Part II S /IEE Measure Phase from DMAICweb.eng.fiu.edu/leet/TQM/chap3_2012.pdf · 2014. 12. 17. ·...

9/4/2012

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Part II

S4/IEE Measure Phase

from DMAIC

Introduction

• Part II (Chapter 3-14) addresses process definition,

process performance, and the quantification of

variability.

• KPOVs and KPIVs are identified through consensus.

• Basic analysis tools are introduced:

• Six Sigma measures

• Measurement systems analysis (MSA)

• Failure mode and effects analysis (FMEA)

• Quality function deployment (QFD)

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Introduction

5 Components in S4/IEE Measure Phase:

• Plan project and metrics

• Baseline project

• Consider lean tools

• MSA

• Wisdom of the organization

Chapter 3

Measurements and

S4/IEE Measure Phase

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Introduction

• An objective of the measure phase is the development

of a reliable and valid measurement system of the

business process identified in the define phase. • How an inappropriate tracking methodology can lead to

the wrong activity (firefighting);

• Overview of basic descriptive statistics;

• Data gathering, presentation, and simple statistics;

• Introductory discussion of confidence interval and

hypothesis testing;

• Attribute vs. continuous data;

• Ineffectiveness of visual inspections;

• Examples of experiment traps.

3.1 Voice of the Customer

• VOC assessment is needed up front when executing

S4/IEE projects at the 30,000-foot level.

• Define your customer.

• Obtain customer wants, needs, and desires.

• Ensure that focus of project is addressing customer needs.

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3.1 Voice of the Customer

• Important customer key process output categories are

classified with regard to their area of impact: • Critical to quality (CTQ): flatness, diameter, etc.

• Critical to delivery (CTD): on-time, accuracy, etc.

• Critical to cost (CTC)

• Critical to satisfaction (CTS)

• Important key process input issues are classified as critical

to process (CTP)

• The format of a tree diagram can be useful to ensure a

linkage between customer requirements and process

performance metrics. NeeddriversCTQs

• Tree diagram can also be used to describe the hierarchy of

critical to (CT) categories at various level.

3.1 Voice of the Customer:

Critical to Satisfaction (CTS) Tree

Cleveland Service Shop Generates Most Defects with a

Failure Rate of 89% Late Deliveries

Sources of

Variation

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3.2 Variability and

Process Improvements

• Variability is everywhere.

• Common cause vs. special cause

• If variability is too large because of special causes,

attempts need to be made to avoid the source of special

cause.

• If variability is too large because of common causes, the

process needs to be changed.

3.3 Common vs. Special Causes

and Chronic vs. Sporadic problems

• J. M. Juran (Juran and Gryna 1980) considers the

corrective action strategy for sporadic and chronic

problems.

• W. Edwards Deming addresses this basic issue using a

nomenclature of special causes and common causes

(Deming 1986).

• Process control charts are tools that can be used to

distinguish these two types of situations.

• Sporadic problems are defined as unexpected changes in

the normal operating level of a process.

• Chronic problems exist when the process is at a long-term

unacceptable operating level.

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• With sporadic problems the corrective action is to bring the

process back to the normal operating level.

• The solution to chronic problems is a change in the normal

operating level of the process.

• Solving these two types of problems involves different

basic approaches.



The Juran’s control sequence (Juran and Gryna 1980) is

basically a feed-back loop that involves the following steps:

1. Choose the control subject (i.e., what we intend to

regulate).

2. Choose a unit of measure.

3. Set a standard or goal for the control subject.

4. Choose a sensing device that can measure the control

subject in terms of unit of measure.

5. Measure actual performance.

6. Interpret the difference between the actual and standard.

7. Take action, if any is needed, on the difference.

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Breakthrough sequence for solving chronic problems 1. Convince those responsible that a change in quality level is desirable

and feasible.

2. Identify the vital few projects; that is, determine which quality problem

areas are most important.

3. Organize for breakthrough in knowledge; that is, define the

organization mechanisms for obtaining missing knowledge.

4. Conduct the analysis; that is, collect and analyze the facts that are

required and recommend the action needed.

5. Determine the effect of proposed changes on the people involved and

find ways to overcome the resistance to change.

6. Take action to institute the changes.

7. Institute controls to hold the new level.

3.4 Reacting to Data

76.2

78.2

74.1

74.1

75.0

74.5

75.0

75.0

71.8

76.7

77.8

77.1

75.9

76.3

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77.5

77.0

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77.1

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78.3

72.7

76.3

78.5

76.0

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77.6

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75.6

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76.9

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3.4 Reacting to Data

• Population parameters

• Sample statistics

• Simple Random Sampling

– Random variable (x): a response from sample

taken randomly from population

• Sampling error

• Confidence interval

3.5 Sampling

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• Dot Plot

– A simple procedure to illustrate data

positioning and its variability. Along a

numbered line, a dot plot displays a dot for

each observation.

• Histogram

– Discrete Data: Tally for each outcome

– Continuous Data: Frequency within each

class (group, cell)

3.6 Simple Graphic Presentations

3.7 Example 3.2: Histogram

2.2

2.6

3.0

4.3

4.7

5.2

5.2

5.3

5.4

5.7

5.8

5.8

5.9

6.3

6.7

7.1

7.3

7.6

7.6

7.8

7.9

9.3

10.0

10.1

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3.7 Example 3.2: Dot Plot

3.8 Sample Statistics (Mean, Range, Std. Deviation, and Median)

• Sample Mean (𝑥 )

– A measure of central tendency.

– It is the arithmetic average of the data values

𝑥 = 𝑥𝑖𝑛𝑖=1

𝑛

• Sample Median (𝑥50)

– A measure of central tendency.

– The number at (n+1)/2 rank

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• Sample Range (R)

– A measure of dispersion of data.

– It is the difference between the highest and

lowest value of a set of data

– Sample size, outliers

• Sample Standard Deviation (s)

– is the square root of the sample variance.

• Sample Standard Deviation (s)

𝑠 =1

𝑛 − 1 (

𝑛

𝑖=1

𝑋𝑖 − 𝑋 )2 =

1

𝑛 − 1 (

𝑛

𝑖=1

𝑋𝑖2 − 𝑛𝑋 2)

– Degree of freedom n (nu) = n-1

• Sample Variance (s2)

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• Continuous data can assume a range of

numerical responses on a continuous

scale. (e.g., micrometer reading)

• Attribute (categorical or qualitative) data

can assume only discrete levels. (e.g.,

operator, machine, number of defects,

pass/fail)

• Logic pass/fail

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3.9 Attribute vs. Continuous

Data Response

• Transactional workflow metric (could similarly apply to

manufacturing; e.g., inventory or time to complete a

manufacturing process): Random sample of last year’s

invoices where the number of days beyond the due date

was measured and reported (i.e., days sales outstanding

[DSO]). If an invoice was beyond 30 days late, it was

considered a failure or defective transaction. The

number of nonconformances was divided by the sample

size to estimate the nonconformance rate of the overall

process. • Note that this procedure would not be the recommended strategy within

S4/IEE, since much information is lost in the translation between continuous

and attribute data.

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Data Response: Examples

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• Transactional quality metric: Random sample of last

year’s invoices, where the number of defects in filling out

the form were measured and reported. The number of

defective transactions was divided by the sample size to

estimate the defective rate of the process.


year’s invoices, where the invoices were examined to

determined if there were any errors when filling out the

invoice. Multiple errors or defects could occur on one

invoice. The total number of defects was divided by the

sample size to estimate the defect rate of the process.

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year’s invoices, where the invoices were examined to

determined if there were any errors when filling out the

invoice or within any other step of the process. Multiple

errors or defects could occur when executing an invoice.

The total number of defects when the invoice was

executed was divided by the total number of

opportunities for failure to estimate the defect per million

opportunity (DPMO) rate of the process.

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• Manufacturing quality metric: Random sample of parts

manufactured over the last year where the diameter of

the parts were measured and reported. If the part was

beyond specification limits, it was considered a defective

part or a "failure." The number of non-conformances

was divided by the sample size to estimate the

nonconformance rate of the overall process. • Note that this procedure would not be the recommended strategy within

S4/IEE, since much information is lost in the translation between continuous

and attribute data.

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• Manufacturing quality metric: Random sample of printed

circuit boards over the last year where the boards were

tested for failure. The number of defective boards was

divided by the sample size to estimate the defective rate

of the process.


circuit board over the last year where the boards were

tested for failure. Multiple failures could occur on one

board. The total number of defects was divided by the

sample size to estimate the defect rate of the process.

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circuit board over the last year where the boards were

tested for failure. Multiple failures could occur on one

board. The total number of defects on the boards was

divided by the total number of opportunities for failure

(sum of the number of components and solder joints

from the samples) to estimate the defect per million

opportunity (DPMO) rate of the process.

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• Still remain a very large single form of inspection

activity.

• Characteristics often do not completely describe

what is needed, and the inspectors need to

make their own judgment.

• A visual inspection does not necessarily address

the real desires of the customer.

• Visual inspections often lead to the thinking that

quality can be inspected into a product.

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3.10 Visual Inspections

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• Hypothesis tests are used when decisions need

to be made about a population.

• Hypothesis tests involve a null hypothesis (H0)

and an alternative hypothesis (Ha)

• Two risks (errors) can be involved within a

hypothesis test: and

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3.11 Hypothesis Testing and Interpretation of ANOVA Computer Output

• Null (H0): Mean of population equals the criterion. Alternative

(Ha): Mean of population differs from the criterion.

• Null (H0): Mean response of machine A equals mean response

of machine B. Alternative (Ha): Mean response of machine A

differs from machine B.

• Null (H0): Mean response from the proposed process change

equals the mean response from the existing process. Alternative

(Ha): Mean response from proposed process change does not

equal the mean response from the existing process.

• Null (H0): There is no difference in fuel consumption between

regular and premium fuel. Alternative (Ha): Fuel consumption

with premium fuel is less.

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3.11 Hypothesis Testing

Examples

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3.11 Hypothesis Testing Interpretation of ANOVA Computer Output

Source df Seq SS Adj SS Adj MS F P

A 1 0.141 0.141 0.141 0.34 0.575

B 1 31.641 31.641 31.641 75.58 0.000

C 1 18.276 18.276 18.276 43.66 0.000

D 1 0.331 0.331 0.331 0.79 0.395

E 1 0.226 0.226 0.226 0.54 0.480

Error 10 4.186 4.186 0.419

Total 15 54.799

Possible Experimentation Traps:

• Irrational subgroups

• Sampling scheme

• Measurement error

• Poor experiment design strategy

• Erroneous assumptions

• Data analysis errors

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3.12 Experimentation Traps

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Consider that the data in Table 3.3 are the readings (in

0.001 of cm) of a functional gap measured between two

mechanical parts. The design specifications for this gap

were 0.008 0.002 cm. This type of data could be expected

from the measurements in a manufacturing line, when the 16

random parts were taken over a long period of time.

Need to consider:

• how samples are selected when making such an

assessment of the capability/performance of the

response;

• the precision and accuracy of the measurement system

are often overlooked.

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3.13 Experimentation Trap: Example 3.3 Measurement Error and Others

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3.13 Experimentation Trap: Table 3.3

Obs 1 2 3 4 5 6 7 8 9 10

1 2.99 7.88 9.80 6.86 4.55 4.87 5.31 7.17 8.95 3.40

2 6.29 6.72 4.04 4.76 5.19 8.03 7.73 5.04 4.58 8.57

3 2.65 5.88 4.82 6.14 8.75 9.14 8.90 4.64 5.77 2.42

4 10.11 7.65 5.07 3.24 4.52 5.71 6.90 2.42 6.77 5.59

5 5.31 7.76 2.18 8.55 3.18 6.80 4.64 10.36 6.15 9.92

6 5.84 7.61 6.91 3.35 2.45 5.03 6.65 4.17 6.11 4.63

7 2.17 7.07 4.18 4.08 7.95 7.52 2.86 6.87 5.74 7.48

8 4.13 5.67 8.96 7.48 7.28 9.29 8.15 8.28 4.91 8.55

9 7.29 8.93 8.89 5.32 3.42 7.91 8.26 6.60 6.36 6.10

10 5.20 4.94 7.09 3.82 7.43 5.96 6.31 4.46 5.27 6.42

11 5.80 7.17 7.09 5.79 5.80 6.98 8.64 7.08 5.26 4.46

12 5.39 2.33 3.90 4.45 6.45 6.94 1.67 6.97 5.37 7.02

13 10.00 3.62 5.68 5.19 7.72 7.77 7.49 4.06 2.54 5.86

14 9.29 7.16 7.18 5.57 3.53 7.12 6.14 10.01 6.69 4.80

15 4.74 9.39 7.14 4.42 7.69 3.71 2.98 2.20 7.89 9.60

16 5.19 7.98 2.36 7.74 5.98 9.91 7.11 5.18 5.67 5.92

𝑥 5.77 6.74 5.96 5.42 5.74 7.04 6.23 5.97 5.88 6.30

s 2.41 1.86 2.30 1.59 1.97 1.69 2.19 2.38 1.42 2.14

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• It is typically desirable to have a measurement system

that is at least 10 times better than the range of the

response that is of interest.

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• Sources of the measured variability of parts (T2 ):

– Repeatability (12): the ability of an appraiser to get a

similar reading when given the same part again;

– Reproducibility (22): the ability of differing appraisers

obtaining a similar reading for the same part;

– Measurement tool-to-tool (32)

– Within lots (42)

– Between lots (52)

– T2 = 1

2 + 22 + 3

2 + 42 + 5

2

– The precision of the measurements of parts is

dependent on T2

– The accuracy depends upon any bias that occurs

during the measurements.

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3.14 Experimentation Trap: Example 3.4 Lack of Randomization

Test

Number

Duration

of

Pressure

(sec) Strength

(lb)

1 10 100

2 20 148

3 30 192

4 40 204

5 50 212

6 60 208

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3.14 Experimentation Trap: Example 3.4 Lack of Randomization

Test

Number

Duration

of

Pressure

(sec) Strength

(lb)

1 30 96

2 50 151

3 10 190

4 60 200

5 40 210

6 20 212

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• The following strategy was used to determine if

resistance readings on wafers are different when

taken with 2 types of probes and/or between

automatic and manual readings.

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3.15 Experimentation Trap: Example 3.5 Confused Effects

Automatic Manual

Probe Type 1 G1, G2, G3, G4 G1, G2, G3, G4

Probe Type 2 G5, G6, G7, G8,

G9, G10, G11, G12

G5, G6, G7, G8, G9,

G10, G11, G12

Initial Experiment Strategy

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3.15 Experimentation Trap: Example 3.5 Confused Effects

Automatic Manual

Probe 1 Probe 2 Probe 1 Probe 2

G1

G2

G3

G4

G5

G6

G7

G8

G9

G10

G11

G12

Revised Experiment Strategy

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• A system under development had 3 different functional

areas. In each of these areas there were two different

designs that could be used in production.

• 8 special systems were built

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3.16 Experimentation Trap: Example 3.6 Independently Designing and

Conducting an Experiment

System

Number

Functional Area

A B C

1 + + + 2 + + - 3 + - + 4 + - - 5 - + + 6 - + - 7 - - + 8 - - -

• It is important for the designer to have some involvement

in the details of the test activity.

• With communication, the designer may also find other

unknown characteristic of the design/process that is

important.

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3.16 Experimentation Trap: Example 3.6 Independently Designing and

Conducting an Experiment

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• Random sampling plans are based on the assumption that

errors are independent and normally distributed.

• If appropriate, randomization is introduced as an

approximation alternative when conducting an experiment.

• If data dependence can be modeled, it is possible to

develop procedures that are more sensitive than those that

depend only on randomization.

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3.17 Some Sampling Considerations

• Select what to measure: Consider the questions that need

to be answered and the data that will help answer these

questions. Consider also the final and internal customers to

the process and how the measures will be tracked and

reported.

• Develop operational definitions: Consider how to clearly

describe what is being measured to ensure that there is no

miscommunications.

• Identify data source(s): Consider where someone can

obtain data and whether historical data can be used.

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3.18 DMAIC Measure Phase

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• Prepare collection and sampling plan: Consider who will

collect and compile the data and the tools that are

necessary to capture the data. Create a data-sampling

plan that addresses any potential data integrity issues.

• Implement and refine measurement: Consider what could

be done to assess an initial set of measures and

procedures for collecting the data before expending a lot of

resource collecting/compiling questionable data. To ensure

ongoing data integrity, consider what procedures will be

followed to monitor data-collection practices over time.

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3.18 DMAIC Measure Phase

Part II S /IEE Measure Phase from DMAICweb.eng.fiu.edu/leet/TQM/chap3_2012.pdf · 2014. 12. 17. ·...

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