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Transcript of six sigma BB3
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
How to make sure that your true
process population dynamics arerepresented by your sample data.
How many datapoints do I
need?
Sampling
Concepts
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Objectives Be able to select the proper sampling
strategy.
Be able to calculate the proper sample
size for a given confidence level and
confidence interval.
Be able to define confidence level, power
factor, alpha risk and beta risk.
Be able to calculate the proper sample
size for a hypothesis test or DOE.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
How Much Data Do You Need?It depends on what questions you are trying to answer?For example
Determining Process Capability (Baselining)
Your focus should be to collect enough baseline data to capture an entireiteration or cycle of the process.
An iteration should account for the different types of
variation seen within the process.
Cycles, shifts, seasonal trends, product types,
volume ranges, cycle times, demographic mixes, etc.
If historical data are not available, a data collection plan should be
instituted to collect the appropriate data.
Hypothesis Testing (comparing means/variances)Later in this section we will show you that your focus should be on other
statistical characteristics of the sample, such as, mean, variance, risk and
the level of confidence desired for seeing differences.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Strategy Review
What must a sample be?
Random.
Unbiased.
Representative.
What kind of sampling can we do?
PopulationItems exist and theircharacteristics are stable.
ProcessItems continue to be produced and
their characteristics may change as theprocess varies.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Strategy Review
Sampling Strategies
Random Sample - Each unit has an equal probability of
being selected in a sample (typically used for populationstudies).
Rational Subgroup Each unit is collected at point A in aprocess everynth hour. Usually multiple sequential units arecollected (typically used for process studies).
Stratified Random Sampling - Randomly sample within astratified category or group. Sample sizes for each groupare generally proportional to the relative size of the group.
Systematic Sampling - Sample every nth one (Ex: collectingevery 4th unit).
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
XXXX
XXX
XXXX
XXXX
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XXXXXX
XXXXXXXX
XXXX
XXXXXXXXXXXXXX
XXXX
XXXXX
Population
Sample
XXXX
XXX
Sampling Strategy NewCluster Sampling
The population is composed of small groups called clusters.
There is very li ttle variation in the demographics of the clusters. Data is gathered in detail within one (or a few) cluster(s).
i.e. all the tellers in one representative banking center or allcall representatives in one representative call center.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Exercise 1
1. We want to monitor our item processing associates on aregular basis to see if errors are going up.
2. Without spending a lot of money, we want to know whetherthe people in Charlotte prefer Bank of America orWachovia.
3. A DFSS team needs to thoroughly understand our affluent
urban customers to better develop products for their needs.
4. For planning purposes our Supply Chain Managementneeds to know how long it takes to enter into contracts. Wedeal with many types of suppliers in many different areas ofthe country.
5. We want to know how accurate our bills are to ourcorporate customers. It will take about 15 minutes toreview each bill for accuracy. Bills are issued monthly, butevenly throughout the month (I.e. not all end-of-monthbilling).
Random
RationalSubgroup
StratifiedRandom
Systematic
Cluster
Match the sampling situation with the best sampling strategy.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
How Much Data Do You Need?How many actual data points do you need to collect for
your sample? Green belt class introduced the following
sample size formulas:
2s96.1
n
= n = sample size
s = standard deviation
p = proportion defective
= precision, , of theestimate at 95% confidence
)p1(p96.1n
2 =
Continuous data form
Discrete data form
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10These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sample Size Calculator
Open the Excel fi le called: SamplCal4.x
This application can be used effectively for determining ini tial sample sizes required for
process studies or descriptive statistics of process information. It should not be used
for hypothesis testing. Minitab is the recommended sample size calculator for
hypothesis testing or experimental studies.
Estimated Sample Sizes for Continuous Data at 99%, 95% and 90% Conf idence Levels
Enter Population Size Here* 1,000,000 Precision Sample Size Sample Size Sample Size
(d)99% 95% 90%1 167 97 68
Enter Estimated Standard Deviation Here 5 2 42 25 17
(If unknown, use 1/6 of the known range of the data) 3 19 11 8
4 11 7 5
* For process sampling use the total number of 5 7 4 3
items produced in the time period you wish 6 5 3 2
to characterize. The popu lation size is used 7 4 2 2
to adjust sample size with the Finite Population 8 3 2 2Correction Factor 9 3 2 1
10 2 1 1
11 2 1 1
12 2 1 1
13 1 1 1
14 1 1 1
15 1 1 1
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11These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Exercise 2 Each month we want to monitor the errors made on
deposits in each region. We want to know where we are
within 1%. We believe the error rate is 11.5%. How manysamples should we take in each region, each month?
After sampling for a few months, we have found that the
error rate is only 8.1%. Additionally, our boss wants us toreport it in Sigma Level to the closest tenth. At this level
we calculated that 0.1 Sigma Level is about 1.4%, so that is
the most precision we will need. Now how many samples
should we take?
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January 3 2005 ver.4.4 - Action Legal Copy Service.
Sample Sizes for
Hypothesis Testing
his isthe newstuffwithinit b
Right, this
is the newstuff with
Minitab.
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January 3 2005 ver.4.4 - Action Legal Copy Service.
Sample Size Concepts
Smaller sample sizes:
Less Cost
Quicker data collection
Higher risks
- chance of missing animportant effect (false
negative)
- chance of declaring an
effect important whenit is not (false positive)
Wider confidence
intervals
Larger sample sizes:
Higher costs
Longer time to get data
Lower risks (but not zero)
- smaller real effects and
more likely to be declared
significant
Tighter confidence intervals
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14These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Risks and Power
Alpha (): The risk associated with f inding that something is
significant when in reality it is not. The risk of chasing anunimportant X. The risk of doing the wrong thing.
Beta (): The risk associated with stating that an input or process is
not different when it is. This is the risk of missing animportant X. The risk of doing nothing.
Power (1-): The chance of correctly rejecting an X when indeed it should
be rejected. Power is the likelihood that you wil l identify a
significant difference when one exists.
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January 3 2005 ver.4.4 - Action Legal Copy Service.
Alpha/Beta Risks
Alpha, , is the risk of f inding a difference when there really isnt one.Beta, , is the risk ofnotnot finding a difference when there really is one.
Truth is:Truth is:
Testsays:
Test
says:H0H0 HaHa
H0H0
HaHa
Type IIError
Type IError
CorrectCorrect
DecisionDecision
CorrectCorrect
DecisionDecision Risk also called:
Type II error
Risk - also called:Type I error
A fire alarm sounds,
but there is no fire.
Or we deny a loan to
a credit worthyperson.The fire alarm is silent, but
there is a fire. Or we approve
a loan for a non-credit worthy
person.
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16These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Alpha Risk Graphically
Truth is: Both samples are from the same population.
If X2 here, conclude
one population;
correct!
Sample 1
Risk Area
If X2 here, conclude
two populations;
Type 1 Error.
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17These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Beta Risk Graphically
Truth is: Samples are from different populations.
Power (1-) is theprobability of detecting
the dif ference, , and isrepresented by the
area in Population 2
less the beta risk area.
If X2 here, conclude
one population;
Type 2 Error.
Sample 1
If X2 here, conclude
two populations;
correct!
Population 2 Risk AreaRisk Area
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18These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Power (1-) is theprobability of detecting
the dif ference, , and isrepresented by the
area in Population 2
less the beta risk area.
Beta Risk Graphically
Truth is: Samples are from different populations.
If X2 here, conclude
one population;
Type 2 Error.
If X2 here, conclude
two populations;
correct!
Sample 1
Population 2Risk Area Risk Area
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19These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Terminology
n: The number of units making up the sample size. May be expressed
differently depending on the situation. For a DOE, n may be the number
of experimental runs. In a two sample t-test, n could represent the
number of observations for each group.: (alpha) Your chance of a false positive, which is the p-value at whichyou start calling things statistically significant.
: (beta) Your chance of a false negative.: (delta) The size of the real effect you want to be sure to detect if in fact it
is there. Often expressed as a multiple of .
: (sigma) The standard deviation of the noise variation when factors areheld fixed.
Power: Your chance of detecting a real effect, i.e., declaring it to be
statistically significant. You want this high. Power = 1-
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Using Minitab to Determine
Sample SizeStat>Power and Sample Size
Minitab can calculate power or sample sizes for:
1-sample t & 2-sample t1 Proportion & 2 Proportions
One-way ANOVA
2-level factorial designs
Enter and , plus two of n, , or (1-), andMinitab wil l solve for the third!Enter and , plus two of n, , or (1-), andMinitab will solve for the third!
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
General Sample Size Formula
The sample size formula presented earlier in this module is
actually a simplified version of the general formula that is given
below:
datadiscretefor)p1(p)ZZ(
n
datacontinuousfors)ZZ(
n
2
2
=
=
/2
/2
Note: The formula used earlier assumed Z = 0 or = 0.50. Fora hypothesis test, a = 0.5 implies a power of 50%. You wouldhave a 50% chance of seeing a significant difference if it were
actually there.
Note: The formula used earlier assumed Z = 0 or = 0.50. Fora hypothesis test, a = 0.5 implies a power of 50%. You wouldhave a 50% chance of seeing a significant difference if it were
actually there.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sample Size Example 1
We want to see if the average time to process a second
mortgage application is the same for two banking centers. A
2-sample t-test was selected. Our best (planning) estimate
for the average time is around 15 days with a standarddeviation, = 2 days.The sample size must be large enough to provide a 95%
chance of detecting a difference (if it exists) in the average
processing times, as small as 3 days (because a 3 daydifference is of practical signif icance to us). Using an
alpha risk of 0.05, what sample size would you recommend?
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Minitab
1. Fill in two, leaving one empty.
2. Put in Standard
Deviation. 3. Click Options.
4. Choose Ha and enter .
5. OK.
6. OK.
Stat>Power and Sample Size>2-Sample t
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Minitab
Power and Sample Size
2-Sample t Test
Testing mean 1 = mean 2 (versus not =)
Calculating power for mean 1 = mean 2 + difference
Alpha = 0.05 Sigma = 2
Sample Target Actual
Difference Size Power Power
3 13 0.9500 0.9561
Power and Sample Size
2-Sample t Test
Testing mean 1 = mean 2 (versus not =)
Calculating power for mean 1 = mean 2 + difference
Alpha = 0.05 Sigma = 2
Sample Target Actual
Difference Size Power Power
3 13 0.9500 0.9561
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Comparison of proportions:
Card Services wants to compare the default rate of a private
labeled credit card (PLC) against Visa to see if the Visa default rate
is really larger. PLC has claimed a default rate of 1 percent or less.
The default rate for Visa is roughly 1.5 percent. We want to be at
least 90 percent sure (power) to find a significant difference if i t
exists and are willing to take a 5 percent risk ().What is the required sample size (for each credit card)?
What is your false negative risk ()?
Sampling Exercise 3
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Designed experiment:
A Six Sigma team want to conduct a 23 factorial with replicates.
Assuming an = .05, the team needs an 80 percent assuranceof detecting at least a 2 percent difference (effect) on Y .Typical experimental variation with factors held fixed(determined from an earlier pilot study) is about 1.5 percent ( =1.5%).
How many replicates will you have to run to achievethe 80% detection assurance?
Sampling Exercise 4
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
ase power n
1
2
3
4
5
6
Co ns tant Co ns tant
Constant Constant
Constant Constant
Co ns tant Co ns tant
Constant Constant
Co ns tant Co ns tant
?
?
?
?
?
?
Fill in the relationships chart (hint: refer to the general
formula to determining the sample size).
Sampling Exercise 5
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Sampling Summary
Sample size depends on:
What level of risk youre willing to take.
What size difference you want to detect.
How powerful you want the test to be.
Before collecting data, you should think about the sampling
strategy and sample size requirements to ensure that you
have an appropriate amount of data for drawing
conclusions.
Choosing the right sample size allows us to better manage
our risks of making a wrong decision or missing an
important factor.
Sample size determination should include practicalconsiderations, like economics, as well.
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These materials contain information that is proprietary and confidential to Bank of America. These materials shall not be duplicated. 2005 Bank of America. All rights reserved.
January 3 2005 ver.4.4 - Action Legal Copy Service.
Black Belt Key Learnings
Does this tool have an application to my current project?
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This tool can help me answer the following questions:
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What are the key learnings about this tool and/or subject?________________________________________________________________________
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How comfortable will I be in training my team on this tool?
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