Chapter 3 QUality Control

8/9/2019 Chapter 3 QUality Control

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Chapter 3

Fundamentals of Statistical

Studies


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Definition of Statisticsy Statistics is the study of variation, interactions

and, operational definitions.

y Statistics is the study of data to provide a

basis for action on a population or process.


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Types of Statistical Studiesy Enumerative studies are statistical

investigations that lead to action on a staticpopulation (that is, a group of items, people,

etc. that exist in a given time period and/or ata given location).

y Analytic studies are statistical investigationsthat lead to action on a dynamic process.

y Since this is a text on quality improvement,the primary focus will be on analytic studies.


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Enumerative Studiesy Basic Concepts

yA population (oruniverse) is the totality of units,items, or people of interest that exist in a given timeperiod and/or given location Administration.

yA frame is a list of the items in a population.

y The gap is the difference between the frame andthe population.

yA sample is a portion of the frame under

investigation, and is selected so that informationcan be drawn from it about the frame.


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y Basic Conceptsy

Nonrandom samples are selected on the basis ofconvenience (convenience sample), the opinion ofan expert (judgment sample), or a quota to ensureproportional representation of certain classes ofitems, units, or people in the sample (quota

sample).y All nonrandom samples have the same shortcoming they're

subject to an unknown degree of bias in their results.

y This bias is caused by the absence of a frame.

y Nonrandom samples should be used only when betterinformation is too costly to obtain.


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y Seven steps are involved in selecting a simple randomsample:

y Step 1. Count the number of elements in the frame, N.y Step 2. Number the elements in the frame from 1 through N. If N

is 25, then the elements in the frame should be numbered from 01through 25. All elements must receive an identification numberwith the same number of digits.


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y Step 3. Select a page in a table of random numbers. Forexample, selecting a page and starting point yields.

19 30 40

09 28 78

31 13 98

67 60 69

61 13 39

04 34 62

05 28 56

73 59 90

54 87 09

42 29 34

27 62 12

49 38 69

29 40 93


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Sample Number Identification

Number

Items

1 19 S

2 09 I

3 04 D

4 05 E

5 13 M

6 12 L

Step 4. On the selected page of random numbers, select acolumn of numbers, select a starting point in that column,and use as many digits as there are digits in N (two digits

in the case of N = 25). For example, beginning with thetop of our column, selecting, and using the first two digitsof each number in that column, the first random number is19.


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y Step 5. Determine the necessary sample size.

y Step 6. From the chosen column on the selected page,

select the first six two-digit numbers between 01 and 25,inclusive. If a number is encountered that is smaller than 01(e.g., 00) or larger than 25 (e.g., 31), ignore the number andcontinue down the column. If an acceptable numberappears more than once, ignore every repetition andcontinue moving down the column until six unique numbers

between 01 and 25 have been selected. If the bottom of thepage is reached before six unique random numbers areobtained, go to the top of the page and move down the nexttwo-digit column.

y Step 7. Finally, analyze the information as a basis foraction.


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y Two important points to remember are:1. different methods of measurement will also yield

different results.2. different samples of size six will yield different results,

and

y Random samples, however, don't have bias, andthe sampling error can be held to known limitsby increasing the sample size.


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Conducting an Enumerative Study

y The following 13 steps present a guide forconducting an enumerative study.

y The steps are the same whether the study is basedon a complete count of the population or a sample.


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y Step 1. Specify the reason(s) you want toconduct the study (for example, to estimate the

average number of sick days per employee in theXYZ Company in 2002). If this average is greaterthan 8.0 days, then a new health care plan will beinstituted. If it is less than or equal to 8.0 days,

the current plan will be maintained.


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y Step 2. Specify the population to be studied. In ourexample, the population would be all full-time

employees in the XYZ Company in 2002. Anemployee is considered full-time in 2001 if he hadfull-time status designation at any time during theyear.


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Step 3. Construct the frame (a list of all full-time

employees).E

veryone who will use the study'sresults as a basis for action must agree that theframe represents the population upon which theywant to take action.


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Step 4. Perform secondary research (such as the

examination of pre-published data) to determinehow much information is already available aboutthe problem under investigation. For example,check the Human Resources Department'srecords.


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Step 5. Determine the type of study to beconducted (for example, mail survey, personalinterviews, analysis of units). In this example, wewould analyze employee absentee cards for2002.


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Step 6. Make it possible for respondents to

give clear, understandable information, and/orfor the researcher to elicit clear,understandable information. For example, themethod for analyzing absentee cards shouldbe clear and straightforward. Consider the

problem of non-response. In this example, besure no absentee cards are missing, andmake sure the data gatherers know how tointerpret the absentee cards.


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Step 7. Establish the sampling plan to be used,determine the amount of allowable error in theresults, and calculate the cost of the samplingplan. At this stage, Steps 1 and 2 may needrevisions due to cost considerations. Forexample, we may decide to draw a simple

random sample of employee absentee cardsusing random numbers, at a cost of $1 per card,assuming an allowable error of one quarter of aday in the estimate.


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Step 7 requires a random sample. The result of anonrandom sample in an enumerative study isworth no more than the reputation of the personwho signs the report.


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Step 8. Establish procedures to deal with the non-responses and differences between interviews,testers, inspectors, and so on. For example, beable to assess differences in collected data due todifferences in the data gatherers' abilities.


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Step 9. Prepare unambiguous instructions for thedata gatherers that cover all phases of datacollection.


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Step 10. Establish plans for data handling,including format of tables, headings, and numberof classes.


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Step 11. Pretest the data-gathering instrument anddata-gathering instructions.


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Step 12. Conduct the study and the tabulations. Itis critical that the study be carried out according

to plans. From the gathered data, calculate thesampling errors of interest. This is important sothat the study's users can understand the degreeof uncertainty present in the study results. In our

example, we would calculate the standard errorfor the average number of days absent peremployee.


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Step 13. Interpret and publish the results so thatdecision makers can take appropriate action. For

example, if the average number of days absent peremployee is greater than eight, then establish thenew health care program.


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y The concept of a population does not exist for ananalytic study because future process output,which does not yet exist, cannot be part of thepopulation.

yA frame cannot exist without a population.

y

Lack of a population and frame makes itimpossible to draw a random sample to study aprocess's behavior.


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y Models can be used to study these cause-and-effect systems.

y These models include flowcharts of a process,simulations of the process, and cause-and-effectdiagrams.

y In an analytic study (unlike an enumerative

study), there is no underlying statistical theorythat enables quantification of uncertainty.


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y Expert opinion is invaluable in understanding themagnitude of the uncertainty caused by changesto a process.

y Generally, this uncertainty is best explained by anexpert who is involved with the process understudy.


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y Improvement or innovation of a process is

accomplished using the Plan-D

o-Study-Act(PDSA) cycle.

y The PDSA cycle is used to narrow the differencebetween process performance and customer

(either internal or external) needs and wants.


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y The aim of the PLAN stage is to determine an improvement orinnovation to a process that will narrow the difference betweenprocess performance and customer needs and wants. (i.e. old

flowchart to new flowchart)y The DO stage of the PDSA cycle requires that planned

experiments be conducted to determine how best toimplement the PLAN established in the previous stage.Experiments should be conducted on a small scale, using alaboratory, an office or plant site, or, with his consent, even a

customer's location.y The aim of the STUDY stage is to determine if the PLAN has

been effective in decreasing the difference between processperformance and customer needs and wants.

y In the ACT stage, the PLAN should be integrated into theprocess.


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y Errors in Analytic Studies

yA type one erroroccurs when action is taken on aprocess when it should have been left alone.

yA type two erroroccurs when we fail to take actionon a process when action is appropriate.


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y Design of Analytic Studies

y We can increase our degree of belief in a predictionfrom an analytic study by considering:y Building of knowledge in a sequential fashion

y Testing over a wide range of conditions

y Selection of units for the study


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y Building of Knowledge in a Sequential Fashiony Experiments performed in the iterations of the PDSA cycle,

in combination with theory about the process from subjectmatter experts, may increase the degree of belief inpredictions about the future behavior of the process understudy.

y This degree of belief is increased as sequential predictionsabout the process's future behavior come closer to the

actual performance of the process.


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y Testing over a Wide Range of Conditions

y The degree of belief in the predictive value of the

knowledge gained from an analytic study is increased if theanalytic study yields the same results over a wide range ofconditions.

y Only an expert in the subject matter under study can answerquestions such as how wide a range of conditions isadequate to have a degree of belief sufficient to make aprediction, or how close to actual conditions must theexperimental conditions be to have a degree of belief highenough to make predictions.


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y Selection of the Units for the Study

y Since there is no frame in an analytic study, there can be no

random sample and quantifiable degree of uncertainty in aprediction about the future.

y Judgment samples are used to conduct analytic studies.


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yAnalysis ofData from Analytic Studiesy A Stable Process

y A stable process provides a forum for a subject matterexpert to conduct experiments to gain knowledge to predictthe future behavior of the process.

y Graphical Analysis

y The general approach for conducting analytic studies relies

on graphical techniques, such as control charts, whichutilize both statistical knowledge and subject matterknowledge to learn about the process to predict its futurebehavior.


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Distinguishing Between Enumerativeand Analytic Studies

y If a 100 percent sample of the frame answers thequestion under investigation, the study isenumerative; if not, the study is analytic.

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Chapter 3 QUality Control