quality charts

8/19/2019 Quality Charts

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Box and Whisker Plot

A box and whisker plot is a graphical method of displaying variation in a set of data. In most cases a histogram

provides a sufficient display; however, a box and whisker plot can provide additional detail while allowing multiple sets

of data to be displayed in the same graph. Some types are called box and whisker plots with outliers.

Why Use a Box and Whisker Plot?

Box and whisker plots are very effective and easy to read. hey summari!e data from multiple sources and display

the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier,

more effective decision"making.

When to Use a Box and Whisker Plot

#se box and whisker plots when you have multiple data sets from independent sources that are related to each other

in some way. $xamples include test scores between schools or classrooms, data from before and after a process

change, similar features on one part such as cam shaft lobes, or data from duplicate machines manufacturing the

same products.

Box and Whisker Plot Procedure

A box and whisker plot is developed from five statistics.

%. &inimum value ' the smallest value in the data set

(. Second )uartile ' the value below which the lower (*+ of the data are contained

. &edian value ' the middle number in a range of numbers

-. hird )uartile ' the value above which the upper (*+ of the data are contained

*. &aximum value ' the largest value in the data set

or examp le, given the following (/ data points, the five re)uired statistics are displayed.

0umber 1ata

% %% &inimum2 %%

( %%3

%%4

- %(%

* %(-

(nd 5uartile2 %(-


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3 %(-

6 %(*

7 %(3

4 %(3

%/ %(3

&edian2 %(3.*

%% %(6

%( %(6

% %(7

%- %(4

%* %/

rd 5uartile2 %/

%3 %/

%6 %%

%7 %(

%4 %

(/ %3 &aximum2 %3

0ote that for a data set with an even number of values, the median is calculated as the average of the two middle

values.

8ere are the data represented in box and whisker plot format.


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9eft2 he center represents the middle */+, or */th percentile of the data set and is derived using the lower and

upper )uartile values. he median value is displayed inside the :box.: he maximum and minimum values are

displayed with vertical lines :whiskers:< connecting the points to the center box.

=ight2 or comparison, a histogram of the data is also shown, showing the fre)uency of each value in the data set.

Box and Whisker Plot Example

Suppose you wanted to compare the performance of three lathes responsible for the rough turning of a motor shaft.

he design specification is %7.7* >?" %./ mm.

1iameter measurements from a sample of shafts taken from each roughing lathe are displayed in a box and whisker

plot.

%. 9athe % appears to be making good parts, and is centered in the tolerance.

(. 9athe ( appears to have excess variation, and is making shafts below the minimum diameter.

. 9athe appears to be performing comparably to 9athe %. 8owever, it is targeted low in the tolerance, and

is making shafts below specification.

Create a Box and Whisker Plot

1ownload the box and whisker plot template. &ost software packages that perform statistical analysis can create box

and whisker plots.

References

http://asq.org/sixsigma/tools-exchange/docs/box-plot.xlshttp://asq.org/sixsigma/tools-exchange/docs/box-plot.xls


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%. @uran, @. &. and rank &. ryna, Juran’s Quality Control Handbook, Fourth Edition, &craw'8ill, Inc.,

%477.

(. ortman, Bill, Certified Six Sigma Black Belt rimer, !e"ision #$, 5uality Council of Indiana.


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Check Sheet

Also called2 defect concentration diagram

A check sheet is a structured, prepared form for collecting and analy!ing data. his is a generic tool that can be

adapted for a wide variety of purposes.

When to Use a Check Sheet

• hen data can be observed and collected repeatedly by the same person or at the same location.

• hen collecting data on the fre)uency or patterns of events, problems, defects, defect location, defect

causes, etc.

• hen collecting data from a production process.

Check Sheet Procedure

%. 1ecide what event or problem will be observed. 1evelop operational definitions.

(. 1ecide when data will be collected and for how long.

. 1esign the form. Set it up so that data can be recorded simply by making check marks or Ds or similar

symbols and so that data do not have to be recopied for analysis.

-. 9abel all spaces on the form.

*. est the check sheet for a short trial period to be sure it collects the appropriate data and is easy to use.

3. $ach time the targeted event or problem occurs, record data on the check sheet.

Check Sheet Example

he figure below shows a check sheet used to collect data on telephone interruptions. he tick marks were added as

data was collected over several weeks.

Check Sheet Example

$xcerpted from 0ancy =. agueEs he 5uality oolbox, Second $dition, AS5 5uality Fress, (//-, pages %-%'%-(.

Create a Check Sheet

rack up to %/ defects on each day of the week. his tool also creates a histogram, bar chart and Fareto chart using

the check"sheet data. Start using the check sheet tool $xcel, 7* GB


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Control Chart

Also called2 statistical process control

he control chart is a graph used to study how a process changes over time. 1ata are plotted in time order. A control

chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower

control limit. hese lines are determined from historical data. By comparing current data to these lines, you can drawconclusions about whether the process variation is consistent in control< or is unpredictable out of control, affected

by special causes of variation


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• Lbvious consistent or persistent patterns that suggest something unusual about your data and

your process.

Figure 1 Control Chart2 Lut"of"Control Signals

*. Continue to plot data as they are generated. As each new data point is plotted, check for new out"of"

control signals.

3. hen you start a new control chart, the process may be out of control. If so, the control limits calculated

from the first (/ points are conditional limits. hen you have at least (/ se)uential points from a period

when the process is operating in control, recalculate control limits.

$xcerpted from 0ancy =. agueEs he 5uality oolbox, Second $dition, AS5 5uality Fress, (//-, pages %**"%*7.

emplate created by 1ean Christolear.

http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224


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Design of Experiments D!E"

his branch of applied statistics deals with planning, conducting, analy!ing and interpreting controlled tests to

evaluate the factors that control the value of a parameter or group of parameters.

A strategically planned and executed experiment may provide a great deal of information about the effect on a

response variable due to one or more factors. &any experiments involve holding certain factors constant and alteringthe levels of another variable. his Lne'actor'at'a'ime or LA< approach to process knowledge is, however,

inefficient when compared with changing factor levels simultaneously.

&any of the current statistical approaches to designed experiments originate from the work of =. A. isher in the early

part of the (/th century. isher demonstrated how taking the time to seriously consider the design and execution of

an experiment before trying it helped avoid fre)uently encountered problems in analysis. Gey concepts in creating a

designed experiment include blocking, randomi!ation and replication.

A well'performed experiment may provide answers to )uestions such as2

• hat are the key factors in a processM

• At what settings would the process deliver acceptable performanceM

• hat are the key, main and interaction effects in the processM

• hat settings would bring about less variation in the outputM

A repetitive approach to gaining knowledge is encouraged, typically involving these consecutive steps2

%. A screening design which narrows the field of variables under assessment.

(. A Jfull factorialK design which studies the response of every combination of factors and factor levels, and

an attempt to !one in on a region of values where the process is close to optimi!ation.

. A response surface design to model the response.

Blocking: hen randomi!ing a factor is impossible or too costly, blocking lets you restrict randomi!ation by carrying

out all of the trials with one setting of the factor and then all the trials with the other setting.

Randomization: =efers to t he order in which the trials of an experiment are performed. A randomi!ed se)uence

helps eliminate effects of unknown or uncontrolled variables.

Replication: =epetition of a complete experimental treatment, including the setup.

Contributed by Geith &. Bower, www.GeithBower.com.

utorial !emplate

• 1esign of $xperiments utorial

• 1esign of $xperiments emplate $xcel, %/- GB


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#istogram

A fre)uency distribution shows how often each different value in a set of data occurs. A histogram is the most

commonly used graph to show fre)uency distributions. It looks very much like a bar chart, but there are important

differences between them.

When to Use a #istogram• hen the data are numerical.

• hen you want to see the shape of the dataEs distribution, especially when determining whether the output

of a process is distributed approximately normally.

• hen analy!ing whether a process can meet the customerEs re)uirements.

• hen analy!ing what the output from a supplierEs process looks like.

• hen seeing whether a process change has occurred from one time period to another.

• hen determining whether the outputs of two or more processes are different.

• hen you wish to communicate the distribution of data )uickly and easily to others.

#istogram Construction

%. Collect at least */ consecutive data points from a process.

(. #se the histogram worksheet to set up the histogram. It will help you determine the number of bars, the

range of numbers that go into each bar and the labels for the bar edges. After calculating & in step ( of

the worksheet, use your Hudgment to adHust it to a convenient number. or example, you might decide to

round /.4 to an even %./. he value for & must not have more decimal places than the numbers you will

be graphing.

. 1raw x" and y"axes on graph paper. &ark and label the y"axis for counting data values. &ark and label the

x"axis with the ' values from the worksheet. he spaces between these numbers will be the bars of the

histogram. 1o not allow for spaces between bars.

-. or each data point, mark off one count above the appropriate bar with an D or by shading that portion of

the bar.

#istogram $nalysis

• Before drawing any conclusions from your histogram, satisfy yourself that the process was operating

normally during the time period being studied. If any unusual events affected the process during the time

period of the histogram, your analysis of the histogram shape probably cannot be generali!ed to all time

periods.

• Analy!e the meaning of your histogramEs shape.

"pical histogram shapes and #hat the" mean $$

$xcerpted from 0ancy =. agueEs (he Quality (oolbox , Second $dition, AS5 5uality Fress, (//-, pages (4("(44.

Create a #istogram

1ata Foints 8istogram $xcel, 6* GB< ' Analy!e the fre)uency distribution of up to (// data points using this simple,

but powerful, histogram generating tool.

http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram-worksheet.htmlhttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram-worksheet.htmlhttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.htmlhttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.htmlhttp://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/data-point-histogram.xlshttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram-worksheet.htmlhttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.htmlhttp://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/data-point-histogram.xls


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Check Sheet 8istogram $xcel, 6 GB< ' Analy!e the number of defects for each day of the week. Start by tracking

the defects on the check sheet. he tool will create a histogram using the data you enter.

emplate created by 1ean Christolear.

Scatter Diagram

Also called2 scatter plot, D'N graph

he scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between

them. If the variables are correlated, the points will fall along a line or curve. he better the correlation, the tighter the

points will hug the line.

When to Use a Scatter Diagram

• hen you have paired numerical data.

• hen your dependent variable may have multiple values for each value of your independent variable.

• hen trying to determine whether the two variables are related, such asO

o hen trying to identify potential root causes of problems.

o After brainstorming causes and effects using a fishbone diagram, to determine obHectively

whether a particular cause and effect are related.

o hen determining whether two effects that appear to be related both occur with the same

cause.

o hen testing for autocorrelation before constructing a control chart.

Scatter Diagram Procedure

%. Collect pairs of data where a relationship is suspected.

(. 1raw a graph with the independent variable on the hori!ontal axis and the dependent variable on the

vertical axis. or each pair of data, put a dot or a symbol where the x"axis value intersects the y"axis

value. If two dots fall together, put them side by side, touching, so that you can see both.<

. 9ook at the pattern of points to see if a relationship is obvious. If the data clearly form a line or a curve, you

may stop. he variables are correlated. Nou may wish to use regression or correlation analysis now.

Ltherwise, complete steps - through 6.

-. 1ivide points on the graph into four )uadrants. If there are D points on the graph,

• Count D?( points from top to bottom and draw a hori!ontal line.

• Count D?( points from left to right and draw a vertical line.

• If number of points is odd, draw the line through the middle point.

*. Count the points in each )uadrant. 1o not count points on a line.

3. Add the diagonally opposite )uadrants. ind the smaller sum and the total of points in all )uadrants.

A P points in upper left > points in lower right

B P points in upper right > points in lower left

5 P the smaller of A and B

0 P A > B

http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/check-sheet-histogram.xlshttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/check-sheet-histogram.xls


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6. 9ook up the limit for 0 on the trend test table.

• If 5 is less than the limit, the two variables are related.

• If 5 is greater than or e)ual to the limit, the pattern could have occurred from random chance.

Scatter Diagram Example

he QQ"-// manufacturing team suspects a relationship between product purity percent purity< and the amount of

iron measured in parts per million or ppm points in lower right P 4 > 4 P %7

B P points in upper right > points in lower left P > P 3

5 P the smaller of A and B P the smaller of %7 and 3 P 3

0 P A > B P %7 > 3 P (-

hen they look up the limit for 0 on the trend test table. or 0 P (-, the limit is 3.

5 is e)ual to the limit. herefore, the pattern could have occurred from random chance, and no relationship is

demonstrated.


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Scatter %iagram Example

Scatter Diagram Considerations

• 8ere are some examples of situations in which might you use a scatter diagram2

o Rariable A is the temperature of a reaction after %* minutes. Rariable B measures the color of

the product. Nou suspect higher temperature makes the product darker. Flot temperature and

color on a scatter diagram.

o Rariable A is the number of employees trained on new software, and variable B is the number of

calls to the computer help line. Nou suspect that more training reduces the number of calls. Flot

number of people trained versus number of calls.

o o test for autocorrelation of a measurement being monitored on a control chart, plot this pair of

variables2 Rariable A is the measurement at a given time. Rariable B is the same measurement,but at the previous time. If the scatter diagram shows correlation, do another diagram where

variable B is the measurement two times previously. Geep increasing the separation between

the two times until the scatter diagram shows no correlation.

• $ven if the scatter diagram shows a relationship, do not assume that one variable caused the other. Both

may be influenced by a third variable.

• hen the data are plotted, the more the diagram resembles a straight line, the stronger the relationship.

• If a line is not clear, statistics 0 and 5< determine whether there is reasonable certainty that a relationship

exists. If the statistics say that no relationship exists, the pattern could have occurred by random chance.

• If the scatter diagram shows no relationship between the variables, consider whether the data might be

stratified.• If the diagram shows no relationship, consider whether the independent x"axis< variable has been varied

widely. Sometimes a relationship is not apparent because the data donEt cover a wide enough range.

• hink creatively about how to use scatter diagrams to discover a root cause.

• 1rawing a scatter diagram is the first step in looking for a relationship between variables.

$xcerpted from 0ancy =. agueEs he 5uality oolbox, Second $dition, AS5 5uality Fress, (//-, pages -6%'-6-.

http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224


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%ish&one Diagram

Also Called2 Cause'and'$ffect 1iagram, Ishikawa 1iagram

Rariations2 cause enumeration diagram, process fishbone, time'delay fishbone, C$1AC cause'and'effect diagram

with the addition of cards


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Fish&one %iagram Example

or example, under the heading J&achines,K the idea Jmaterials of constructionK shows four kinds of e)uipment

and then several specific machine numbers.

0ote that some ideas appear in two different places. JCalibrationK shows up under J&ethodsK as a factor in the

analytical procedure, and also under J&easurementK as a cause of lab error. JIron toolsK can be considered a

J&ethodsK problem when taking samples or a J&anpowerK problem with maintenance personnel.

$xcerpted from 0ancy =. agueEs (he Quality (oolbox , Second $dition, AS5 5uality Fress, (//-, pages (-6'

(-4.

Create a %ish&one Diagram

Analy!e process dispersion with this simple, visual tool. he resulting diagram illustrates the main causes and

subcauses leading to an effect symptom


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Pareto Chart

Also called2 Fareto diagram, Fareto analysis

Rariations2 weighted Fareto chart, comparative Fareto charts

A Fareto chart is a bar graph. he lengths of the bars represent fre)uency or cost time or money


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If all complaints cause e)ual distress to the customer, working on eliminating document"related complaints would

have the most impact, and of those, working on )uality certificates should be most fruitful.

$xample %

$xample (

$xcerpted from 0ancy =. agueEs (he Quality (oolbox , Second $dition, AS5 5uality Fress, (//-, pages 63"67.

Create a Pareto Chart

Analy!e the occurrences of up to %/ defects. Start by entering the defects on the check sheet. his tool creates a

Fareto chart using the data you enter. Start using the Fareto chart tool $xcel'indows, 7* GB


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Strati'cation

Stratification is a techni)ue used in combination with other data analysis tools. hen data from a variety of sources

or categories have been lumped together, the meaning of the data can be impossible to see. his techni)ue

separates the data so that patterns can be seen.

When to Use Strati'cation

• Before collecting data.

• hen data come from several sources or conditions, such as shifts, days of the week, suppliers or

population groups.

• hen data analysis may re)uire separating different sources or conditions.

Strati'cation Procedure

%. Before collecting data, consider which information about the sources of the data might have an effect on

the results. Set up the data collection so that you collect that information as well.

(. hen plotting or graphing the collected data on a scatter diagram, control chart, histogram or other

analysis tool, use different marks or colors to distinguish data from various sources. 1ata that are

distinguished in this way are said to be Jstratified.K

. Analy!e the subsets of stratified data separately. or example, on a scatter diagram where data are

stratified into data from source % and data from source (, draw )uadrants, count points and determine the

critical value only for the data from source %, then only for the data from source (.

Strati'cation Example

he QQ'-// manufacturing team drew a scatter diagram to test whether product purity and iron contamination were

related, but the plot did not demonstrate a relationship. hen a team member reali!ed that the data came from three

different reactors. he team member redrew the diagram, using a different symbol for each reactorEs data2


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0ow patterns can be seen. he data from reactor ( and reactor are circled. $ven without doing any calculations, it

is clear that for those two reactors, purity decreases as iron increases. 8owever, the data from reactor %, the solid

dots that are not circled, do not show that relationship. Something is different about reactor %.

Strati'cation Considerations

• 8ere are examples of different sources that might re)uire data to be stratified2

o $)uipment

o Shifts

o 1epartments

o &aterials

o Suppliers

o 1ay of the week

o ime of day

o Froducts

Survey data usually benefit from stratification.

•

Always consider before collecting data whether stratification might be needed during analysis. Flan tocollect stratification information. After the data are collected it might be too late.

• Ln your graph or chart, include a legend that identifies the marks or colors used.

$xcerpted from 0ancy =. agueEs (he Quality (oolbox , Second $dition, AS5 5uality Fress, (//-, pages -7*'-76.

Create a Stratication Diagram

http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224


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Stratification 1iagram $xcel, 67 GB< ' Analy!e data collected from various sources to reveal patterns or relationships

often missed by other data analysis techni)ues. By using uni)ue symbols for each source, you can view data sets

independently or in correlation to other data sets.

http://asq.org/sixsigma/tools-exchange/docs/stratification-diagram-template.xlshttp://asq.org/sixsigma/tools-exchange/docs/stratification-diagram-template.xls


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Sur(ey

Rariations2 )uestionnaire, e"survey, telephone interview, face"to"face interview, focus group.

Surveys collect data from a targeted group of people about their opinions, behavior or knowledge. Common types of

surveys are written )uestionnaires, face'to'face or telephone interviews, focus groups and electronic e"mail or eb

site< surveys.

Surveys are commonly used with key stakeholders, especially customers and employees, to discover needs or

assess satisfaction.

When to Use a Sur(ey

• hen identifying customer re)uirements or preferences.

• hen assessing customer or employee satisfaction, such as identifying or prioriti!ing problems to

address.

• hen evaluating proposed changes.

• hen assessing whether a change was successful.

• Feriodically, to monitor changes in customer or employee satisfaction over time.

Sur(ey Basic Procedure

0ote2 ItEs often worthwhile to have a survey prepared and administered by a research organi!ation. 8owever, you will

still need to work with them on the following steps so that the survey will be most useful.

%. 1ecide what you want to learn from the survey and how you will use the results.

(. 1ecide who should be surveyed. Identify population groups; if they are too large to permit surveying

everyone, decide how to obtain a sample. 1ecide what demographic information is needed to analy!e and

understand the results.

. 1ecide on the most appropriate type of survey.

-. 1ecide whether the surveyEs answers will be numerical rating, numerical ranking, yes'no, multiple choice

or open"endedTor a mixture.

*. Brainstorm )uestions and, for multiple choice, the list of possible answers. Geep in mind what you want to

learn, and how you will use the results. 0arrow down the list of )uestions to the absolute minimum that

you must have to learn what you need to learn.

3. Frint the )uestionnaire or interviewersE )uestion list.

6. est the survey with a small group. Collect feedback.

• hich )uestions were confusingM

• ere any )uestions redundantM

• ere answer choices clearM ere they interpreted as you intendedM

• 1id respondents want to give feedback about topics that were not includedM Lpen"ended

)uestions can be an indicator of this.<

• Ln the average, how long did it take for a respondent to complete the surveyM

• or a )uestionnaire, were there any typos or printing errorsM Also test the process of tabulatingand analy!ing the results. Isit easyM 1o you have all the data you needM

7. =evise the survey based on test results.


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4. Administer the survey.

%/. abulate and analy!e the data. 1ecide how you will follow through. =eport results and plans to everyone

involved. If a sample was involved, also report and explain the margin of error and confidence level.

Sur(ey Considerations

• Conducting a survey creates expectations for change in those asked to answer it. 1o not survey if action

will not or cannot be taken as a result.

• Satisfaction surveys should be compared to obHective indicators of satisfaction, such as buying patterns for

customers or attendance for employees, and to obHective measures of performance, such as warranty data

in manufacturing or re"admission rates in hospitals. If survey results do not correlate with the other

measures, work to understand whether the survey is unreliable or whether perceptions are being modified,

for better or worse, by the organi!ationEs actions.

• Surveys of customer and employee satisfaction should be ongoing processes rather than one"time events.

• et help from a research organi!ation in preparing, administering and analy!ing maHor surveys, especially

large ones or those whose results will determine significant decisions or expenditures.

$xcerpted from 0ancy =. agueEs (he Quality (oolbox , Second $dition, AS5 5uality Fress, (//-, pages -76'-74,

-4-.
http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224http://asq.org/quality-press/display-item/index.html?item=H1224

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