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Six Sigma

Six Sigma Statistics Six Sigma Statistics Companies often collect large amounts of data that are valuable sources of information to establish measures of process performance. But although customer surveys, rejection reports, expenses incurred in warranty claims, etc. are available, we often calculate the wrong indices. First Time Yield (the ratio of the number of accepted units to the number of units tested) has been traditionally used to assess process performance. However, this concept is flawed since the reality of rework and replacement of scrapped units is not considered, rendering management blind to the fact that we often do not produce quality products and services the first time. Products or services are often the result of many process steps. It is rare to find products or services that are the direct result of a single process step. Final Yield is the calculation of First Time Yield at the last process step, and much like First Time Yield, it is not an accurate measure of process performance. The concept of the Hidden Factory includes the amount of work required to produce a good unit above and beyond entitlement (the amount of work actually needed to produce a good unit of output the first time). The consequences of the Hidden Factory include longer cycle times, increased inventories, etc. To uncover the Hidden Factory, Six Sigma introduces two measuring indices: Throughput Yield and Rolled Throughput Yield. Throughput Yield represents the probability of producing a defect-free unit in a process step, while Rolled Throughput Yield represents the probability of producing a defect-free unit in a series of process steps. Both metrics can be calculated from either discrete or continuous data and the standard normal distribution tables. When using discrete data, Throughput Yield is approximated using the formula YTP = e-DPU. From continuous data, it is calculated as YTP = 1 - probability (defect). The probability of producing a defect is calculated as the appropriate area under the standard normal curve. Rolled Throughput Yield is calculated as the multiplication of the Throughput Yield values of each of the process steps involved in producing the output, or using the formula e-TDPU where TDPU stands for "Total Defects Per Unit". Throughput Yield and Rolled Throughput Yield have deep business implications. We can now assess the true performance of our processes, no matter how unflattering this picture may be. In some instances a First Time Yield of 90% translates into a Throughput Yield of only 37%. On the bright side, once we know where we stand, we can set breakthrough targets and objectives. Moreover, we can track improvement over time using complete measuring indices. The Normalized Yield is a single and equivalent value that is assigned to a series of process steps involved in producing an output. This is used to characterize all the steps involved in producing the output when the Total Defects Per Units at the final step is known. In this sense, we say that Normalized Yield represents a "kind of average" Yield value for a series of process steps. Metrics Flow Down is a tool commonly used at the beginning of the life cycle of a product or service, typically during the design stage as a "what if" tool. For example, If we want to achieve a Six Sigma level and we know the


process and product breakdown, then we can set targets at each of the lower levels in the breakdown that will render a Six Sigma product. Once data become available, later in the product life cycle, we can compare actual against target levels. Finally, Metrics Roll Up is a helpful tool for calculating the resulting Sigma value of a product or process. It is commonly used to benchmark products and services across groups or industries. Key Questions • What is "first-time yield" and how does it differ from "probability of zero defects"? • What is "throughput yield", how is it computed, and what are its business implications? • What is "rolled-throughput yield", how is it computed, and what are its business implications? • What is "normalized yield", how is it computed, and what are its business implications? • How can yield be converted into a "Sigma" value and how can this value be used? • How can yield data be hierarchically pooled (or decomposed) and how can these values be used?

Key Questions First Time Yield (YFT) is the ratio of the number of units that pass inspection (S) to the number of units tested (U). It does not represent the probability of zero defects because units are accepted regardless of the presence of rework and replacement of scrapped units. Throughput Yield (YTP), represents the probability of producing a defect-free unit in a process step. It is calculated from discrete data (YTP = e-DPU where DPU means "Defects per Unit"), or continuous data (the appropriate area under the normal curve). The Hidden Factory is considered, thus providing a true picture of process performance. Rolled Throughput Yield (YRT) represents the probability of producing a defect-free unit in a series of process steps. It is calculated by multiplying the Throughput Yield values of each step, or using the formula YRT = e-TDPU where TDPU means Total Defects Per Unit. Normalized Yield (YNORM) is a single, equalized Yield value assigned to all steps in a group of "k" process steps. It is calculated as the kth root of Rolled Throughput Yield, and is used to benchmark processes and products. A Sigma value, Zst (Sigma short term) is used to compare performance across various products or processes. To obtain a Sigma value from a Yield value, we first calculate the probability of a defect (1 - Yield) and using the standard normal tables, we find the corresponding Z value. Then we perform the appropriate correction (shift and drift) using the "truth table". Yield values can be "Rolled Up" using the product or process hierarchy to characterize a product or process. Likewise, this hierarchy can be use to "Flow Down" Yield values and to set improvement targets for Quality levels.


3Six Sigma Statistics

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First Time Quality is not …- After Discarding and Starting over Again

- After Rework- After Corrections

- After Force-Fitting- After Scrap

- After …

First Time Quality1_

04_0

1_00

2

First Time Quality A Champion and a Six Sigma Master Black Belt reflect on the concept of First Time Quality, highlighting the fact that historically we used mathematical ratios and proportions to represent the status and health of our processes. "I remember", says the Champion "…how we used to plot many graphs depicting the amount of scrap and rework for a given month. We used to show trends and set objectives to contain and lower the number of rejections, ultimately controlling labor and cost". "Yes, that was prior to implementing Six Sigma. Today the objective remains the same, but we plot DPMO (Defects Per Million Opportunities), Sigma values and other metrics that help us measure our products and processes and, by identifying and solving problems,quality improves, cost goes down and we keep our customers satisfied". "It is interesting to see how much one factor (variation) can influence our processes. After we began to understand and started to control variation, our processes started improving. Adopting metrics such as Yield (the probability of producing good units of output), Throughput Yield, Rolled Throughput Yield and Normalized Yield helps to measure, uncover, and eliminate the Hidden Factory". "Now that we are on our way to becoming a Six Sigma company, we understand the importance of using the proper metrics, operating robust processes and having defect free units of output… the first time!"



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Finding Artifacts to EstimateCapability

1_04

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003

Findings Artifacts to Estimate Capability During the implementation of Six Sigma, we often believe that there is no readily available information or numbers to estimate our existing level of process performance. We believe that a considerable effort is required to measure the existing situation and to identify trends, strengths, and areas for improvement. However, companies .measure certain activities and record the data which could provide valuable information as a starting point for a capability evaluation. Among the many sources of information, there are: Quality records (rejection reports): Customer surveys: • Records of Cost of Poor Quality (COPQ); • Records of customers' complaints; • Records of returned goods or items: • Warranty replacements and repairs, etc. Much like an archaeologist looks for artifacts of past civilizations to discover how ancient societies lived, Six Sigma practitioners can "dig out" existing records to begin assessing the performance of our existing processes and products. All these sources provide a "ball park" figure of the number of defects per unit. From this number, we can calculate Throughput Yield or Rolled Throughput Yield values, which in turn lead to Sigma values.



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The Hidden Factory

Input Operation Inspect

Rework

NOTOK

OKOutput

Quality =Customer satisfaction

= Profits

HiddenFactory

Scrap

1_04

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004

The Hidden Factory When a Six Sigma Black Belt inquires about the Hidden Factory, the Master Black Belt clarifies, "The Hidden Factory is a concept related to productivity, value and money. It includes all work and costs invisible to our accounting system. In practice, the constituents of the Hidden Factory vary depending on how we measure costs and business performance. Another way of defining the Hidden Factory is all work required to produce one good unit of output above and beyond entitlement (the amount of work actually needed to produce a good unit of output the first time)". Hidden Factories are not exclusive to manufacturing. They in any department, shop, or but its effects are felt across the business. Longer cycle times, increased costs, and inefficient use of resources are some of the consequences of the Hidden Factory. In Six Sigma, we strive to uncover and eliminate this Hidden Factory. A team member says, "As part of my weekly tasks, I compile data recorded in the Non Conformance Reports. I see that report no. C320363 indicates that for the rejection of certain parts, we incurred material costs of $4,678 and labor costs of $4,700. Is this part of Hidden Factory"? The Master Black Belt answers, "Not really. These costs are measured and reported, so they are visible. However, other costs, such as the amount of time the operator correcting defective units, are not specified anywhere, therefore they are part of the Hidden Factory.



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The Origins of the Hidden Factory

10 cups producedevery cycle

Plastic Injection Machine

PlasticPellets

Operator Verifies

OK

NotOK

RecycleMaterial

ShredPlastic

The HiddenFactory

Send toInspection

1_04

_01_

005

The Origins of the Hidden Factory To further understand the concept of the Hidden Factory, a participant in the training session asks what causes the Hidden Factory? The Master Black Belt explains that the way we measure and account for performance can create a Hidden Factory. "We know that First Time Yield is a flawed measuring index. Well, let's illustrate. Imagine that we are producing plastic cups in an injection process, and that 10 cups can be produced in the same mold. Let's remember that a typical plastic injection process consists of plastic pellets (input) going into a mold with cavities, and through pressure and temperature changes we produce our cups (output). After injection, we usually use a blade to trim the excess plastic around the edges." "Say that the operator notices that 5 out of 10 cups are good. What will he do? Well, he will take the 5 good cups and send them to inspection, while the other 5 cups will be shredded and put back into the injection process." "In this scenario, First Time Yield is 100% (5 cups tested and 5 cups accepted by inspection). Now, was there any material lost? No. The defective units were recycled back into the process to produce good units. This may not be typically shown in any material cost report, but there is a Hidden Factory. The time spent remaking defective units, both for the operator and the machine, comprises a hidden factory which is not captured in any cost structure."



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Hand Backs and the HiddenFactory

PRODUCTION

INSPECTION

A rejection reportmakes us all look bad,so fix this unit before I

inspect it.Sure, just leave it

with the other unit tofix.

Accepted Units

Units to Rework

QUALITY

1_04

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006

Hand Backs And The Hidden Factory "A source of the Hidden Factory can be what is known as "hand backs", states the Master Black Belt. "Companies typically reprimand poor quality. However, this can lead to finding ways of hiding poor quality to avoid being punished. The following scenario illustrates a "hand back." A particular inspector is a good friend of a machine operator. He knows that the way he reports defects will bear influence on who is reprimanded, so instead of recording a certain defect, he goes back to his friend and suggests repairing the unit before it is inspected. This way, he says, the unit will be accepted and no one will get into trouble." A Champion asks,"Should we reward employees for finding defects". The Master Black Belt explains, "If we take this scenario to the extreme and praise everyone who finds defects, then perhaps human nature would make us create defects in order to be praised". The Master Black Belt concludes by suggesting that businesses should keep a neutral attitude towards finding and correcting defects while promoting quality. "If we punish poor quality, then people will be afraid of reporting defects, and if we reward them for finding defects, human nature might lead us to create some defects that otherwise would not be produced. However, if we encourage Quality in our processes the first time, there will be no defects to detect or correct".



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The HiddenFactory

12Not OK

Scrap andcomplete anew Form

Erase &Fix Form

150Forms

Submitted(U)

OperatorVerify

138FormsPassed(S)

CompletingForm

YFT = S/U = 138/150 = 92.0%

FormFirst Time Yield (YFT)

Yield after inspection or test

Inspection

First Time Yield (YFT)

PROCESSSTEP

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007

First Time Yield (YFT) A Black Belt has been assigned a project related to the completion of specific order forms. The objective of the project is to reduce the cycle time and the errors in completing the forms. Specifically, the objective is to eliminate the number of errors on each form, and to reduce the cycle time from 4 to 1 working days, and the out of time performance from 43% to 0. To establish the First Time Yield, the Black Belt analyzes 250 forms and finds that 75 (30%) are rejected due to improper completion. First Time Yield is then calculated as 70%. After implementing the project, the Black Belt collects 150 forms and finds that 12 were rejected, thus concluding that the Yield after implementing the improvement project has increased to 92%. Discussing these results with a Master Black Belt, they both conclude that the First Time Yield calculations are not representative of the real performance of the process. Factors such as inspection and rework are not included in the calculation of first time Yield, nor are the corrections made by the person filling the form before processing the forms, nor the forms discarded and re-started for a second or even a third time. The Master Black Belt then explains another limitation of the first time First Time Yield. By considering "passed units" only, we don't account for the amount of resources (time, cost, etc.), nor the cycle time of each unit. Moreover, the calculation of first time Yield has no conceptual meaning. It is merely the expression of a ratio of units accepted over units inspected".



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200Units

Submitted(U)

198Units

Passed(S)

First Time Yield (YFT)Yield after inspection or test

NotOK

Scrap

Rework

Operation


YFT = S/U = 198/200 = 99.0%

2 unitsNOT OK

InspectionVerify

The HiddenFactory

How ManyUnits

Not OK?

1_04

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008


A Black Belt working on a project related to the roll bending process listens to a team member who is not convinced of the need to undertake the project. He argues that if in the preceding month, only 2 pieces were rejected out of 200 units submitted for inspection, the process Yield is 99% and it is not necessary to further improve it. The Black Belt, knowing that the First Time Yield is not representative of the level of process performance, asks a few questions: "Did the operator verify the units before sending them for inspection? Did he perform any rework? And were some units scrapped and replaced with new ones?" The team member replies: "Well, yes. It is the operator's responsibility to ensure that what he delivers to inspection is good." The team member begins to see the Black Belt's point of view and says: "I see, if the units need correcting, it is because they were not that good in the first place, so the 99% Yield is not representative of the process performance". "Correct" says the Black Belt. "If the operator spends 5 minutes correcting a minor defect in a unit, 20 minutes for a major correction, and no time to correct a unit with no defects, then the cycle time of those three units would be different even if all three units were accepted by inspection. Since cycle time is different, cost is also different. The information revealed by measuring First Time Yield provides no insight about cost structure. A unit that cost 20 hours of rework is considered as good as a unit produced right the first time, which highlights the limitation of first time Yield." The Black Belt and the team member recognize the existence of a Hidden Factory and the need to calculate the real performance, so they agree to cooperate in the Six Sigma project.



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1st

Step2nd

Step

0Not OK

25Aircraft

certificated(S)

FinalInspection

nth

FinalStep

Including theHidden Factory

25Aircraft

Submitted(U)

Final Yield (YFINAL)

Yield = 100%Aircraft Final Yield

Yield after final inspection

AircraftManufacturing

Process

1_04

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009

Final Yield (YFINAL) At the beginning of the Six Sigma journey, we often wonder if we really need to improve our processes. For example, in the aircraft industry, we believe that if an aircraft is certificated, our products will have a Final Yield of 100%. However, we don't have highly efficient processes. We simply correct defects produced throughout the manufacturing process in pre-flight, and thus believe that Final Yield is high. Reflecting on this statement makes us realize that if our products pass final inspection, it doesn't mean that we are producing Six Sigma products. In the classical sense, Final Yield is nothing else than a synonym of First Time Yield (YFT), calculated at the end of a series of process steps. This index has shortcomings because it does not uncover the Hidden Factory. Another weakness of this measure is the fact that final inspection is a system level inspection. In other words, not every CT characteristic is tested at this level, thus there is no guarantee that a customer will not experience problems with the quality of our product. Let's say that our product contains 100 CT characteristics, and that we analyze two units of output. The first unit undergoes 27 rework steps to correct defects, while the second unit only has 1 correction. In terms of Final Yield, both units would fail inspection, and thus Final Yield would equal zero. But, is the magnitude of the problem equal for both units? Surely not, and a measuring index such as Final Yield provides no insight to these problems. As we will see, Rolled Throughput Yield, accounts for these facts and provides a much more realistic portrait of the situation.



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The HiddenFactory

DPU = 1.0

NotOK

Scrap

Rework

165 UnitsSubmitted

157 UnitsPassed(after

rework orrepair)

61 Units(Expected)53 Units

(Actual)D = 0

104 UnitsD ≥ 1

Throughput Yield (YTP)

YTP = e-DPU = e-1.0 = .3679 ≈ 37%Approximate with Poisson;

96 UnitsRepaired

8 UnitsScrapped

VerifyOperation

YTPThroughput Yield

(Probability of a unit with zero defects)

Throughput Yield (YTP) The concept of Throughput Yield represents the probability of producing one unit of output in a process step with zero defects. It is measured prior to any form of rework, thus uncovering the Hidden Factory and providing a true picture of process performance. To illustrate the difference between First Time Yield and Throughput Yield, let's say that 65 units go into a process and that 157 are accepted by inspection. Also, let's say that 8 units are defective beyond repair so we scrap them, and that historically we know that on average we find one defect per unit of output for this process (DPU = 1). First Time Yield is 95% since 8 units were scrapped over a total of 165 units produced (157/165). A closer look reveals that 104 units had defects, and that out of these, 8 were scrapped while the rest (96) were reworked and later accepted by inspection. The actual number of units found to be right first time was 53. Calculating the throughput Yield of the process (YTP = e-DPU), we obtain 37% In other words, we expect 165 x 0.37 = 61 units to be defect-free over time. As we might see the expected and actual number of defect-free units is similar. Thus, Throughput Yield provides an insight to real process performance and uncovers the Hidden Factory. This also explains why sometimes the values of First Time Yield and Throughput Yield are so different (90% versus 37%). The concept of Throughput Yield is used with discrete or continuous data. For discrete data, we can use the Poisson distribution when the number of opportunities for nonconformance is large and the probability of an event is small. Given the nature of most processes, these conditions are usually met.



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The Reciprocal Nature of Data

And an equiva-lent Z value ...

We can startfrom either ...

Discrete Datae-DPU

ContinuousData

P(Defect)

To obtainYield ...

P(Defect)

Yield

That weadjust ...

± 1.5 SigmaShift

3.67 + 1.5 =Long-Term Adjustment

And finallyobtain.

A “Sigma”Value

5.17Short-Term

1_04

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010

The Reciprocal Nature of Data A Six Sigma Black Belt in training reflects on the relationship between discrete and continuous types of data and the concept of Throughput Yield. Yield is the general term to denote the probability of producing defect-free units of output. From discrete data, we calculate Throughput Yield using the formula YTP = e-DPU. From continuous data, Throughput Yield is calculated from the appropriate area under a Normal curve. Since we can work with either continuous or discrete data to calculate Yield values, the Black Belt concludes that if both types of data result in the probability of producing defect-free units, then the data must be reciprocal in nature. A Master Black Belt agrees and adds: "To calculate yield, we can work with either discrete or continuous data, and remember, we must always report and compare Sigma values using the Sigma Short Term (Zst)". The following guidelines help us decide whether data is short- or long- term in nature -and how to convert it to Sigma Short-Term. If data is: • Recorded over many cycles, it is considered as long term (add a 1.5 Sigma shift); • Recorded over short periods of time, or cycles, it is considered as short term (no adjustment is required); • Discrete by nature, it is considered long term (add a 1.5 Sigma shift); • Continuous by nature and recorded under the constraints of sequential random sampling, it is considered

short-term (no adjustment is required).



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Receive partsfrom supplier

RightFirstTime

95.5% Yield Following ReceivingInspection (YTP)

97% Machining OperationsYield (YTP)

94.4% FinishingOperations Yield (YTP)

Waste*

Waste*Waste*YRT = .955 x .97 x .944

= 87.45%

125,500 parts per milliondefectives

Rolled Throughput Yield (YRT)

= 87.45%* Wasted resources (time, money, etc.)

1_04

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011

Rolled Throughput Yield (YRT) A Champion and a Master Agent discuss the concept of combining Yield values. "To properly measure the performance of a department when a series of process steps are involved, we use the metric Rolled Throughput Yield", says the Master Agent. He draws a flow of liquid passing through a series of three funnels, where some liquid passes on to the second and third funnel, and some liquid spills on the floor. "Imagine that the can at the top represents the material received from a supplier. It enters the department and, at each step, there is some spillage. The process steps have a Throughput Yield of 95.5%, 97% and 94.4% respectively, so the probability of the liquid reaching the final bucket is equal to the product of the individual Yield values. 0.955 x 0.970 x 0.944 = 0.8745 or 87.45%". The Champion then adds, "It seems that Rolled Yield decreases rapidly as the number of steps increases". "That is correct" replies the Master Agent. This is why we can then conclude that in order to produce a Six Sigma product or service, it is necessary to achieve very high Throughput Yield values for each of the process steps". "Since Rolled Yield is the product of Throughput Yield values, this concept considers the Hidden Factory, and thus reflecting the true performance of our processes. Since rework and scrap are included, then the cost structure of all units going into the process is included. It then follows that in striving for Six Sigma, new measures arise. With new measures, we ask new questions and in turn have new direction. Six Sigma is a fundamental change in paradigm on how we run our business in order to better satisfy our customers, and better make shareholders see value in the stock."



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YRT = Π YTPik

i=1

Number of units (u)

YRT = e-TDPU

Step 1Yield1

Step 2Yield2

Step 3Yield3

Step kYieldk

Input Output

DEFECTS

YRT = Probabilityof a unit going

through all processsteps with zero

defect

YRT = YTP1 x YTP2 x YTP3 x ….. x YTPk

Example: with atotal defect per unitTDPU = 0.2261YRT = e-0.2261 = 79.8%

Rolled Throughput Yield (YRT)

...

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Rolled Throughput Yield A Six Sigma team is working on a project related to the procurement of a component. The members know that five steps are involved in producing the component and they discuss the best metric to use to evaluate the performance of all process steps together. The Six Sigma Agent indicates that the best measure of process performance is the Rolled Throughput Yield, which is equal to the product of the Throughput Yield of the individual process steps. If these steps have individual Yields of 98%, 93%, 95%, 98% and 94% respectively, then the Rolled Throughput Yield equals 79.76%. This value represents the probability that the component will be defect free after completing the five process steps. Another member of the team asks if there is an alternative method of calculating the Rolled Throughput Yield when the individual Yield values are not known. The Six Sigma Agent explains,"If we know the number of defects per unit (DPU) at each step, then we add them up to know the total number of defects per unit (TDPU), and then e-TDPU is a good approximation of the Rolled Throughput Yield. For example, if TDPU equals 0.2261 then YRT e–0.2261, in other words, YRT = 79.76%". The team agrees on both methods of calculating Rolled Throughput Yield, and also recognizes that this measure is function of the number of defects produced. Likewise, if the Rolled Throughput Yield is known, then the negative natural logarithm of this value equals total defects per unit (TDPU). In other words -ln(.7976) = 0.2261.



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YTP1 YTP2 YTP3 YTPkInput Output

Step 1 Step 2 Step 3 Step k

YNORM YNORMYNORMYNORM

NORMALIZEDYIELD

kRTNORM YY =

10 step process i.e. k = 10YRT = 36.8%YNORM = 90.5%

%5.90368.10 =

Normalized Yield (YNORM)

...

1_04

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013

Normalized Yield A Six Sigma Agent from Human Resources is analyzing a particular process involving a form. He knows that there are 10 steps involved in the process and calculates that the Rolled Throughput Yield is equal to 36.8%. When the team wants to assign Yield values to each of the ten steps, one member suggests dividing 36.8% over ten steps. They quickly realize that this would not be the correct method to calculate the Normalized Yield. Another member then incorrectly suggests that since the Rolled Throughput Yield equals 36.8%, then all steps should have the same Throughput Yield (36.8%). After several discussions, the Six Sigma Agent points out that the Normalized Yield is equal to the kth root of the Rolled Throughput Yield, where k equals the number of process steps. He explains to the team that this is a form of "average" that represents an equalized value applicable to all steps of the process. The team then calculates the 10th root of 0.368 and concludes that each step has a Normalized Yield equal to 90.5%.



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XXXXConceptualDefinition

Initial AircraftSizing XXXXXXXX

MarketCompetition

AnalysisXXXX

- Identify CompetitorsTOP=3

- Perform analysisTOP=4

- Prepare reportTOP=1

XXXX

TOP=61 DPMO=200

TOP=22TOP=15 TOP=24

DPMO=26

DPMO=13

DPMO=79

TOP=8TOP=16

Metrics Flow Down

1_04

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014

Metrics Flow Down To illustrate the concept of Metrics Flow Down, let's look a partial representation an engineering process as defined in the Bombardier Engineering System. We can use the process "Conceptual Definition" at the top of the figure to illustrate the concept of Flow Down. Several studies have demonstrated that there are 61 total opportunities for defects (TOP). Under current circumstances, this process produces around 200 defects per million in the short-term. In other words, it is a 3.4 Sigma process. If we know the breakdown of opportunities for each level, we can use the concept of Metrics Flow Down to estimate the number of DPMO for each component of the process "Conceptual Definition". For example, if "Initial Aircraft Sizing" represents 39.34% (24/61) of the opportunities of "Conceptual Definition", and this process produces 200 DPMO, then "Initial Aircraft Sizing" produces around 79 DPMO (200 x 0.3934). In the same fashion, we calculate the DPMO levels for "Market Competition Analysis", "Perform Analysis" and so on. The previous example uses data already available, but "Metrics Flow Down" can also be used to establish goals during the "product development phase", when no actual data is available. For example, given the same number of opportunities, if we establish a goal of 3.4 DPMO (Six Sigma) for "Conceptual Definition", the following values would represent the goal in DPMO for each component of the process: 1.33 DPMO, 0.44 DPMO and 0.07 DPMO What would be the value for each step, if a goal of reducing DPMO by a factor of 10 is established? That is, the total DPMO for the "Conceptual Definition" is set at 20.



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Metrics Flow Down

Global ExpressSystem LevelAt the System level:Line Characteristic D U m TOP DPU DPO DPMO Shift Z.B

1 Fuselage 0.3249 1 1,010 1010 0.000322 322 1.5 4.912 Doors 0.0326 1 320 320 0.000102 102 1.5 5.213 Stabilizers 0.0183 1 240 240 0.000076 76 1.5 5.29

Grand 0.3758 1570 1570 0.000500 500 1.5 4.79

Sub-system LevelAt the Subsystem level: FuselageLine Characteristic D U m TOP DPU DPO DPMO Shift Z.B

1 Forward Fuselage 0.0042 1 115 115 0.000037 37 1.5 5.472 Nose Fuselage 0.0336 1 325 325 0.000104 104 0.5 4.213 Center Fuselage 0.0046 1 120 120 0.000038 38 1.5 5.464 Fuselage assy 0.0645 1 450 450 0.000143 143 1.5 5.13

Grand 0.0691 1010 1010 0.000322 322 1.5 4.91

Element (Unit) LevelAt the Element (Unit) level: Center FuselageLine Characteristic D U m TOP DPU DPO DPMO Shift Z.B

1 Main Landing Gear Wheel Bins 0.0005 1 40 40 0.000013 13 1.5 5.712 Center Fuselage Floor 0.0006 1 45 45 0.000014 14 1.5 5.683 Center Fuselage Floor-Panels 0.0004 1 35 35 0.000011 11 1.5 5.75

Grand 0.0010 120 120 0.000038 38 1.5 5.46

Global express

DPMOSystem = 500

1_04

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Metrics Flow Down A Six Sigma Agent uses records from the Quality department and the product breakdown to construct a table. He flows down the metric DPMO to the sub-system and element levels to illustrate how a process that seems to be performing well (14 DPMO) can impact the system level which is at 500 DPMO. The agent then presents his findings with a Master Agent and a Champion and discusses the Metrics Flow Down. At the system level we have three main components: Fuselage, doors and stabilizers. The number of DPMO is strictly calculated horizontally, but since in this example the number of units equals one, then the same result is obtained adding the DPMO values: 322, 102 and 76 DPMO for a total system level of 500 DPMO. If we focus on the fuselage (322 DPMO), we see that it is made of four components at the sub-system level: Forward, nose, center fuselage, and the fuselage assembly. Records from the Quality department show that each component produces 37, 104, 38 and 143 DPMO respectively. A similar breakdown can be made for the Center Fuselage, which is made of the Main Landing Gear Wheel Bins, Center Fuselage Floor and Center Fuselage Floor-Panels. At this level, we see that the Center Fuselage Floor produces 14 DPMO, and thus we can see how a process with 14 DPMO impacts a 500 DPMO system level product. The Agent, along with the Champion and the Master Agent,sets a goal to improve the quality of the system level by a factor of 10. The Agent is asked to calculate the new values for DPMO at the various levels. They also agree to track actual data and to compare it to the set goal on a monthly basis.



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lyze

System LevelAt the System level:Line Characteristic D U m TOP DPU DPO DPMO Shift Z.B

1 Fuselage 14 1010 0.013861 13,861 1.5 3.70 2 Doors 11 320 0.034375 34,375 1.5 3.32 3 Stabilizers 5 240 0.020833 20,834 1.5 3.54 4 Assembly 10 125 0.080000 80,000 1.5 2.91

Grand= 40 1695 0.023599 23,600 1.5 3.48

Global Express

Subsystem LevelAt the Subsystem level: FuselageLine Characteristic D U m TOP DPU DPO DPMO

1 Foreward Fuselage 1 120 0.008333 8,333 2 Nose Fuselage 2 320 0.006250 6,250 3 Center Fuselage 8 120 0.066667 66,667 4 Fuselage assy 3 450 0.006667 6,667

Grand= 14 1010 0.013861 13,861

At the Subsystem level: DoorsLine Characteristic D U OP TOP DPU DPO DPMO

1 Passenger/Crew Door 7 120 0.058333 58,333 2 Emergency Exit 3 160 0.018750 18,750 3 Door assy 1 40 0.025000 25,000

Grand= 11 320 0.034375 34,375

At the Subsystem level: StabilizersLine Characteristic D U OP TOP DPU DPO DPMO

1 Vertical Stabilizers 1 80 0.012500 12,500 2 Rudder 1 120 0.008334 8,334 3 Stabiliser assy 3 40 0.075000 75,000

Grand= 5 240 0.020834 20,834

DPMO=23 600

Metrics Roll Up

Unit LevelAt the Unit level: Forward FuselageLine Characteristic D U m TOP DPU DPO DPMO

1Forward Fuselage Floor 0 40 1 40 0 0 -

2Forward Fuselage Floor-Panels 1 40 1 40 0.025 0.025 25,000

3Crawlway Floor Panels 0 40 1 40 0 0 - Grand= 1 120 0.008333 8,333

At the Unit level: Nose FuselageLine Characteristic D U m TOP DPU DPO DPMO

1 Nose Fuselage Floor 2 160 1 160 0.0125 0.0125 12,500

2Nose Fuselage Floor-Panels 0 160 1 160 0 0 - Grand= 2 320 0.00625 6,250

At the Unit level: Center FuselageLine Characteristic D U m TOP DPU DPO DPMO

Main Landing Gear

1_04

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016

Metrics Roll Up A Six Sigma Agent explains to a manager how the Sigma value for a particung data pertinent to the Nose Fuselage Floor and Panels at the unit level. We found that these processes produce 12,500 and 0 DPMO for a total of 6,250 DPMO …" The manager interrupts: "I see that the line is labeled "Grand", but surely 6,250 is not the addition of 12,500 plus zero?" She replies: "This is because the total DPMO is calculated horizontally and not as an addition of the steps' DPMO. If we have 2 defects over a total of 320 opportunities, then DPMO equals 6,250". "Working with a Master Agent, we then used our data, plus the data from obtained from other Six Sigma projects related to the forward fuselage, nose fuselage, etc, and rolled up the values to the system level to characterize the product." The Manager recognizes that by using this tool, we can quickly make comparisons across products, processes, and even companies and industries. Various metrics can be used to roll up these values: DPMO, Yield values, etc. and this approach is applicable to all processes in transactions, engineering, etc.



Ana

lyze

Benchmarking Charts

302928272625242322212019181716151413121110 9 8 7 6 5 4 3 2 1Characteristic

5.6915.2685.7765.8526.0725.8365.8955.6986.0005.5496.0006.2145.4055.7505.5815.4825.9245.8816.0005.6115.6205.6846.2145.5525.8085.3575.5565.8945.7275.919

ZBench

1.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.5001.500ZShift

1482 9 7 2 7 6

13 1

26 0 1

47112234 5 6 0

201914 1

25 8

5725 6

12 5

PPM

0.0000140.0000820.0000090.0000070.0000020.0000070.0000060.0000130.0000010.0000260.0000000.0000010.0000470.0000110.0000220.0000340.0000050.0000060.0000000.0000200.0000190.0000140.0000010.0000250.0000080.0000570.0000250.0000060.0000120.000005

DPO

0.0240.1350.0170.0110.0060.0170.0100.0230.0010.0420.0000.0030.0780.0180.0380.0610.0110.0100.0000.0340.0310.0250.0030.0420.0140.0980.0410.0100.0200.012DPU

1222333 1167772 1263474 1187675 1657434 1655103 1261692 1186001 1220609 1164478 1198217 1645695 1166125 1218885 1205101 1259910 1650441 1184325 1203399 1217161 1162831 1258128 1648110 1182650 1215437 1201697 1161184 1256346 1180976 1615476TotOpps

172416471782167523312331178216751724164717022331164717241702178223311675170217241647178223311675172417021647178216752331Opps

709.010709.030709.020709.060711.040710.040708.020708.060708.010707.030704.005706.004708.030707.010708.050707.020708.040707.060707.050706.010706.030706.020707.040706.060705.010706.050705.030705.020705.060693.040

Units

17 96 12 8 4

12 7

16 1

30 0 2

55 13 27 43 8 7 0

24 22 18 2

30 10 69 29 7

14 8

Defs

Report 7: Product Performance

1000000

100000

10000

1000

100

10

1

6543210

Z.Bench (Short-Term)

PPM

Report 8A: Product Benchmarks

Zone of AverageTechnology

Zone of

Typical

Control

3.0

2.5

2.0

1.5

1.0

0.5

0.0

6543210

Z.Shift

Z.Bench (Short-Term)

World-Class

Performance

Report 8B: Product Benchmarks

Total3534333231Characteristic

5.6745.7125.9515.7895.5705.629

ZBench

1.5001.5001.5001.5001.5001.500ZShift

1513 4 92418

PPM

0.0000150.0000130.0000040.0000090.0000240.000018

DPO

0.0230.0070.0150.0390.031DPU

44873554 1265256 1169419 1224057 1189351 1206803TotOpps

17821647172416751702Opps

710.020710.030710.010710.060709.050

Units

673 16 5 11 28 22

Defs

Report 7: Product Performance (continued)

1_04

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017

Benchmarking Charts During an improvement project review, a Six Sigma Champion congratulates a group of Six Sigma teams on the achievements obtained for a particular product. "The fuselage package that we manufacture is a key component of our business. I am pleased to see that we have concentrated our Six Sigma efforts on this product, and the Six Sigma teams, assigned to improve the 35 critical characteristics, have collectively helped us achieve a Sigma level of 5.674." When asked to provide further details on report no. 7, a Six Sigma Agent explains: "From data provided by the various teams, we used the Product Report function of Minitab to obtain a 'global picture' of the complete package. Each characteristic has a particular line indicating the level of Defects Per Unit (DPU), Defects Per Opportunities (DPO), Parts Per Million (PPM) and Z Benchmark (Zbench). Report no. 8A graphs various levels of PPM against Sigma values (Zbench), and shows the targets we need to set to achieve a Six Sigma level. Finally, report no. 8B is also an excellent indicator to determine if our problem is one of control or technology. The vertical region between 3 and 4.5 Sigma indicates that typically, we find issues of technology, whereas if there is a Sigma shift of between 1.0 and 2.0, it indicates a problem of control. As we can see, our package today is produced with adequate technology. The triangles on the graph (from report no. 7) show the range of our current processes, (5.674 Sigma), and our path to achieve Six Sigma. When the Champion asks why the reports indicate "short -term" next to Zbench, the Six Sigma Agent explains that by convention, all Sigma values are reported and compared using short term values (Zst).


Lessons Learned • Historically, we have used the wrong indices to measure process performance. The concepts of First Time

Yield and Final Yield do not account for the Hidden Factory, thus giving an overvalued measure of Yield. • The term Yield is used to denote the probability of producing defect-free units of output. Mathematically, it is

equal to 1 – p (defects). • Yield can be calculated from either discrete or continuous data. • The Hidden Factory is a concept that denotes all the amount of work above and beyond the requirements

necessary to produce one good unit of output. • Customer surveys, records of returned goods, warranty costs, data on rejection reports are some of the

records that are commonly available in companies that can offer a starting point in Six Sigma to determine process capability.

• First Time Yield is the ratio of the number of units that pass inspection (S) to the total number of units tested

(S). • Final Yield is the calculation of First Time Yield after the last process steps in a series of process steps is

completed. • Throughput Yield (YTP) represents the probability of producing a defect-free unit in a process step. When

using discrete data, Throughput Yield can be approximated using the formula e-DPU where DPU stands for "Defects Per Unit". When using continuous data, Throughput Yield values are calculated as the appropriate area under the normal curve (area under the curve and between the specification limits).

• Rolled Throughput Yield (YRT) represents the probability of producing a defect-free unit in a series of process

steps. It is calculated by multiplying the Throughput Yield values of each process steps involved in producing the output, or by using the formula e-TDPU, where TDPU stands for "Total Defects Per Unit".

• A Normalized Yield (YNORM) is a single and equivalent Yield value assigned to each of the process steps

involved in producing an output. It characterizes all process steps assigning a "kind of average" Yield value, and is calculated as the kth root of Rolled Throughput Yield, where k is the number of process steps involved.

• When reporting and comparing Sigma values, the metric Zst (short term) is used. • Metrics Flow Down can be used as a "what if" tool during the design phase of a new product or process.

Using this tool, we can set performance objectives at all levels of the product or process breakdown, and then compare these values against actual data as it becomes available.

• Metrics Roll Up allows us to calculate a value that characterizes a product or service, given the Throughput

Yield values of the process steps involved in producing the output. It is often used to benchmark products or processes across units, companies or even industries.

• The Minitab "Product Report" function can be used to characterize a product and to generate a Benchmark

chart.

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