six sigma fundamentals - · pdf filesix sigma six sigma fundamentals six sigma fundamentals...

Copyright – All Rights Reserved

Six Sigma

Six Sigma Fundamentals Six Sigma Fundamentals Six Sigma is a data-driven process re-engineering methodology resulting in paradigm shifts in the way a company behaves, treats its customers, and produces its products. It has been used for over 15 years in a number of companies including General Electric, Allied Signal and Texas Instruments. Six Sigma performance implies a level of process and product performance of no more than 3.4 defects per million opportunities. Five Sigma, in turn, is 233 per million, Four Sigma is 6,210 per million, while Three Sigma implies 66,807 per million opportunities. Most companies in North America are between 3 and 4 Sigma, while truly world-class performers are Six Sigma or better. Six Sigma companies produce vastly superior, reliable, and customer-satisfying products, faster, better, cheaper, and more efficiently than their competitors, translating higher quality for their customers into lower costs for themselves. Companies which are at Three or Four Sigma, are typically not actively trying to improve themselves, are often stagnant and complacent, fighting to stay one step ahead of the competition, and not really aware of how poorly they are performing. They also typically do not believe Six Sigma Performance is viable. For any process, variation is the main reason for poor performance, and the key focus of Six Sigma. Defects arise from variation, arising in turn from either process, material, or design inadequacies. A defect results when a characteristic doesn't conform to a standard, and can be uniformly or randomly distributed in a process. Closely related to the concept of defects is the metric Defects per Unit. In this chapter DPU and the associated concepts are discussed. Another concept closely related to defects is Process Yield. The larger the number of defects in a production batch, the lower the yield. There are several types of yield, such as first-time yield, rolled throughput yield and normalized yield. These metrics are closely linked to defects, defects per unit, and the process' Sigma value. Process Capability is also discussed in this chapter, which refers to the ability of a process to perform to the target and specifications set out for it. Processes can be precise and/or accurate, according to the inherent variation and how well targeted they are. Process targeting is determined by the statistic called Mean, the average value of the process output variable, while process variation, or spread, is measured by the statistic Standard Deviation. One of the most important tools for achieving Six Sigma process capability is Process Benchmar-king. This powerful tool is used to compare processes or products within the industry, between industries, or even between geographical areas or countries. A tool called Benchmarking Chart is a powerful way to "baseline" various processes or products so they may be meaningfully compared. Companies embarking on the road to Six Sigma adopt a Roadmap which is a four-step process to characterize and optimize their processes to render them virtually impervious to variation. The term Roadmap refers to the need to "breakthrough" the so-called "Five Sigma Wall". It has been shown that progression from 3 to 4 to 5 to Six Sigma capability is exponential, and the jump from 5 to Six Sigma is extremely difficult. Making the first few Sigma gains can be achieved by continuous improvement tools, but "breaking through" the wall requires the implementation of the Roadmap. The Roadmap is divided into four phases. The first phase is Process Measurement, where a "snapshot" is taken of the process to determine the current state of capability. The next phase is Process Analysis, where the data collected in the Measurement phase is analyzed to determine the relationships between the process variables, and determine the direction the process improvement is to take. The third stage is Process Improvement, where certain process input variables, determi-ned in the Analysis phase to


be critical to optimum process performance, are subjected to an extremely powerful statistical tool called Design of Experiments. DOE is used to study, in a rigorous manner, the performance of the process at a variety of different input settings. The result is a process which has been optimized to run at peak efficiency, on target, with a minimum of variation. The final stage of the Roadmap is Process Control, where the tools of Statistical Process Control are brought to bear on the optimized process. The process is monitored on an on-going basis to ensure the process itself does not begin to vary from the optimized state achieved during Phase Three, Improvement. Key Questions • What is Six Sigma and how does it relate to our business? • How does Six Sigma help us focus on customer satisfaction and competitive

capability? • How does Six Sigma improve product, technology, and organizational capability? • What type of results can be expected through the adoption of Six Sigma? • What are the global success criteria for implementing and deploying Six Sigma? • What are the initial steps for setting Six Sigma in motion? Key Questions Six Sigma is a process reengineering methodology which has been embraced by Bombardier and will be implemented throughout the organization in the coming years. It will result in major shifts in our ways of thinking and our ways of doing business, and will ultimately lead to quantum leaps in process and product quality. Producing superior products, delivered in a timely manner and at the best possible price will translate into highly satisfied customers and marketplace domination. The Six Sigma methodology focuses on the drastic reduction of process variation and product defects. The result is processes which are very robust, which make very efficient use of resources and assets, and which result in highly efficient organizations. Achievement of Six Sigma process capability will result in processes which yield less than 3.4 defects per million opportunities. Ultimate results will include reductions in Cost of Poor Quality, increases in market share, reduced cycle times and inventory levels and increased product reliability. Successful implementation of Six Sigma is achieved through careful planning and program control, benchmarking of all processes and the application of the Roadmap. It is vital to focus on the few processes where advantage can be taken of the Leverage Effect to yield maximum results. Rigorous control and management of business metrics and designing products and processes for Six Sigma are also vital. Six Sigma is implemented by achieving total management and employee support, instituting rigorous program controls, assuring proper training and coaching, and ensuring projects are properly scoped to achieve most efficient use of resources.


Recognize the Need for Change A Manager is reflecting on the fact that we are in business to make money, and that we make money by satisfying the needs of our customers. Recognizing that customer focused organizations align their activities with their customers requirements, the manager notes that the needs of the customer can be defined in terms of quality, delivery and price. The Manager remembers Mikel J. Harry's words "we don't know what we don't know", … "If we don't know, we can not act, if we can not act, the risk of loss is high. If we do know and act, the risk is managed. If we do know and do not act, we deserve the loss" and that "Ignorance is not bliss, it is the food of failure and the breeding ground for loss." The Manager is convinced that the only way to improve performance is to have a clearer perspective of the current performance through metrics. Many companies have proven that the Six Sigma approach has improved their performance to world class levels. Six Sigma has been in industry for over 15 years and is in wide-spread use in companies such as Motorola, General Electric, Allied Signal, Texas Instruments and many others. Six Sigma as a Value Benchmarking in industry over the last decade has shown that the average company is in the range of three to four Sigma. Sadly, many of these companies are firmly set in their ways, complacent in the knowledge that they are at least as good as their competition. Among the traits shared by these stagnant companies are: • Profitable and growing • Market prices declining • Competitors increasing • Have a quality assurance program • Spending 10-25% of sales dollars on repairing or reworking product before it ships • Unaware that world-class companies have similar processes that are greater than 100X more defect-free • Believe that a zero-defects goal is neither realistic nor achievable • Have 10X the number of suppliers required to run the business • 5-10% of the firm's customers are dissatisfied with product, sales, or service and will not recommend that

others purchase products or services Note: Historically 1 in 25 unsatisfied customers express their dissatisfaction. 1 unsatisfied customer

typically tells 7-10 others. History has shown that there are a number of major differences in philosophy, policies and procedures, actions, behaviors, and beliefs, between companies which are at Four Sigma capability and those which are at Six Sigma. Probably the biggest single difference between a true Six Sigma company and those companies that are stuck permanently at Four Sigma, is the mindset. The under-achieving companies are complacent, unaware and unable to accept the idea that they must make quantum leaps in process quality if they are to gain, and keep, their competitive advantage. The benefits of achieving Six Sigma are clear and obvious, both from the company's standpoint, and more importantly, from their customer's standpoint. The company is able to produce its product in the most efficient means possible, resulting in an end product which is very competitively priced and of the highest possible quality. Truly, "The highest quality producer is the lowest cost producer". Realistically, if all departments of a company are operating at Six Sigma, then the products will be at the top of their market and far ahead of the competition. It should be remembered that product quality is not an automatic guarantee of success; even a product with Six Sigma manufacturing quality will fail in a market place that does not want it, or where it is not adequately supported.


1-7/4Six Sigma Fundamentals

Primary Sources of Variation

Inadequate DesignMargin

InsufficientProcess

Capability

UnstableParts andMaterial

Region of Six Sigma Synergy

Primary Sources of Variation Process variation, the enemy of true Six Sigma process capability, has been shown to have three main causes: • Insufficient process capability caused by processes which produce relatively high numbers of defective units • Inadequate design margin, which results in unnecessarily and unreasonably tight process specifications

(sometimes tighter than the customer requires) • Unstable parts and materials, usually caused by vendors who are not able to control their own processes and

ship materials which in turn yield variation in the customer's processes The inevitable result of excessive process variation is the production of defects, which occurs when units are produced which are outside the required specifications.



Rec

ogni

ze

Histogram and the Normal Distribution

Units of Measureµ

Units of Measure

Probabilityof a DefectArea of Yield

Performance Limit

The Normal Curve

The Histogram

0

5

10

15

20

25

1.238 1.240 1.242 1.244

Raw DataFr

eque

ncy

Histogram and the Normal Distribution When measuring processes for the purpose of Six Sigma data collection, it is important to remember that there are two basic types of data, discrete and continuous. Discrete data can only assume certain values such as Yes/No, On/Off or a numerical, counting value such as 1, 2, 3, etc. Discrete data cannot be meaningfully subdivided. Continuous data can assume a range of values such as a temperature scale or a set of weights. These scales, such as degrees or pounds, can be meaningfully subdivided. A good way to represent a situation is to transform data into a picture; the histogram. It represents the distribution of this data. In most of the cases, these distributions are similar to the normal distribution represented by the bell shape curve. The normal distribution makes it possible to compute, with a high degree of confidence, the probability of defects.



Rec

ogni

ze

Shape, Location and Spread

s = σ = ( Xi - X )2Σ

i=1

n

n - 1

X = µ = XiΣ

i=1

n

n^

^

Variable X Measurements

75 80 75 65 7085 70 70 85 7060 80 80 80 6580 75 75 70 8570 75 75 75 8580 55 70 70 8565 70 80 75 6575 85 90 80 6570 75 75 80 8075 95 90 60 65

Number of Cases = 50Mean = 75Median = 75Standard Deviation = 8.3299Range = 40Variance = 69.388Minimum = 55Maximum = 95

Values of X

0

2

4

6

8

10

12

14

50 60 70 80 90 100 110

Freq

uenc

y

Shape, Location and Spread The majority of process data will be normally distributed (Bell shape curve). If the histogram is not bell shaped, the data should be investigated further . The term "Measures of Location" refers to the various ways in which the central tendencies of the data distribution can be calculated and displayed. Generally, the value of the mean (average): x is the best way to estimate the central tendency: ? of the most common distributed data. The third important characteristic of a distribution is the spread (variation). Generally, we estimate this variation by calculating: • The range (R), or • The standard deviation (s or σ).



Rec

ogni

ze

µ

Specification Limits

USLLSL

T

µ

Relatively little data is outside the SpecLimits so the defect rate is

comparatively low

USL

T

LSL

Much of the data is beyond the SpecLimit so the Defect Rate is very high

Specification Limits Specification Limits, which are expression of customer needs, are literally and figuratively the "goalposts" by which defects are determined. If the process output is not within the specifications set out for the process, then a defect has occurred. In the manufacturing environments, specifications are usually set by the Engineering functions. Operators have a clear set of limits to work to, usually set out on engineering drawings, and when the output of their process is above the Upper Specification Limit (USL), or below the Lower Specification Limit (LSL), then we say that a defect has been produced. Examples of Performance Limits in manufacturing processes include such things as dimensional tolerances on machined parts or temperature or pressure limits on the fabrication of composite parts.


12Six Sigma Fundamentals

Rec

ogni

ze

Specification Limits (Cont’d)

0

Mean

UpperLimit

24h 48h

Frequency

Much of the data is beyond theLimit so the defect rate is very high

Time todeliver

informationpackage

Specification Limits (Cont'd) To illustrate the application of Performance Limits in the administrative/transactional world, consider the following example. A Six Sigma Black Belt was beginning a project in Marketing, aiming to reduce the cycle time to ship customer information packages. In an effort to benchmark the current process and arrive at a current Sigma value for the process, the Black Belt had to relate the concept of defects to the request for information process. When a potential customer first communicates with Marketing and requests information, the clock starts ticking. The goal is then to get that information into the customer's hands as soon as possible. If Marketing's yardstick for success is 48 hours at the latest, then that becomes the Upper Specification Limit. (Note that this is a case of a one-sided Spec Limit, and this is typical of cycle-time processes.) So, if the information does not reach the customer within 48 hours of his or her requesting it, then the delivery time is outside the Spec limit and then we would say a defect has occurred. For example, similar situations often exist in the engineering environment with regard to drawing schedules. Unfortunately, specifications are relatively rare in the administrative/transactional world, compared to the manufacturing world. A major change in mindset is required in implementing Six Sigma in the transactional environment, as it necessarily requires the institution of process specifications, where none existed before.



Rec

ogni

ze

Probability and Defects

0

50

100

150

200

250

300

1.233 1.235 1.237 1.239 1.241 1.243 1.245 1.247

USLLSL

ProcessCapability

Report

Num

ber o

f Par

ts

Probability and Defects One of the most critical conceptual relationships to understand in learning the Six Sigma methodology is the idea of probability of defects and the yield of a process. During data collection for a Six Sigma project, the following production results were noted: • A total of 1,000 parts were produced. • 22 parts were greater than the Upper Spec Limit. • 31 parts were less than the Lower Spec Limit. • Therefore 22+31=53 parts were rejected of which 12 were scrapped. If we now consider that we had 1 opportunity for defect per part, and that we built 1000 parts, then we have 1000 opportunities for defect. This could be considered to be the number of times we "rolled the dice". If the roll of this manufacturing dice produced 53 defects, then basic probability theory states that the probability of defect is 53/1000 =.053, or 5.3%. In other words, 5.3% of the time we attempted make a good unit, we made a defective one. Turning this concept around, then if 5.3% of the time we made a defective unit, then 100-5.3 or 94.7% of the time we made a good one. We would then say that the process yield is 1 - .053 = .947, or 94.7%



Rec

ogni

ze

A Tale of Two Sigmas

µ

T

+ ∞- ∞

6σ

USL

σ = (Xi- µ)2Σi=1

N

N

Z = SL - µσ x

A Tale of Two Sigmas One of the more confusing aspects of learning Six Sigma, is the relationship between process Standard Deviation, which is denoted by the Greek letter sigma σ and the process Sigma value, known as Z. When output data of a process is collected and analyzed, two of the first statistics to be calculated are the Mean and the Standard Deviation. The Mean, or average value, is compared to the process target, to see how accurately the process is actually performing. The Standard Deviation determines the spread of the data around the Mean, and is the prime measure of process variation. Clearly, the larger the Standard Deviation is, the worse the process is performing. The Standard Deviation of the process, denoted by the Greek letter σ, is NOT the process Sigma Value. The process Sigma value, or Z, on the other hand, relates the variation of the process to the output's Specification Limits, relative to the process Mean. The process Sigma value is defined conceptually as the number of Standard Deviations which can fit between the Mean and the Specification Limit. If the process is performing well, with small variation, then the Standard Deviation of the output will be small, and many such Standard Deviations can fit between the Mean and the Spec Limit. The Sigma value of this process will be relatively large. On the other hand, if the process is "sloppy" with a large Standard Deviation, which is not a good situation, then few such Sigmas can fit between the Mean and the Spec Limit, and the process Sigma value will be small.



Rec

ogni

ze

Shifts and Drifts

Problem with Spread

Desired

CurrentSituationAccurate

(but not precise)

LSL USLT

Nominal USLLSL

Short-TermPerformance

(st)

Long-TermPerformance

(lt)

LSL USL

Long-Term

Short-Term

δ

Desired

Problem with Centering

LSL T USL

Dynamic Mean

CurrentSituationPrecise(but not

accurate)

Shifts and Drifts The design team asks the Six Sigma Black Belt to explain how the Six Sigma approach may help them to design better products. The Black Belt takes this opportunity to detail the concept of process shifts and drifts. The team recognizes that any process varies and that this variation is independent of the specified tolerance. The team also recognizes that the process center is independent of the design target. Historically, a typical process will shift and drift by approximately 1.5 σ over time. The Six Sigma Black Belt shows the combination of those two variations (spread plus shifts and drifts) which ends up in the process long term variation. This variation is due to many causes. It is due to the combined effects of the trivial many (white noise) plus the vital few (black noise). With a Six Sigma short term process the probability to produce out of specs results, even with a 1.5 sigma shift, is 3.4 parts-per-million of defects. In this case the process is said to be robust to variation. The Black Belt makes the engineering team aware that they need to take this into account during the design phase.



Rec

ogni

ze

The Standard Normal Deviate(Z value - short- and long-term)

Z Area Z Area Z Area Z Area

0.00 .500000000 1.51 .065521615 3.02 .001263795 4.53 .0000029990.05 .480061306 1.56 .059379869 3.07 .001070234 4.58 .0000023690.10 .460172290 1.61 .053698886 3.12 .000904215 4.63 .0000018670.15 .440382395 1.66 .048457216 3.17 .000762175 4.68 .0000014690.20 .420740315 1.71 .043632958 3.22 .000640954 4.73 .0000011530.25 .401293634 1.76 .039203955 3.27 .000537758 4.78 .0000009030.30 .382088486 1.81 .035147973 3.32 .000450127 4.83 .0000007050.35 .363169226 1.86 .031442864 3.37 .000375899 4.88 .0000005500.40 .344578129 1.91 .028066724 3.42 .000313179 4.93 .0000004280.45 .326355105 1.96 .024998022 3.47 .000260317 4.98 .0000003320.50 .308537454 2.01 .022215724 3.52 .000215873 5.03 .0000002580.55 .291159644 2.06 .019699396 3.57 .000178601 5.08 .0000001990.60 .274253121 2.11 .017429293 3.62 .000147419 5.13 .0000001540.65 .257846158 2.16 .015386434 3.67 .000121399 5.18 .0000001180.70 .241963737 2.21 .013552660 3.72 .000099739 5.23 .0000000910.75 .226627465 2.26 .011910681 3.77 .000081753 5.28 .0000000700.80 .211855526 2.31 .010444106 3.82 .000066855 5.33 .0000000530.85 .197662672 2.36 .009137469 3.87 .000054545 5.38 .0000000410.90 .184060243 2.41 .007976235 3.92 .000044399 5.43 .0000000310.95 .171056222 2.46 .006946800 3.97 .000036057 5.48 .0000000241.00 .158655319 2.51 .006036485 4.02 .000029215 5.53 .0000000181.05 .146859086 2.56 .005233515 4.07 .000029215 5.58 .0000000181.10 .135666053 2.61 .004527002 4.12 .000019047 5.63 .0000000101.15 .125071891 2.66 .003906912 4.17 .000015327 5.68 .0000000081.20 .115069593 2.71 .003364033 4.22 .000012305 5.73 .0000000061.25 .105649671 2.76 .002889938 4.27 .000009857 5.78 .0000000041.30 .096800364 2.81 .002476947 4.32 .000007878 5.83 .0000000031.35 .088507862 2.86 .002118083 4.37 .000006282 5.88 .0000000031.40 .080756531 2.91 .001807032 4.42 .000004998 5.93 .0000000021.45 .073529141 2.96 .001538097 4.47 .000003968 5.98 .0000000011.50 .066807100 3.01 .001306156 4.52 .000003143 6.03 .000000001

ZZZ ShiftSTLT−=

µ−σ

=Ζ SL

Ζµ

T

SL

The Standard Normal Deviate (Z value – short- and long-term) The painting team wants to establish the probability of defects of its process related to the paint thickness. The Six Sigma Black Belt explains that the standard normal deviate table can be used for this purpose. The team needs to establish the Z value for the process. This represents how many Sigmas (standard deviations) the specification limit is away from the average for any normally distributed process. Once the Z value has been computed the area under the curve and hence the probability of defects can be determined. For a process with a calculated Z short term of 3.01 this corresponds to 0.001306156 i.e. 0.13% probability of defects. But, when considering the process shifts and drifts of 1.5 sigma, the Z long-term is 1.51. Then, the Black Belt emphasizes the probability of having defects is then 0.065521655 i.e. 6.55%; or 65,522 PPM. Meanwhile, back at the purchasing department, a Champion is reviewing the result of a Six Sigma project aimed at reducing purchase order defects. The project has resulted in an improvement from Zlt = 1.66 to Zlt = 3.07. This new Z long-term represents 0.107% probability of defects i.e. 1,070PPM. The Champion is pleased with this as the previous defect rate was 48,457PPM. The Champion and the team then reflect on the need for further improvement and agree to revise the project goal to achieve a Six Sigma level of performance (4.5 sigma long-term).


Sampling While working on the shop floor one day, collecting data for a project, a Six Sigma Black Belt noticed a machinist carefully re-arranging the finished pieces on an inspection tray. The process was repeated a number of times. The Black Belt asked another of the machinists what the operator was doing, and he replied "Those parts are going out to an inspector who always samples his inspection pieces from the corners of the tray. This guy is simply guaranteeing that his best units will be the ones inspected". Statistically correct sampling of process output is critical to the success of data collection. There are a number of types of sampling available to the Six Sigma Black Belt, including: • Random Sampling; • Stratified Sampling; • Sequential Sampling. It is essential that when designing a sampling plan, the sample must be representative of the process output during the sampling period. • The above example, the sample was taken at regular intervals in order to show variation in central tendency

and spread of the process. • The second sampling may cause us to miss some process variation. • It should be noted that the sampling size may be as small as one single piece.



Rec

ogni

ze

The Bathtub Curve

Design Related Failures

Quality Failures

FailureRate

Time

Every failure is the result of a defect in the design, process, or material.

Infant Mortality Useful Life Wearout

The Bathtub Curve As we know, producibility is inextricably linked to variation. From this vantage point, it is easy to see how variation is the principal determinant of product quality. In turn, the many facets of product quality either directly or indirectly contribute to the overall reliability of the end product, and hence to customer satisfaction. As a result of this domino relationship, we may say that the assurance of optimum product reliability is directly tied to an organization's ability to take a design concept from development on through production which, to a large extent, is tied to variation. In order to better grasp such interconnectivity, let us consider the classical "bathtub" reliability curve. The bathtub curve is formed by the blending of three different curves. First, there is the portion of the bathtub effect that is due to quality failures. When a new unit of product fails after a short period of operation, we say that it was an "infant mortality," for obvious reasons. The second part of the curve is due to the inherent characteristics of the design. The product failure rate, attributable to the design, would tend to form a straight line across the graph, thereby forming the floor of the bathtub curve. The third and last curve on the graph is related to natural "wear-out" of the individual elements that comprise the product. It is important to understand the concept of the Bathtub Curve and its representation of temporal failure patterns. Six Sigma is focused on improving process quality, and one major result of this is to lower the Bathtub Curve by reducing failure rates and thereby improve customer satisfaction.



Rec

ogni

ze

Reliability & Capability

Failure Rate

Failure Rate

Poor ProcessCapability

USLLSL USL LSL

Very highprobabilityof defects

Excellent ProcessCapability

$

Very lowprobabilityof defects

Very highprobabilityof defects

Very lowprobabilityof defects

Reliability & Capability Given that inspection and test efficiency are relatively constant from unit to unit, it is reasonable to assert that escaping defects will increase as manufacturing, component, and material variation increases. Whenever the rate of escaping defects increases, we can expect a higher field failure rate, due to the weakened condition of product as a function of increased variation. Hence, we may say that the need for burn-in increases as manufacturing capability diminishes. However, if the initial capability of the processes, components, and material is high enough to ensure that any given unit of product will not fail during initial operation, there would be little, if any, need for test, inspection, or burn-in. Thus, a product could be manufactured and shipped without unnecessary delay and cost. In light of the latter arguments, it may now be reasoned that the ability to forecast reliability is highly dependent upon a measure of the interplay within and between the design, manufacturing processes, and material. In addition, we may also say that the cost-effective optimization of reliability requires that we "design for producibility." This implies that the product designs will be relatively impervious or as some would say, "robust" to natural, unavoidable sources of process, component, and material variation. In turn, this assumes that we have a quantitative knowledge of process, component, and material capabilities.



Rec

ogni

ze

Process Capability

54321

Precise but not Accurate

Accurate but not Precise

Process Capability The Six Sigma Black Belt explains to the team how their customer will evaluate the performance of their department. "One of the most important concepts in quality management is Process Capability. Rather than characterizing a process only in terms such as defects per unit or yield, we could also define it in terms of a capability". "If the output of a process is centered around a target value, but has a wide spread of values, in other words a large standard deviation, the process is accurate but not precise". "On the other hand, if the process has a small standard deviation (less variation) but the average value of the process parameter is far from the target, then we could say that the process is precise but not accurate". Now the Black Belt emphasizes the degree of confidence in the capability indicators. He underlines the direct impact of the data type: continuous or discrete along with the fact that there is an appropriate number of measurements that must be gathered.



Rec

ogni

ze

Process Capability RatiosCp & Cpk

Incr

ease

in th

e nu

mbe

r of r

ejec

ts

LowerSpecification

Cp < 1

Cp = 2.0

UpperSpecification

Con

tinuo

us Im

prov

emen

t LowerSpecification

UpperSpecification Potential Real

Capability Capability

Cp = 2.0 Cpk = 2.0

Cp = 2.0 Cpk = 1

Cp = 2.0 Cpk < 1

Cp = 2.0 Cpk = 0

Cp = 2.0 Cpk < 0

Cp = 2.0 Cpk < -1

Process Capability Ratios Cp & Cpk The Six Sigma Black Belt shows to the team how to calculate the capability indicators pertinent to their process. He explains "Such a ratio, or index, will contrast the distribution spread to the specification width, and would be nondimensional. This allows the comparison of processes to achieve similar tasks. The Cp ratio is also a measure of the potential of a process to produce products within such a tolerance. In other words, a poor Cp will indicate to your customers the risk they encounter with your product". "The Cp helps us to answer the question: Are we able to produce good products?" The Black Belt emphases the second capability ratio. "Another aspect of process capability which is very important is the concept of precision. Is your process centered on target? The process may have little variation (precise) but be far from the target (not accurate). The result of such a situation may be out of specification products. "The Cpk ratio helps us answer the question: Are we making good products?". 6σ process = ZST = 6 Cp = 2 ZLT = 4.5 Cpk = 1.5



Rec

ogni

ze

The Goal of Six Sigma

2 308,5373 66,807

4 6,210 5 233 6 3.4

σ PPM

Process Capability

Defects per Million Opportunities

(Distribution Shifted ± 1.5σ)

The Goal of Six Sigma Members of the Methods department team are asking the Six Sigma Black Belt. "How do we translate Sigma in terms of defects?" The Black Belt explains that Sigma is a statistical criterion which reflects process probability of defects. The sigma scale of measure is precisely correlated to such figures as defects-per-unit, parts-per-million defectives and the probability of failure/error. Historically, process capabilities were calculated with a criterion of ± 3σ and did not consider the 1.5σ process long term shift and drift. The average benchmark for most companies is 4σ i.e. 6,210 PPM. To reduce the consequences of high defect levels, world-class companies now seek process ratings of 6σ i.e. 3.4 defects per million opportunities.


Defects-Per-Unit The Supervisor of the drawing department asks for the help of the Six Sigma Black Belt to improve the situation of excessive drawing mistakes. "The first step is to have a true picture of the situation" advises the Black Belt. Together, they pick randomly a sample of drawings which they examine thoroughly. They note all the defects and the number of opportunities for every drawing considered. As an example, the Six Sigma Black Belt illustrates with egg boxes and chip defects how to divide the defects in two categories: uniform and random defects knowing that the second category is the most difficult to address. Having completed their investigation, they compute the number of defects-per-unit (DPU) and the number of defects per million opportunities (DPMO). With these results the Six Sigma Black Belt is able to evaluate the process sigma performance. Meanwhile, the Manager of Information Technology, responsible for computer purchasing, is concerned about long delays involved in providing computers to internal customers. The Six Sigma Black Belt on this project counts a total of 297 opportunities for defect spread over the 7 forms in use, each one to be formally approved. He suggests to the IT manager to gather defect data on those forms and then compute the DPU and DPMO. This would enable the process sigma value to be established. He also suggests the need for 7 forms should be questioned.



Rec

ogni

ze

LEGEND: = OD

Opportunity for Defects

N

5

4

3

2

Report Name Reporting Period From To

Organization Baseline Period From To

Project Improvement Goal

Department Unit Definition

Deliverable Characteristic

Deliverable ID Units of Measure

Process Upper Specification

Step Target Value

Machine ID Lower Specification

Special Note Default Shift 1.50

Line Characteristic D U OP TOP DPU DPO DPMO Shift Z.B

1 Type A 3 907 30 27,210 0.003 0.0001 110 1.50 5.19

2 Type B 71 919 29 26,651 0.077 0.0027 2,664 1.50 4.29

3 Type C 21 274 84 23,016 0.077 0.0009 912 1.50 4.62

4 Type D 88 335 12 4,020 0.263 0.0219 21,891 1.50 3.52

5 Type E 70 40 30 1,200 1.750 0.0583 58,333 1.50 3.07

6 Type F 89 480 49 23,520 0.185 0.0038 3,784 1.50 4.17

7 Type G 49 160 66 10,560 0.306 0.0046 4,640 1.50 4.10

8 Type H 71 160 34 5,440 0.444 0.0131 13,051 1.50 3.73

9 Type I 7 685 93 63,705 0.010 0.0001 110 1.50 5.20

10 Type J 3 758 24 18,192 0.004 0.0002 165 1.50 5.09

11 Type K 99 633 91 57,603 0.156 0.0017 1,719 1.50 4.43

12 Type L 6 947 97 91,859 0.006 0.0001 65 1.50 5.33

13 Type M 83 187 13 2,431 0.444 0.0341 34,142 1.50 3.32

14 Type N 67 14 31 434 4.786 0.1544 154,378 1.50 2.52

15 Type O 97 498 17 8,466 0.195 0.0115 11,458 1.50 3.78

16 Type P 77 954 2 1,908 0.081 0.0404 40,356 1.50 3.25

17 Type Q 71 887 6 5,322 0.080 0.0133 13,341 1.50 3.72

18 Type R 94 771 101 77,871 0.122 0.0012 1,207 1.50 4.53

19 Type S 46 696 15 10,440 0.066 0.0044 4,406 1.50 4.12

20 Type T 12 128 54 6,912 0.094 0.0017 1,736 1.50 4.42

Grand = 1,124 466,760 0.0024 2,408 1.50 4.32Six Sigma Score car d L1: Version 1.0 Deve lope d by Dr. Mikel J. Harr y

Report Name Reporting Period From To

Organization Baseline Period From To

Project Improvement Goal

Department Unit Definition

Deliverable Characteristic

Deliverable ID Units of Measure

Process Upper Specification

Step Target Value

Machine ID Lower Specification

Special Note Default Shift 1.50

Line Characteristic D U OP TOP DPU DPO DPMO Shift Z.B

1 Type A 3 907 30 27,210 0.003 0.0001 110 1.50 5.19

2 Type B 71 919 29 26,651 0.077 0.0027 2,664 1.50 4.29

3 Type C 21 274 84 23,016 0.077 0.0009 912 1.50 4.62

4 Type D 88 335 12 4,020 0.263 0.0219 21,891 1.50 3.52

5 Type E 70 40 30 1,200 1.750 0.0583 58,333 1.50 3.07

6 Type F 89 480 49 23,520 0.185 0.0038 3,784 1.50 4.17

7 Type G 49 160 66 10,560 0.306 0.0046 4,640 1.50 4.10

8 Type H 71 160 34 5,440 0.444 0.0131 13,051 1.50 3.73

9 Type I 7 685 93 63,705 0.010 0.0001 110 1.50 5.20

10 Type J 3 758 24 18,192 0.004 0.0002 165 1.50 5.09

11 Type K 99 633 91 57,603 0.156 0.0017 1,719 1.50 4.43

12 Type L 6 947 97 91,859 0.006 0.0001 65 1.50 5.33

13 Type M 83 187 13 2,431 0.444 0.0341 34,142 1.50 3.32

14 Type N 67 14 31 434 4.786 0.1544 154,378 1.50 2.52

15 Type O 97 498 17 8,466 0.195 0.0115 11,458 1.50 3.78

16 Type P 77 954 2 1,908 0.081 0.0404 40,356 1.50 3.25

17 Type Q 71 887 6 5,322 0.080 0.0133 13,341 1.50 3.72

18 Type R 94 771 101 77,871 0.122 0.0012 1,207 1.50 4.53

19 Type S 46 696 15 10,440 0.066 0.0044 4,406 1.50 4.12

20 Type T 12 128 54 6,912 0.094 0.0017 1,736 1.50 4.42

Grand = 1,124 466,760 0.0024 2,408 1.50 4.32Six Sigma Scoreca rd L1: Ve rsion 1.0 Developed by Dr. Mike l J. Ha rry

1

1_01

_07_

021

Opportunity for Defects How could we evaluate our engineering process ?" "Well, you provide drawings to manufacturing. These drawings may include defects. Some defects, such as a missing date for one approval signature may not be critical, but others, such as a wrong dimension, would greatly affect the performance of the product. Take these drawings as an example. We count an average of 544 opportunities for defects per drawing. Since these are checked, they are known as active opportunities for defects. Their number is associated with the complexity of the drawing. Now, we found an average of 5 defects, given 0.0092 defects per opportunity i.e. 9,191 defects per million opportunities which corresponds to a Z value of 2.36. Since these data are discrete therefore long-term by nature, we add 1.5 sigma to account for shifts and drifts of long-term data and obtain short-term Z.B of 3.86. This is the sigma level of your process for these drawings".

Note: Z (equivalent) short term is also designated as Z.B (for Z benchmark) which is a metric for Sigma capability of process.

Meanwhile, you may see on these transactional forms, similar opportunities for defects. That means the same approach will be used to establish the sigma value of concerned department. "But, is it the same rules for manufacturing ? asks a Champion. "Take the painting process. We check randomly for visual defects. How many opportunities for defects should we consider ?" "That's a good question!" answers the Six Sigma Black Belt, "you can divide the total checked area into smaller units and count each of these units as an opportunity for defect".



Part-Per-Million Defective

40.00 40.05 40.10 40.15 40.20 40.25 40.30 40.35 40.40

Lower Spec Upper Spec

σµ−

= SLZ

Units of Measure

PerformanceLimit

Ζ

Probabilityof a Defect

Example = .002682

Short-Term CapabilityCp 1.26 Targ 40.17 Mean 40.2148 % >USL Exp 0.27 PPM >USL Exp 2682CPU 0.93 USL 40.34 Mean+3s 40.3497 Obs 0.60 Obs 6000CPL 1.59 LSL 40.00 Mean-3s 40.0799 % <USL Exp 0.00 PPM <LSL Exp 1Cpk 0.93 k 0.26 s 0.0450 Obs 0.00 Obs 0

Part-Per-Million Defective The honing process team is monitoring its process. The latest batch produced is with a defects PPM of 2682. The Six Sigma Black Belt was invited to explain this result. "The Parts-per-million defective is the probability of defects" he explains. Converted in percentage this equates to 0.002682 or 0.2682%. Referring to the standard normal table, the corresponding Z value is 2.78. The team recognize that the average of their process is only 2.78 sigma away from the upper specification. Every one is conscious that it is far from the target of Six Sigma. One member asks: "We just have 0.2682% defects; surely, it is not bad!". The Black Belt however explains that when a 1.5 sigma shift and drift is considered, then the 2.78 Z short term is equivalent to 1.28 Z long term. In such a case, probability of defects is 0.100272 (10.03%) i.e. 100,272 PPM. The team agrees that 100,272 PPM defective is not acceptable and that improvement is required.



Rec

ogni

ze

PPM Conversion Chart

0.00

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

100000.00

1000000.00

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Shifted 1.5σ

B axis

Z or “Sigma” Scale

PPM

A = Long-TermB = Short-Term

Centered

A axis

PPM Conversion Chart A simple and easy way to convert a rate of defects, in the form of a Parts per Million Defective, to the corresponding Sigma value, is to use a PPM Conversion Chart. The Sigma value is calculated via Excel, with the formula =NORMSINV(exp(-DPMO/1E6)). The curve that we arrive at with this equation is, in fact, the long-term process Sigma. It must then be corrected, to eliminate the effects of process Shift and Drift. This is accomplished by adding 1.5 to the long-term Sigma value to give the short-term Sigma. As an example of the use of the chart, consider the conversion of a Part-per-Million value of 500 to its equivalent Long-term Sigma value. The user simply locates the PPM value on the logarithmic vertical axis and reads across until the line intersects the curved line representing a centered distribution. Reading down to the horizontal axis yields the Sigma figure of approximately 3.3. This value corresponds quite well with the true calculated value of 3.29. This also means 4.79 short term (found by adding 1.5 to the long-term value or by reading across to the curved line representing a distribution shifted 1.5σ. A. If you start with defect data, then compute the PPM per opportunity and enter along the "A" axis. Next, project the "A" value to the "B" axis. The resulting number is an estimate of the short-term Z value, or "Sigma" as it is called. B. If you start with a Z or "Sigma" value, then enter along "B" axis. Next, project the "B" value to the "A" axis.

The resulting number is an estimate of the long-term PPM.



Rec

ogni

ze

Note: All Sigma Values Reflect a 1.5σ Shift

Number of Opportunities Inspected

Like

lihoo

d of

Det

ectio

n

1 10 100 1,000 10,000 100,000 1,000,000

0.00

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

2σ

6σ

4σ

Inspection and Complexity

Example: If a product contains 100defect opportunities and the inspectionprocess has a 4 Sigma capability, thelong-term likelihood of detecting a defect(if a defect is present) is about 54%.

Inspection and Complexity In Six Sigma parlance, complexity refers to the number of steps in a process, the number of parts in a unit of production, etc. In any case, increasing complexity results in problems which are detrimental to the attainment of Six Sigma capability. Even with a constant defect rate, as complexity increases, it causes an increase in the level of inspection and test which must be administered to uncover defects, as well as an increase in the potential number of defects. Not surprisingly, as complexity increases, the likelihood of detecting a defect decreases. As inspection and test increase, the time to verify, analyze, repair and re-verify also increases. Since inspection and test are non-value added functions in any process, increased complexity results in higher costs with no added benefits. Closely linked to complexity are the twin concepts of linear and non-linear error propagation. As part count or process steps increase, the defect rate can increase linearly or non-linearly. An example of this can be drawn from the culinary world. If a chef cooks for one person, he or she will have a certain defect rate, or non-performance to specification, probably in the form of dissatisfied customers or botched meals. As the number of meals being produced increases, the likelihood of producing a bad meal will increase. If the number of bad meals doubles in going from 10 to 20 customers, then we have linear error propagation. If the number of bad meals is proportionately higher, then we would have a case of non-linear error propagation.



Rec

ogni

ze

Yield: First Time vs Rolled Throughput

37%or.3679eeY

90% or.90,10090

USY

1.0DPUTP

FT

=−=−=

===

10 Units Repaired 37% ° 90%... why not?

100Units

Submitted

Y.TPThroughput Yield

(Units with Zero Defects)

Defect Number Type Observed A 3 B 1 C 0 D 2 E 4 Total 10

53 Units D=1

DPU = 1.0

37 Units D=0

0 Units Scrapped

Scrap

TheHidden

Operation

Operation Verify 90 Units Passed

Rework

Not OK

Yield: First Time Vs Rolled Throughput The Six Sigma Black Belt asks the director about his department's yield. "We are proud of our 90% yield!" is the answer. "How is it possible? I calculate the process DPU equal to 1, that means its capability is 37%." Is it possible to have 90% and 37% as process yield in the same time? The Six Sigma Black Belt explains that the classical way of calculating the yield is to divide the units passed by the units submitted. In fact this calculation doesn't take into account the hidden operation: defects and rework. In fact, this is a First Time Yield based on the number of units that pass only. The correct yield is the Throughput yield which is the yield prior to any correction. In our case, 90% is the Yield first time and 37% is the true throughput yield.



Rec

ogni

ze

Rolled Throughput Yield1_

01_0

7_02

6

Process Mean Shifted 1.5σ at Each Operation

Operation

Scrap

Rework

NotOK

Scrap

Rework

Non-Value Added(The Hidden Factory)

CustomerQuality

Internal/ExternalSupplier Quality

Producers Quality

Operation Verify

Y.TPThroughput

Yield

Y.TPThroughput

Yield

NotOK

Verify

TPi

m

l1RT YY

=∏=

Value Added(The Visible Factory)

Number of Operations

Rol

led

Yiel

d

1 10 100 1,000 10,000 100,000 1,000,0000.00

1.000.900.800.700.600.500.400.300.200.10

Process Mean Centered

3σ

4σ 5σ

6σ

Number of Operations

Rol

led

Yiel

d

1 10 100 1,000 10,000 100,000 1,000,0000.00

1.000.900.800.700.600.500.400.300.200.10

3σ

5σ

6σ

4σ

Inspect

Rolled Throughput Yield The accounting team presents the yield of one of its processes. They are waiting for praise from the Six Sigma Black Belt. They are disappointed to hear him say: "Your process yield is not 99.4%, indeed it is less than 55%!". "The concept of transactional process yield is exactly the same as a factory situation with multiple process steps. You just told me that this process includes almost 100 steps. Now, if we consider each step to have a 4 sigma rating short term, this means a yield of 99.38% i.e. 6200PPM per step. But, for the 100 steps all together, the rolled throughput yield will only be 53.64%, (99.38% raised to the power 100) i.e. 463,600PPM long term. The questions remaining are: • For how long can we accept this situation? • How much is this performance level costing? • Where should we act to improve the process? Asking these questions may lead to the launch of a Six Sigma project on this process.



Rec

ogni

ze3 4 5 6 7

1,000,000

100,000

10,000

1,000

100

10

12

Sigma Scale of Measure

PPM

Restaurant BillsDoctor Prescription Writing

Payroll ProcessingOrder Writeup

Journal VouchersWire Transfers

Airline Baggage HandlingPurchased Material

Lot Reject Rate

Domestic Airline FlightFatality Rate

(0.43 PPM)

IRS - Tax Advice phone in

(140,000 PPM)

(with ± 1.5 σ shift)

World-Class

AverageCompany

Benchmark - Chart

Benchmark

Entitlement

Baseline

Cycle Time

P(x

)

Benchmark - Chart "We are the best in what we are doing and it is very difficult to compare our business with others". The General Manager was often receiving such messages from his board of directors. "We are good, yes but to what extent?" he asks. "As a first step, we should benchmark our company." Like an archeologist who digs out artifacts to understand the way our ancestors lived, their behavior and their values, the benchmarking evaluator gathers existing data and introduces the complexity factor to establish the company's sigma level. When the results of this Baseline are available, the members of the board of directors realize that their enterprise is only rated at 4 sigma. This result puts them in the group of average companies. Nothing to celebrate! Especially since they now realize that one of their new competitors is in the Six Sigma group i.e. the world-class benchmark! Suddenly, the sales Manager understands why he has such difficulties with this newcomer. "I thought they were dumping in the market but it seems to me this is more serious." "If nothing changes, their prices and our delivery delays will force us out of our market!" says the General Manager. "Do you also realize, with our NC machines and improved processes, we were supposed to have an Entitlement of 5 sigma! This is the capability we could expect with no further investment. Which parts/steps of our process have a leverage effect? These are the priorities that we should address with our Six Sigma projects!"


1-7/27

Rec

ogni

ze

Benchmark - Sigma

Rolled Throughput Yield

Six Sigma Fundamentals

What Conclusions Can We Draw?

# of Parts (Steps) +3σ +4σ +5σ +6σ

1 93.32% 99.379% 99.9767% 99.99966%7 61.63 95.773 99.839 99.9976

10 50.08 93.96 99.768 99.996620 25.08 88.29 99.536 99.993240 6.29 77.94 99.074 99.966460 1.58 68.81 98.614 99.979580 0.40 60.75 98.156 99.9728

100 0.10 53.64 97.70 99.966150 --- 39.38 96.61 99.949200 --- 26.77 95.45 99.932

300 --- 15.43 93.26 99.898400 --- 8.28 91.11 99.864500 --- 4.44 89.02 99.830600 --- 2.36 86.97 99.796700 --- 1.28 84.97 99.762800 --- 0.69 83.02 99.729900 --- 0.37 81.11 99.695

1000 --- 0.20 79.24 99.6611200 --- 0.06 75.88 99.5933000 --- --- 50.15 98.985

17000 --- --- 0.02 94.38438000 --- --- --- 87.880 70000 --- --- --- 78.820

150000 --- --- --- 60.000

Best-In-Class Capability(Distribution Shifted +1.5σ)

Calculators

Watches

PanasonicTelevisionTV Industry

Japan

IC TestEquipment

What Conclusions Can We Draw?

Typical Capability in the US(Distribution Shifted +1.5σ)

# of Parts (Steps) +3σ +4σ +5σ +6σ

1 93.32% 99.379% 99.9767% 99.99966%7 61.63 95.773 99.839 99.9976

10 50.08 93.96 99.768 99.996620 25.08 88.29 99.536 99.993240 6.29 77.94 99.074 99.966460 1.58 68.81 98.614 99.979580 0.40 60.75 98.156 99.9728

100 0.10 53.64 97.70 99.966150 --- 39.38 96.61 99.949200 --- 26.77 95.45 99.932

300 --- 15.43 93.26 99.898400 --- 8.28 91.11 99.864500 --- 4.44 89.02 99.830600 --- 2.36 86.97 99.796700 --- 1.28 84.97 99.762800 --- 0.69 83.02 99.729900 --- 0.37 81.11 99.695

1000 --- 0.20 79.24 99.6611200 --- 0.06 75.88 99.5933000 --- --- 50.15 98.985

17000 --- --- 0.02 94.38438000 --- --- --- 87.880 70000 --- --- --- 78.820

150000 --- --- --- 60.000

Data Clocks USUSUS

US

US

USUS

US

US

Sales Error

Pager

Television

Phone

PortablePhone

Disc Memory

Base station

Benchmark - Sigma The President is interested in evaluating every divisions performance and comparing their rating to other companies considered as "best-in-class". With the Six Sigma benchmarking approach he is able to generate individual department ratings, taking into consideration its own complexity, because this evaluation establishes the sigma level based on the rolled throughput yield. As is typical, the sigma levels for most of the divisions are within the 4 sigma range. The benchmark reveals two pleasant surprises. First, the grinding department has a relative modest number of process steps (40) but its rolled yield is 99.987%. The second, the composite department, which even with a relatively complex process (200 steps), has a rolled yield higher than 99.94%. Consequently, the president is pleased to realize that both are rated in the Six Sigma group of "world-class" companies.



Rec

ogni

ze

Pareto Analysis of Process Inputs

0

10

20

30

40

50

60

70

80

90

100

A B C D E

84

103 2 1

1_01

_07_

029

Perc

enta

ge

Pareto & The Leverage Principle

DPU

/DPM

O

Pareto & The Leverage Principle Once a Process Map, or Process Flow Diagram, has been completed by a Six Sigma Project Team studying a process, one of the most important tools that can be applied is the Pareto Chart. Process inputs and outputs are said to be, respectively, independent and dependent variables, in other words, the Xs and Ys in the expression Y = f(X). The Pareto Chart provides a graphical representation of the Leverage Principle, which says that only a vital few independent process input variables, or Xs, are responsible for the majority of problems with dependent process outputs, or Ys. Conversely, there are a trivial many inputs which, even collectively, have minimal effect on the process output. The Pareto Chart is a powerful tool for prioritizing which process variables need to be studied in order to improve the process, and allows quick determination of which variables can be ignored.



Rec

ogni

ze

Translating Needs Into Requirements

CustomerNeeds

The CTSs are translatedinto critical requirements

related to quality, delivery,and cost.

CTS1,..., CTSK

ProducerRequirements

The vital needsof the customer are

translated intocritical-to-satisfaction

characteristics (CTSs).

CTQ1,..., CTQL

CTD1,..., CTDM

CTC1,..., CTCN

Translating Needs Into Requirements "How does Six Sigma help us focus on customer satisfaction?" the Champion asks, "and how to establish the priority for projects?" "Well!" answers the Six Sigma Master Black Belt, " drawing the CT Tree, CT equal to Critical To, is the exercise which addresses these major concerns. As an example, consider the case of the launching of a new aircraft, say the Global Express". The Master Black Belt shows the three requirements' categories: Quality, Delivery, and Price which represent the customer's needs. He explains how to express those vital needs in customer's Critical To Satisfaction (CTS) requirements: ultra-long range, large cabin, flexible configuration, 8-19 passengers, superior exterior finish, low cost, … "These requirements should then be translated into Critical To Quality (CTQ) characteristics (flying range, painting, flexible configuration, cruising speed, …), Critical To Delivery (CTD) calendars (delivery date, certification date, master schedule, …) and Critical To Cost (CTC) (selling price, interest, warranty, maintenance costs, …)." Having established CTQs, CTCs and CTDs it is then possible to prioritize improvement opportunities and select these as Six Sigma projects.


1-7-29Six Sigma Fundamentals

Rec

ogni

ze

Customer

“Critical To” - CT Tree

Process ( i) Output (Y)

CTQCTDCTC

CTS

Needs

Input

Input X1

CTP

Input

USLLSL USL LSL

Probabilityof Defects

Probability ofNonconformance

to Standard

ProcessCapability

ProductCapability

Y X

Critical-to-Quality Characteristic

CTQj

Defect Opportunity Control Opportunity

The variation inherent in any dependent variable (Y)is determined by the variation inherentin each of the independent variables.

A product requirementwhich impacts quality

delivery, or cost.

One of the “vital few”process variables which

can leverage Y.

Y = f(X)Example

X2 Xn

Critical-to-Process Characteristic

CTQj

Probabilityof Defects

Probability ofNonconformance

to Standard

"Critical To" – CT Tree The Master Black Belt illustrates to the champion the CT Tree concept and the interrelation between the CTs. "In order to meet the CTQ, CTD and CTC requirements we should control the process vital few characteristics; "the knobs" acting on Critical to Process (CTP) parameters (speed, air flow, breaking force, aging time, temperature, cutting speed…). The Champion recognizes that any CTQ, CTD or CTC would constitute an opportunity for nonconformance, so long as it is actively measured and reported. Meanwhile, the Champion realizes that this CT characterization must flow down to lower level processes, since the inputs for one process are the outputs of another process. Those metrics must be specified at every level until the single element/step level with its individual Critical to Quality (CTQ) characteristics (paint thickness, diameter, true position, flatness, hardness, weight, …) identified" The Master Black Belt adds. " With a correct representation of the situation through the CT Tree, it would be easier to prioritize Six Sigma projects, focusing on the vital few CTs with greatest leverage effect."



Rec

ogni

ze

1,000,000

100,000

10,000

1,000

100

10

13 4 5 6 72Sigma Scale of Measure

PPM The Basic Objective

Region of Success

Y

X

= Current Level

CharacterizationMeasurement and Analysis

Phases 1 and 2“Where we are andwhere we must go”

The Driving Need for Breakthrough

Average Company

World-Class

The wall between5σ and 6σ

OptimizationImprovement and Control

Phases 3 and 4“What action we must take to get and stay there”

The Driving Need for Breakthrough The Six Sigma Black Belt has explained to the Engineering management team the advantages of improving the sigma of their process. Having established a process baseline of almost 4.0 Sigma, the Black Belt explains that the number of defects could be reduced from almost 10000 PPM to 3.4 PPM with a Six Sigma process. The team then discusses the effect of drawing errors on the production process particularly with respect to quality, costs, defects, increased delays and, most of all, customer dissatisfaction. The team agrees that world-class performance must be their goal. The Black Belt then explains the need to apply a Breakthrough Strategy if such a performance level is to be achieved. It is important to note that to pass from 2σ to 4σ makes 50 times fewer defects, but from 4σ to 6σ makes about 2000 times fewer defects, more profits and reduced cycle time. During characterization, the focus is on Y's, whereas during optimization the focus is on X's. Our aim is to increase the size of the region of success by acting on both axes.



Rec

ogni

ze

Breakthrough StrategyBreakthrough Phases

Strategy

Characterization

Optimization

Phase 1: Measurement

Phase 2: Analysis

Phase 3: Improvement

Phase 4:Control

Breakthrough Strategy

Measurement1. Select CTQ Characteristic2. Define Performance Standards3. Validate Measurement System

Analysis4. Establish Product Capability5. Define Performance Objectives6. Identify Variation Sources

Improvement7. Screen Potential Causes8. Discover Variable Relationship9. Establish Operating Tolerances

Control10. Validate Measurement System11. Determine Process Capability12. Implement Process Controls

Breakthrough Strategy Measurement

Analysis

Improvement

Control

CapabilityOK?

ModifyDesign?

CapabilityOK?

N

Redesign

N

Y

Y

Y

N

Breakthrough Strategy The production team asks the Six Sigma Black Belt the best way to improve its process in order to obtain a sigma level greater than the actual 3.5 sigma. The Black Belt then explains the best approach to achieve process entitlement beyond this level. He details the four breakthrough phases: Measurement, Analysis, Improvement and Control. The first two phases are accomplished in order to characterize the process and the two others to optimize and maintain it. Through past experience, the Six Sigma Black Belt warns the team members that the task ahead will be difficult, particularly when breaking through the wall between five and Six Sigma. He also emphasizes the advantages in process performance. He reminds them that achieving a Six Sigma level of performance will require application of DFSS (Design For Six Sigma) principles. The Black Belt also explains that the Breakthrough Strategy includes several loops where the team may have to return to earlier steps in order to improve the process and that this is normal and should be understood as part of the learning process. The team recognizes the danger of bypassing some of these steps and realizes the importance of methodically applying the Breakthrough Strategy.


Process Characterization Addressing the difficulty in improving the transactional processes of the Methods department, the Six Sigma Black Belt explains to the team members the two first steps of the Breakthrough Strategy. Phase 1: Measurement This phase is concerned with selecting one or more product characteristics; i.e., dependent variables (Ys), mapping the respective process, making the necessary measurements, recording the results on process "control cards", and estimating the short- and long-term process capability. Phase 2: Analysis This phase entails benchmarking the key product performance metrics. Following this, a gap analysis is often undertaken to identify the common factors of successful performance; i.e., what factors explains best-in-class performance. In some cases, it is necessary to redesign the product and/or process. Process Optimization Having completed its process-characterization, the press-break team asks the Six Sigma Black Belt about the next steps to improve the process. The Six Sigma Black Belt explains the Process-optimization phases of the Breakthrough Strategy. Phase 3: Improvement This phase is usually initiated by selecting those product performance characteristics which must be improved to achieve the goal. Once this is done, the characteristics are diagnosed to reveal the major sources of variation. Next, the key process variables (Xs) are identified by way of statistically designed experiments. For each process variable which proves to give leverage, performance specifications are established. Phase 4: Control This phase is related to ensuring that the new process conditions are documented and monitored via Statistical Process Control methods. After a "settling in" period, the process capability would be reassessed. Depending upon the outcomes of such a follow-on analysis, it may be necessary to revisit one or more of the preceding phases. Design of Experiments (DOE) Improvement A new process of removing the paint from the aircraft prior to repainting is to be studied to reduce the cost, time and improve the quality. The team members are not sure how to attack this huge problem. The process planning shows at least 15 different input factors that may affect the output. The Six Sigma Black Belt explains to the team that the use of a DOE approach would reduce the number of experiments and increase the degree of confidence in the results. He suggests to start with a screening design to isolate the vital few variables from the trivial many. The second step will be a characterization design to establish the effect of the interaction between factors as in the combined effect of pressure and temperature or humidity and granularity of the paint removing powder. If needed, then an optimization design would be performed to establish a reasonably precise mathematical model of the phenomenon investigated. The Black Belt takes the opportunity to emphasize the tremendous effect a better process understanding will have, that a robust process will result and that it will be easy to keep the process in control with a good capability.


Design of Experiments Optimization The Six Sigma Black Belt studies the chem-mill process. After a first screening design of experiments, she performs a second DOE to optimize the process on two factors: pressure and temperature. She draws graphs to present the results to the team. Through her study, based on the experimental outcomes, she determines settings to use to achieve "top of the hill" performance. In other words, designed experiments were used to generate optimum results and then a robust process and product design. Design of Experiments A Basis for Tolerancing The Engineering team is meeting to review the performance of the forming process. The Six Sigma Black Belt shows the results of the design of experiments performed. He shows the effect of the vital few main factors on the outcomes of the process and underlines the region of optimal performance. The design team members realize the advantages to specify certain tolerances to input process parameters in order to achieve a robust design. Most companies do not realize the huge potential of this powerful tool, tolerance design using Design of Experiments, to break through the wall. Process Control Once the full force of the Six Sigma Measurement, Analysis, and Improvement tools have been brought to bear on a process, and it has been re-engineered to achieve a Six Sigma level of capability, the process must be put in a state of statistical control. There are a variety of tools used during the Control phase of a Six Sigma project, and the most important are Control Charts. Control Charts, in effect a form of Time-Series graph, plot the on-going performance of a process, relative to a performance standard, or control limit which is determined from the process' historical variation. If the performance variable, or response, being controlled, goes outside the control limits, then the process can be said to be out of control, and action should be taken.



Rec

ogni

ze

6σ

6σ 6σ

6σ

6σ

6σ 6σ

6σ

6σ

Management Leadership1_

01_0

7_04

0

6σ

FocusCustomer

Process

Process

Manuf.

Process

Process

ProcessSuppliersProcess

Process

Process

Design

Process

ValueQuality-Cost-Time

Data Driven

6σ

6σ 6σ

What webelieve

What wedo

INCREASED PROFITS

USLLSL USL

Very HighProbabilityof Defects

LSL

Very HighProbabilityof Defects

Very LowProbabilityof Defects

Very LowProbabilityof Defects

ExcellentProcessCapability

PoorProcessCapability

Management Leadership Six Sigma philosophy is the star which must guide the entire organization. All Champions know that they must: • Create a vision; • Train, mobilize and support the team; • Define the path; • Realize the gains; • Hold the ground; throughout each of the different phases of Breakthrough: Measure, Analyze, Improve and Control. Champions should concentrate on measuring inputs instead of only results (outputs) and must regularly ask: Do we have the right information to make decisions? What degree of confidence do we have in our figures? Are we addressing the vital few variables which have a leverage effect? What is the sigma of our process? (What is our DPMO?) Is the process robust to variation?


Lessons Learned • We are in a very competitive business. Six Sigma is the proven strategy which will make it possible for

our Company to break through the wall between the "average" and "world-class". • The only way to make money is by satisfying needs. Six Sigma is a powerful tool to improve our

processes. Many major companies have proven the efficiency of the Six Sigma approach in improving their process capability from the "average" to "world-class".

• The Six Sigma Strategy targets the reduction of process variation, hence the output of these processes are better, with a lower probability of defects. Applying this strategy, every one in the organization recognizes the importance of process sigma rating and should continuously strive for improvement.

• Six Sigma reinforces the company's culture and confirms its values. Through Six Sigma standards, sigma ratings are representative of the company's real efficiency.

• The CT Tree will be the prime planning tool to prioritize and improve our processes. Defects per million opportunities and other quality/cost indicators should be commonly used to monitor the evolution of improvement. Six Sigma Black Belts must be dedicated to help teams to solve problems on a regular basis and the results will be documented and publicized. Our processes will be robust to input variations and Engineering will design for manufacturability.

• Six Sigma implementation success factors are: • Six Sigma Champions, business metrics, common process metrics, benchmarking with stretch

goals, application of the Roadmap, Six Sigma Black Belts, success stories, design of experiments (DOE) and statistical process control (SPC). There needs to be a quality and time focus, design-for-manufacturability methods, quality policy and deployment, quality council and associate membership, empowered high-performance work teams.

• At the initial steps of Six Sigma our efforts must be coordinated. We have to apply rigorously the Six Sigma Breakthrough Strategy in order to maximize our chance of success as soon as possible. Our first Sigma projects should be successes to further take advantage of the resulting momentum.

• "What we don't know, we don't know!" Instead of opinion, we have to take decisions based on reliable facts and with a high degree of confidence. The Six Sigma approach is to focus on the vital few which have a real impact on the rolled throughput yield.

six sigma fundamentals - · pdf filesix sigma six sigma fundamentals six sigma fundamentals...

Documents