manager toolbar.

2 In the left pane, double-click Boxplot of Days in the left pane.

aÿh vÿ vÿ ÿ ÿ Bays ,s cÿ Boxplot of Days

ssÿdu4 Wÿs fÿ Days 8

0. ced'kal Easiern

Center Wes'tem

I1< i >

The Projeet Manager displays the boxplot in the Graph window in the right pane.

3-10 Meet Minitab

What's Next Analyzing Data

What's Next The descriptive statistics and ANOVA results indicate that the Western center has the fewest late and back orders and the shortest delivery time. In the next chapter, you create a control chart and conduct a capability analysis to investigate whether the Western shipping center's process is stable over time and is capable of operating within specifications.

Meet Minitab 3-11

Chapter 3 What's Next

3-12 Meet Minitab

4 Assessing Quality

Objectives In this chapter, you:

[] Set options for control charts, page 4-2

[] Create and interpret control charts, page 4-3

[] Update a control chart, page 4-5

[] View subgroup information, page 4-7

[] Add a reference line to a control chart, page 4-7

[] Conduct and interpret a capability analysis, page 4-9

Overview Quality is the degree to which products or services meet the needs of customers. Common objectives for quality professionals include reducing defect rates, manufacturing products within specifications, and standardizing delivery time.

Minitab offers a wide array of methods to help you evaluate quality in an objective, quantitative way: control charts, quality planning tools, and measurement systems analysis (gage studies), process capability, and reliability/survival analysis. This chapter discusses control charts and process capability.

Features of Minitab control charts include:

The ability to choose how to estimate parameters and control limits, as well as display tests for special causes and historical stages.

Customizable attributes, such as adding a reference line, changing the scale, and modifying titles. As with other Minitab graphs, you can customize control charts when and after you create them.

Meet Minitab 4-1

Chapter 4 Evaluating Process Stability

Features of process capability commands include:

[] The ability to analyze many data distribution types, such as normal, exponential, Weibull, gamma, Poisson, and binomial.

[] An array of charts that can be used to verify that the process is in control and that the data follow the chosen distribution.

The graphical and statistical analyses conducted in the previous chapter show that the Western shipping center has the fastest delivery time. In this chapter, you determine whether the center's process is stable (in control) and capable of operating within specifications.

Evaluating Process Stability Use control charts to track process stability over time and to detect the presence of special causes, which are unusual occurrences that are not a normal part of the

process.

Minitab plots a process statistic--such as a subgroup mean, individual observation, weighted statistic, or number of defects--versus a sample number or time. Minitab

draws the:

m Center line at the average of the statistic

i Upper control limit (UCL) at 3 standard deviations above the center line

[] Lower control limit (LCL) at 3 standard deviations below the center line

For all control charts, you can modify Minitab's default chart specifications. For example, you can define the estimation method for the process standard deviation,

specify the tests for special causes, and display process stages by defining historical stages.

@ Set options for control

charts

For additional information on Minitab's control charts, go to Control Charts in the Minitab Help index.

Before you create a control chart for the book shipping data, you want to specify options different from Minitab's defaults for testing the randomness of the data for all control charts.

The Automotive Industry Action Group (AIAG) suggests using the following guidelines to test for specia! causes:

[] Test 1: 1 point > 3 standard deviations from center line

[] Test 2:9 points in a row on the same side of center line

[] Test 3:6 points in a row, all increasing or all decreasing

4-2 Meet Minitab

Evaluating Process Stability Assessing Quality

Also, in accordance with AIAG guidelines, for all future control charts, you want to use a value of 7 for tests 2 and 3. You can easily do this by setting options for your control charts analysis. When you set options, affected dialog boxes automatically reflect your preferences.

Choose Tools )ÿ Options ÿ Control Charts and Quality Tools )ÿ Tests.

Check the first three tests.

Under K for the second test, change the value to 7.

Create X and S chart

Under K for the third test, change the value to 7.

'* Data wÿdow g

Lnyoÿ g poÿ In a rcÿ cÿ saÿe sÿe of center Erie ÿ-

K Imÿt5 tn a roÿ ÿ ÿ,ÿsÿ e¢ aÿ decrÿ 7ÿ--

Esltna4:ÿg Starÿdÿtd DevlO:ÿ ff K poÿs ÿ a row, a&ÿ tÿ aÿ ÿov, n Iÿ Tests

K out of K+I p,:ÿVÿs > 2 staadazd deV, aÿoÿs ffccn cenÿer la-ÿecÿ Ana:yÿ I- (sarÿ sÿde) ,ÿ oat a vÿ,4

other f- K ouÿ ÿff K+I ÿ:6ÿs > 1 standÿd ÿevÿan from Center ÿ I' Steppe Reÿsÿn

K ÿ ÿ a rc'ÿ ÿas'dn I sÿardazd ÿvia6°a °f cerÿer Irÿ lÿ-- system

F K Poÿ"ÿs ÿ a row > I sÿandazd dÿ'ÿaUon from cerÿ ÿ ÿ---

I ÿ I cÿncÿ

5 Click OK.

I If you set options, you can restore Minitab's default settings at any time. For more information,see Restoring Minitab's Default Settings on page 9-6.

Now you are ready to create a contro! chart to see whether the delivery process is stable over time. You randomly select 10 samples for 20 days to examine changes in the mean and variability of delivery time. Create an X and S chart with which you can monitor the process mean and variability simultaneously. Use X and S charts when you have subgroups of size 9 or more.

1 If continuing from the previous chapter, choose File ÿ New, then choose Minitab Project. Click OK. Otherwise, just start Minitab.

2 Choose File ÿ Open Project.

3 Navigate to C:\Program Files\Minitab\Minitab 16\English\Sample Data\Meet Minitab. (Adjust this if you chose to install Minitab to a location other than the default.)

4 Choose Quality.MPJ. Click Open.

5 Choose Stat ÿ Control Charts ÿ- Variables Charts for Subgroups ÿ Xbar-S.

To create a control chart, you only need to complete the main dialog box. However, you can click any button to select options for customizing your chart.

Meet Minitab 4-3

Chapter 4 Evaluating Process Stability

6 Choose All observations for a chart are in one column, then enter Days.

7 In Subgroup sizes, enter Date.

C2 I:ÿys

I Dayÿ

b'ÿbels.. I

Heÿ J O._K J CÿaceH

You can click any tab to open dialog boxes to eustomize your contro! chart. Available tabs depend on whatever is appropriate for the chart type. Parameters, Estimate, Display, and Storage are available for all control charts. Stages, Tests, S Limits, and Box-Cox are available for most charts.

Click Xbar-S Options, then click the Tests tab. Notice this dialog box reflects the tests and test values you specified earlier. (See Set options for control charts on page 4-2.)

Jpr,.,#onn sCÿted tasts for spedeÿ causes ÿ K I poÿt > K ÿtandaÿd da,.,ÿckÿs frocn cent ex k'ÿ 3ÿ

K points In a rovh ÿ increasing or ÿ deoÿeaÿ,g

r K eÿt: ÿ K+I ÿ > I standard davlaÿoÿ from ceÿ,ÿr Snÿ (saÿ'ÿ s;:de) ÿ--

I F Kpoÿtsbarow>lsÿandarddÿvÿhcmcenÿeriÿa(eÿ.herÿ) [6---

Other options are available for specific charts.

9 Click OK in each dialog box.

Graph window output

Xbar-S Chart of Days

1 3 ÿ 7 9 11 13 15 17 19

061

i 3 5 7 ÿ I2 13 15 17 Iÿ

4-4 Meet Minitab

Evaluating Process Stability Assessing Quality

Interpret and S chart

The data points for the Western shipping center fall within the bounds of the control limits, and do not display any nonrandom patterns. Therefore, the process mean and process standard deviation appear to be in control (stable). The mean (X), is 2.985, and the average standard deviation (S) is 0.629.

Update control chart

Graph updating allows you to update a graph when the data change without re-creating the graph. Graph updating is available for all graphs in the Graph menu (except Stem-and-Leat) and all control charts.

After creating the X and S chart, the Western shipping center manager gives you more data collected on 3/23/2009. Add the data to the worksheet and update the control chart.

Add the data to the worksheet

You need to add both date/time data to C1 and numeric data to C2.

1 Click the Data window to make it active.

2 Place your cursor in any cell in C1, then press [End] to go to the bottom of the worksheet.

3 To add the date 3/23/2009 to rows 201-210:

,, First, type 3/23/2009 in row 201 in C1.

Then, select the cell containing 3/23/2009, place the cursor over the Autofill handle in the lower-right corner of the highlighted cell. When the mouse is over the handle, a cross

symbol (+) appears. Press [Ctrl] and drag the cursor to row 210 to fill the cells with the repeated date value. When you hold [Ctrl] down, a superscript cross appears above the Autofill cross symbol (++), indicating that repeated, rather than sequential, values will be added to the cells.

4 Add the following data to C2, starting in row 201:

196 3/22/2009 197 3/22/2009 198 13/22J2009 199 13/22/2009 200 13/22/2009 201 ÿ++ 202 I 208! 2o41

<, I

, F €ÿ-!ÿ ! c2 I c3 Iÿ' Date i Days 195 3/22/2009 2,50

2.85:

2.69

1.83=

3.592.821v t

>i '

3.60 2.40 2.80 3.21 2.40 2.75 2.79 3.40 2.58 2.50

Meet Minitab 4-5

Chapter 4 Evaluating Process Stability

If the data entry arrow is facing downward, pressing [Enter] moves the cursor to the next cell down.

Data entry arrow -- • I cl-D I c2 c3 eatÿ eaÿI

201 /3/23ÿooB, 3.6oi 202 13/23/20091 2.40' 203 13/23/2009 2.80i 204 i3,,"23/2009 ! 3.21i 205 3/23/2009 i 2.401 206 /3,,'23/2009 i 2.75i 207 13/23/2009 i 2,79:, 208 3/23/2009 j 3.40i 209 i3/23/2009ÿ, 2.58! 2,0 i3/23/2oo9 .... 21!! i ;

< , I

5 Verify that you entered the data correctly.

Update the control chart

1 Right-click the X and S chart and choose Update Graph Now.

Graph window output

Xbar-S Chart of Days

zÿ1 : . : . - , : . = ,,z

1 3 s 7 e ÿ1 ;3 lS Z7 ;9 ZZ

..... g=06ÿ07

z ÿ s 7 9 n 13 IS I7 lÿ 21

The X and S chart now includes the new subgroup. The mean (X = 2.978) and standard deviation (S = 0.6207) have changed slightly, but the process still appears to be in control.

To update all graphs and control charts automatically: 1 Choose Tools ÿ Options ÿ Graphics ÿ Other Graphics Options. 2 Check On creation, set graph to update automatically when data change.

4-6 Meet Minitab

Evaluating Process Stability Assessing Quality

View subgroup

information

As with any Minitab graph, when you move your mouse over the points in a control chart, you see various information about the data.

You want to find out the mean of sample 9, the subgroup with the largest mean.

1 Move your mouse over the data point for sample 9.

Graph window output

Xbar-S Chart of Days

Z751

i ÿ ; ÿ ; n 13 ÿs 17 19 21

o21 ............................................ jLÿo.ÿ7ÿl i ÿ ÿ ÿ ÿ fÿ h ÿ ÿt, iÿ 2'i

Interpret results

The data tip shows that sample 9 has a mean delivery time of 3.369 days.

Add reference line

A goal for the online bookstore is for all customers to receive their orders in 3.33 days (80 hours) on average, so you want to compare the average delivery time for the Western shipping center to this target. You can show the target level on the X chart by adding a reference line.

1 Right-click the X chart (the top chart), and choose Add ÿ Reference Lines.

2 In Show reference lines at Y values,

type 3.33.

3 Click OK.

efeÿeace ÿrÿs at ÿ vakÿes: [3.33

hÿ€ÿ refeÿer, ce Ineÿ at ÿ ÿaÿ poÿ;ons: r

J J

Meet Minitab 4-7

Chapter 4 Evaluating Process Capability

Graph window output

Xbar-S Chart of Days

1 3 5 7 9 11 13 15 17 19 21 ,sampÿ

06 g=osm7

I 3 5 7 9 ll 13 I5 17 19 21

Interpret results

The center line (2) is well below the reference line, indicating that, on average, the Western shipping center delivers books faster than the target of 3.33 days. Only subgroup 9 has a delivery time that falls above the reference line (> 3.33).

Evaluating Process Capability After you determine that a process is in statistical control, you want to know whether the process is capable--does it meet specifications and produce "good" parts or

results? You determine capability by comparing the spread of the process variation to the width of the specification limits. If the process is not in control before you assess its capability, you may get incorrect estimates of process capability.

In Minitab, you can assess process capability graphically by drawing capability histograms and capability plots. These graphs help you assess the distribution of the data and verify that the process is in control. Capability indices, or statistics, are a simple way of assessing process capability. Because process information is reduced to a single number, you can use capability statistics to compare the capability of one process to another. Minitab offers capability analysis for many distribution types, including normal, exponential, Weibull, gamma, Poisson, and binomial.

@ For more information on process capability, go to Process Capability in the Minitab Help index.

4-8 Meet Minitab

Evaluating Process Capability Assessing Quality

Conduct capability

analysis

Now that you know the delivery process is in control, conduct a capability analysis to determine whether the book delivery process is within speeification limits and results in acceptable delivery times. The target value of the delivery process is 3.33 days. The upper specification limit (USL) is 6 (an order that is received after 6 days is considered late); no lower specification limit (LSL) is identified. The distribution is approximately normal, so you can use a normal capability analysis.

1 Choose Stat ÿ Quality Tools Capability Analysis ÿ- Normal.

2 Under Data are arranged as, choose Single column. Enter

Days.

3 In Subgroup size, enter Date.

4 In Upper spec, type 6.

5 Click Options. In Target (adds Cpm to table), type 3.33.

Data aÿe arranged as T{aÿffoÿra,,._j

(me a constant 0ÿ an ID coÿa) C" Suÿa,_ oups across io,ÿ ÿi N°raÿ'"

lÿ,sto,!caÿsLaada,ddÿviÿom [-- (,:.pÿonÿ

As with other Minitab commands, you can modify a capability analysis either by specifying information in the main dialog box or by clicking one of the subdialog box buttons.

6 Click OK in each dialog box.

Graph window output

Process Capability of Days

I LSL Process Da, ta

Ta'ÿet 3.33 LÿL 6 Sarnp'e Mean 2.97781 saÿde N 210 StDevCVVÿ) 0.638177

Tÿ÷t

1 I

1,SO 2,25 3.00 3,75 4,50 5.25 6.00

C!oseÿved Pÿforÿ I F:xp, W, thÿ Peffofÿ Exp, Overdl pedorrnance PFf4 < LSL 'ÿI PPf4 < Lÿ * PPM < LSL * PRx4>USL 0.00 PPM>LIÿ_ 1.09 PPM>LLCL 1.10 pFÿvI Toÿ 0.00 PPM Total 1 09 fÿt4 Totÿ 1,10

potÿaI (Wÿ) ,vÿ-ÿty cp CÿL * UKJ 1.ÿ8 Cpk 1.ÿ

Ovÿal Capalÿt,/ pp * PPL * PPU 1,58 Ppk 1.58 Cpm 1.22

Meet Minitab 4-9

Chapter 4 What's Next

Interpret results

All the potential and overall capability statistics are larger than 1.33 (a generally accepted minimum value), indicating the Western shipping center's process is capable and, therefore, delivers orders in an acceptable amount of time.

The Cpm value (the ratio of the specification spread, USL - LSL, to the square root of the mean squared deviation from the target value) is 1.22, which indicates that the process does not meet the target value. The X chart with the reference line shows that the process average fell below the target value, indicating favorable results. You conclude that customers, on average, are getting their orders sooner than the goal of

3.33 days.

For more information on how to interpret capability analyses, go to the Capability Analysis topics in the StatGuide.

Save project Save all of your work in a Minitab project.

1 Choose File 1,- Save Project As.

2 Navigate to the folder in which you want to save your files.

3 In File name, type My_Quality.MPl.

4 Click Save.

What's Next The quality analysis indicates that the Western shipping center's process is in control and is capable of meeting specification limits. In the next chapter, you design an experiment and analyze the results to investigate ways to further improve the order and delivery process at the Western shipping center.

4-10 Meet Minitab

5 Designing an Experiment

Objectives In this chapter, you:

[] Become familiar with designed experiments in Minitab, page 5-1

[] Create a factorial design, page 5-2

[] View a design and enter data in the worksheet, page 5-5

[] Analyze a design and interpret results, page 5-6

[] Create and interpret main effects and interaction plots, page 5-9

Overview

Design of experiments (DOE) capabilities provide a method for simultaneously investigating the effects of multiple variables on an output variable (response). These experiments consist of a series of runs, or tests, in which purposeful changes are made to input variables or factors, and data are collected at each run. Quality professionals use DOE to identify the process conditions and product components that influence quality and then determine the input variable (factor) settings that maximize results.

Minitab offers four types of designed experiments: factorial, response surface, mixture, and Taguehi (robust). The steps you follow in Minitab to create, analyze, and graph an experimental design are similar for all design types. After you conduct the experiment and enter the results, Minitab provides several analytical and graphing tools to help you understand the results. While this chapter demonstrates the typical steps for creating and analyzing a factorial design, you can apply these steps to any design you create in Minitab.

Meet Minitab 5-1

Chapter 5 Creating an Experimental Design

Features of Minitab DOE commands include:

[] Catalogs of experimental designs from which you can choose, to make creating a design easier

Automatic creation and storage of your design once you have specified its properties

[] Ability to display and store diagnostic statistics, to help you interpret the results

[] Graphs that assist you in interpreting and presenting the results

In this chapter, you want to further improve the amount of time it takes to get orders to customers from the Western shipping center. After evaluating many potentially important factors, you decide to investigate two factors that may decrease the time to

prepare an order for shipment: the order processing system and packing procedure.

The Western center is experimenting with a new order processing system and you want to determine if it will speed up order preparation. The center also has two different packing procedures and you want to investigate which one is more efficient. You decide to conduct a factorial experiment to find out which combination of factors results in the shortest time to prepare an order for shipment. The results of this experiment will help you make decisions about the order processing system and packing procedures used in the shipping center.

I or more information on the types of designs that Minitab offers, go to DOEin the Minitab Help index.

Creating an Experimental Design

Before you can enter or analyze measurement data in Minitab, you must first create an experimental design and store it in the worksheet. Depending on the requirements of your experiment, you can choose from a variety of designs. Minitab helps you select a design by providing a list of all the available designs. Once you have chosen the design and its features, Minitab automatically creates the design and stores it in the worksheet for you.

Select design You want to create a factorial design to examine the relationship between two factors, order processing system and packing procedure, and the time it takes to prepare an order for shipping.

1 If continuing from the previous chapter, choose Hle 1,ÿ New, then choose Minitab Project. Click OK. Otherwise, just start Minitab.

5-2 Meet Minitab

Creating an Experimental Design Designing an Experiment

Choose Stat ÿ DOE ÿ Factorial ÿ Create Factorial Design.

3 Click Display Available Designs.

Name factors and set factor

levels

For most design types, Minitab displays all the possible designs and number of required runs in the

Display Available Designs dialog box.

Click OK to return to the main dialog box.

Under Type of Design, choose 2-level factorial (default generators).

In Number of factors, choose 2.

Click Designs.

The box at the top shows all available designs for the design type and the number of factors you chose. In this example, because you are conducting a factorial design with two factors, you have only one option: a full factorial design with four runs. A two-level design with two factors has 22 (or four) possible factor combinations.

When you create a design in Minitab, initially only two buttons are enabled, Display Available Designs and Designs. The other buttons are enabled after you complete the Designs subdialog box.

tÿ,e oÿ pesÿa a" ÿz4evd fectorÿ (,ÿ 9eneÿ'aors)J (z to lS fÿors) C 2-kÿvd fad4otkÿ ÿ gÿaÿOt 5) (2 to 15 f,ÿ-ÿoÿs) C 24evel st:4tÿot (hatd4e-dÿrÿ factors) (2 to 7 fact.s) " Iÿdÿ*tt-ÿ deÿ (2 to 47 fa,:toÿs)

<" _GeneraJ M factcÿ design (2 to 15 factors)

,.miÿer cf factors: ÿ Dÿst:ÿaz Avÿ Des;ÿ"' !

Avÿabÿ Factodÿ Deÿ31s (ÿ ReÿJcÿ)

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AVÿ Resoÿtÿ II1 Fÿ,ÿ(ÿtÿBLÿ De ÿiÿns FaÿLofs RUnS Fad.oÿs RURÿ FaÿLors Rurÿ

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12-15 2O,24,20,36,...,48 Zÿ-3! ÿ36,40,44,48 44ÿ7 48 16-19 20,24,2B,32,...,ÿ8 32-35 36,ÿ0,44,48

)eÿ Ruÿ Resobÿon 2**(k-p)

f:unÿ'ber °f [ÿÿes fcÿ c°mer p°ÿt$;

8 In Number of replicates for corner points, choose 3.

9 Click OK to return to the main dialog box. Notice that Minitab enables the remaining buttons.

Minitab enters the names and levels you enter for each factor into the worksheet and uses the names as the labels for the factors on the analysis output and graphs. If you do not enter factor levels, Minitab sets the low level at-1 and the high level at 1.

Meet Minitab 5-3

Chapter 5 Creating an Experimental Design

Click Factors.

Click the first row of the Name column to change the name of the first factor. Then, use the arrow keys to navigate within the table, moving across rows or down columns. In the rOW for:

'f.aor i aÿ ! rypÿ i to. ] .Jÿ j

i Pÿ rÿa -Ja 8

i Factor A, type OrderSystem in Name, New in Low, and Current in High. Under Type, choose Text.

m Factor B, type Pack in Name, A in Low, and B in High. Under Type, choose Text.

3 Click OK to return to the main dialog box.

Randomize and store

design

By default, Minitab randomizes the run order of all design types, except Taguchi designs. Randomization helps to ensure that the model meets certain statistical assumptions and can also help reduce the effects of factors not included in the study.

Setting the base for the random data generator ensures you obtain the same run order every time you create the design. While you usually would not do this in practice, setting the base gives the same run order that is used in this example.

1 Click Options.

2 In Base for random data generator, type 9.

3 Make sure Store design in worksheet is checked. Click OK in each dialog box.

fdd lÿ€ÿa .... ¢; Do ÿ fdd (" , , J, , ¢" Foÿd ea ÿ faÿtÿs C rÿ .... : [ ....

R ÿdeÿze r_cÿ /

J_Ba5e for rarÿaÿ dÿa ÿ-ÿratorÿ [9Y IDÿ _ cÿ,__j

5-4 Meet Minitab

Viewing the Design Designing an Experiment

Viewing the Design Every time you create a design, Minitab stores design information and factors in worksheet columns. Open the Data window to see the structure of a typical design. You can also open the worksheet DOE.MTW in the Meet Minitab data folder, which includes the design and the response data.

View design Choose Window Worksheet 1.

1 ! 2¸ z i 11 3i 4 4 i 3 5i I 6 j 12 7 i 10 8 i 7 9 i 6 loi B 111 5 t2 1 9

1 1 1 Current A 2 l 1 New B 3 1 1 Current B 4 1 1 New [3 5 1 1 New A 6 1 1 Current B 7 I I Current A 8 I I New B 9 1 1 Current A

10 1 1 Current 13 11 1 1 New A 12 1 1 New A

The RunOrder column (C2), which is randomly determined, indicates the order in which you should collect data. If you do not randomize a design, the StdOrder and RunOrder columns are the same.

In this example, because you did not add center points or block the design, Minitab sets all the values in C3 and C4 to 1. The factors are stored in columns C5 and C6, labeled OrderSystem and Pack. Because you entered the factor levels in the Factors subdialog box, you see the actual levels in the worksheet.

You can use Stat ÿ DOE 1ÿ Display Design to switch back and forth between a random and standard order display, and between a coded and uncoded display in the worksheet.

To change the factor settings or names, use Stat ÿ DOE Iÿ Modify Design. If you only need to change the factor names, you can type them directly in the Data window.

Entering Data After you conduct the experiment and collect the data, you can enter the data into the worksheet. The characteristie you measure is called a response.

In this example, you measure the number of hours needed to prepare an order for shipment. You obtained the following data from the experiment:

14.72 9.62 13.81 7.97 12.52 13.78 14.64 9.41 13.89 13.89 12.57 14.06

( Meet Minitab 5-5

Chapter 5 Analyzing the Design

Enter data into

worksheet

In the Data window, click the column name cell of C7 and type Hours.

Type the observed hours listed above into the Hours column of the Data window.

StdOrderlRunOrder CenterPt! Blocks i OrclerSyslem' Pack . Hours I t 2

You can enter data in any 3 columns except in those 4

5 containing design information. .6 You can also enter multiple i! responses for an experiment, i01 one per column, it !

!2i

2 I 1 1 Current A 14.72 11 2 1 1 New B 9.62 4 3 1 1 Current B 13.81 3 4 1 1 iNew B 7.97 1 5 1 = 1 =New A 12.52

12 6 1 1 Current B 13.78 10 7 1 1 Current A 14.64 7 8 1 1 New B 9.41 6: 9 1 I Cu,ent A 13.69 8 10 1 1 Current B 13.89 5: 11 I 1 New A 12.57 9 12 I I New A ÿv

• ........ >

I Print a data collection form by choosing File ÿ Print Worksheet and making sure Print Grid

' Lines is checked. Use this form to record measurements while you conduct the experiment.

Analyzing the Design Now that you have created a design and collected the response data, you can fit a model to the data and generate graphs to evaluate the effects. Use the results from the fitted model and graphs to see which factors are important for reducing the number of hours needed to prepare an order for shipment.

Fit a model Because you have created and stored a factorial design, Minitab enables the DOE >- Factorial menu commands Analyze Factorial Design and Factorial Plots. At this point, you can fit a model or generate plots, depending on the design. In this example, you fit the model first.

Choose Stat ÿ DOE ÿ Factorial Analyze Factorial Design.

In Responses, enter Hours.

You must enter a response column before you can open the subdialog boxes.

¢7 Hoÿ5

VCÿOÿU.,. j

5-6 Meet Minitab

Analyzing the Design Designing an Experiment

Click Terms. Check to make sure

thatA: OrderSystem, B: Pack and AB are in the Selected Terms box.

When analyzing a design, always use the Terms subdialog box to select the terms to include in the model. You can add or remove factors and interactions by using the arrow buttons. Use the check boxes to include blocks and center points in the model.

F1 i, ; ,ÿ , ! F ...... , , '

Click OK.

Click Graphs.

Under Effects Plots, check Normal and Pareto.

EIfettÿ Nots mal F ÿmÿ t7 P aeto

Effects plots are only available in factorial designs. Residual plots, helpful in checking model assumptions, can be displayed for all design types.

7 Click OK in each dialog box.

Reÿduaÿ fÿ- Pots: ' Rehear C ÿa.-ÿarÿzed ÿ _Deÿed

F Rÿidÿ vÿ ÿdÿ C Ecur la m,-m F Reÿ vÿrÿ Eaÿ5:

Identify important

effects

Session window output

You can use both the Session window output and the two effects plots to determine which effects are important to your process. First, look at the Session window output.

Factorial Fit: Hours versus OrderSystem, Pack

Estimated Effects and Coefficients for Hours (coded units)

Term Effect Coef SE Coef T P Constant 12.573 0.1929 65.20 0.000 OrderSystem 3.097 1.548 0.1929 8.03 0.000 Pack -2.320 -1.160 0.1929 -6.01 0.000 OrderSystem*Pack 1.730 0.865 0.1929 4.49 0.002

S = 0.668069 PRESS = 8.0337 R-Sq = 93.79% R-Sq(pred) = 86.02% R-Sq(adj) = 91.46%

Meet Minitab 5-7

Chapter 5 Analyzing the Design

Analysis of Variance for Hours (coded units)

Source DF Seq SS Adj SS Adj MS Main Effects 2 44.9152 44.9152 22.4576

OrderSystem I 28.7680 28.7680 28.7680 Pack i 16.1472 16.1472 16.1472

2-Way Interactions i 8.9787 8.9787 8.9787 OrderSystem*Pack i 8.9787 8.9787 8,9787

Residual Error 8 3.5705 3.5705 0.4463 Pure Error 8 3.5705 3.5705 0.4463

Total ii 57.4645

F 50.32 64.46 36.18 20.12 20.12

P 0.000 0.000 0.000 0.002 0.002

Estimated Coefficients for Hours using data in uncoded units

Term Coef Constant 12.5733 OrderSystem 1.54833 Pack -1.16000 OrderSystem*Pack 0.865000

You fit the full model, which includes the two main effects and the two-way interaction. Use the p-values (P) in the Estimated Effects and Coefficients table to determine which effects are significant. Using oÿ = 0.05, the main effects for order

processing system (OrderSystem) and packing procedure (Pack) and the OrderSystem*Pack interaction are statistically significant; that is, their p-values are less than 0.05.

Interpret effects plots

Next, evaluate the normal probability plot and the Pareto chart of the standardized effects to see which effects influence the response, Hours.

To make the normal

probability plot the active window, choose Window I,ÿ Effects Plot for Hours.

Significant terms are identified by a square symbol. OrderSystem (A), Pack (B), and OrderSystem* Pack (A* B) are significant

= o.o5).

Normal Plot of the Standardized Effects (response is Hours, Alpha = 0.05)

/ /

/ ÿA/

/ /

2 To make the Pareto chart

1 -5',0 -2.5 0.0 2,5 5.0 7.5 10.0

Slandardized Effect

the active window, choose Window * Effects Pareto for Hours.

5-8 Meet Minitab

Drawing Conclusions Designing an Experiment

Minitab displays the absolute value of the effects on the Pareto chart. Any effects that extend beyond the reference line are

significant at the default level of 0.05.

OrderSystem (A), Pack (B) and OrderSystem* Pack (A* B) are all significant

o.o5).

Pareto Chart of the Standardized Effects (response is Hours, Alpha = 0.05)

2.306 L

1 l

1 1 2 a 4 s i ÿ

Standardized Effect

Drawing Conclusions

Display factorial plots

Minitab provides design-specific graphs you can use to interpret your results.

In this example, you generate two factorial plots that enable you to visualize the effects--a main effects plot and an interaction plot.

1 Choose Stat 1,- DOE * Factorial ÿ Factorial Plots.

2 Check Main Effects Plot, then click Setup. F _rmterÿoa Faÿt ,, J

F C_utÿ ¢ÿ ,, J

Type oD4eÿ to Lÿe il Fÿs 6" O_ata ÿ'ÿaÿ r- ÿted r4ear, s

3 In Responses, enter Hours.

4 Select the terms you want to plot:

[] Click A:Or&rSystem under Available. Then click ÿ to move A:OrderSystem factor to Selected.

[] Repeat these actions to move B:Pa& to Selected. Click OK.

f r,, ÿ,. ÿ.osponsosl Factors tO Include N Pÿts

A_vailable: 5elecÿed=

__I J -

<< ]

.... l oÿu ...... j

5 Check Interaction Plot, then click Setup.

6 Repeat steps 3 and 4.

Meet Minitab 5-9

Chapter 5 Drawing Conclusions

7 Click OK in each dialog box.

Evaluate plots Examine the plot that shows the effect of using the new versus current order processing system, or using packing procedure A versus B. These one-factor effects are called main effects.

1 Choose Window ÿ Main Effects Plot for Hours to make the main effects plot active.

This point shows the mean of all runs usinc the current order processing system.

This point shows the mean of all runs using the new order processing system.

Main Effects Plot for Hours Data Means

PackOrdelSyÿm

_/ NeW Curnÿnt

\ k

This line shows / the mean of all

the response (Hours) in the experiment.

The order processing system and packing procedure have a similar effect on order preparation time. That is, the line connecting the mean responses for the new and current order processing system has a slope similar to slope of the line connecting the mean response for packing procedure A and packing procedure B. The plot also indicates that orders using:

[] The new order processing system took less time than orders that used the current order processing system.

I Packing procedures B took less time than orders that used packing procedure A

If there were no significant interactions between the factors, a main effects plot would adequately describe where you can get the biggest payoff for changes to your process. Because the interaction in this example is significant, you should next examine the interaction plot. A significant interaction between two factors can affect the interpretation of the main effects.

5-10 Meet Minitab