2. intro. to six sigma

QUALITY TOOLS & TECHNIQUES

By: -Hakeem–Ur–Rehman

IQTM–PU 1

TQ TINTRODUCTION TO SIX SIGMA

SIX SIGMA DEFINED In a narrow sense…

A metric based on Statistical Measure called Standard Deviation

In a broader, business sense… WORLD CLASS QUALITY providing a BETTER product or

service, FASTER, and at a LOWER COST than our competitors.

VARIATION… “the enemy of the customer satisfaction”

WHAT IS SIX SIGMA? DIFFERENT OPINIONS ON THE DEFINITION OF

SIX SIGMA: Six Sigma is a PHILOSOPHY: This perspective views all work as

processes that can be defined, measured, analyzed, improved and controlled. Processes require inputs (x) and produce outputs (y). If you control the inputs, you will control the outputs: This is generally expressed as y = f(x).

Six Sigma is a SET OF TOOLS: The Six Sigma expert uses qualitative and quantitative techniques to drive process improvement. A few such tools include statistical process control (SPC), control charts, failure mode and effects analysis and flowcharting.

Six Sigma is a METHODOLOGY: This view of Six Sigma recognizes the underlying and rigorous approach known as DMAIC (define, measure, analyze, improve and control). DMAIC defines the steps a Six Sigma practitioner is expected to follow, starting with identifying the problem and ending with the implementation of long-lasting solutions. While DMAIC is not the only Six Sigma methodology in use, it is certainly the most widely adopted and recognized.

Six Sigma is a METRIC: it uses the measure of sigma, DPMO (Defect Per Million Opportunities), RTY (Rolled Throughput Yield) etc.

WHAT IS A SIX SIGMA … As a

Measure?

1.5 Sigma Shift

Theory

WHAT IS A SIX SIGMA … As a

Metric?Each of these metrics serves a different purpose and may be used at different levels in the organization to express the performance of a process in meeting the organization’s (or customer’s) requirements. We will discuss each in detail as we do through the course.

1. Defects2. Defects Per Unit (DPU)3. Parts Per Million (PPM)4. Defects Per Million Opportunities (DPMO)5. Yield6. First Time Yield7. Rolled Throughput Yield (RTY)8. Sigma Level

SIX SIGMA: Metrics (Cont…)

DPU(Defects / Unit)

(# of Defects / # of Units)

Say: 10 Defects, 100 PairsDPU = 10/100 = 0.1 (10%)

DPO(Defects /

Opportunity)

(# of Defects) / (# of Units X # of Defect Opportunities / Unit)

Say: 10 Defects, 100 Pairs,2 Opportunities / CartonDPO = 10/(100 X 2) = 0.05 or 5% for each type


DPMO(Defects / M.

Opportunities)

DPO X 106

Say: 10 Defects, 100 Pairs2 types of defectsDPMO = 0.05 X 106 = 50,000

SIGMAConsult Z–Table or

Excel

Sigma Level

Yield =1–DPO =1–0.05 = 95 %

From M.S. Excel:=Normsinv(%Yield)

+1.5

50,000 DPMO = 3.145σ

SIGMA LEVEL: CONVERSION TABLEDefects per1,000,000

Successrate

SigmaLevel

Defects per1,000,000

Successrate

SigmaLevel

933,000 7% 0.0 54,800 94.52% 3.1919,000 8% 0.1 44,600 95.54% 3.2903,000 10% 0.2 35,900 96.41% 3.3885,000 12% 0.3 28,700 97.13% 3.4864,000 14% 0.4 22,800 97.72% 3.5841,000 16% 0.5 17,900 98.21% 3.6816,000 18% 0.6 13,900 98.61% 3.7788,000 21% 0.7 10,700 98.93% 3.8758,000 24% 0.8 8,200 99.18% 3.9726,000 27% 0.9 6,210 99.379% 4.0691,000 31% 1.0 4,660 99.534% 4.1655,000 34% 1.1 3,470 99.653% 4.2618,000 38% 1.2 2,560 99.744% 4.3579,000 42% 1.3 1,870 99.813% 4.4540,000 46% 1.4 1,350 99.865% 4.5500,000 50% 1.5 968 99.903% 4.6460,000 54.0% 1.6 687 99.931% 4.7421,000 57.9% 1.7 483 99.952% 4.8382,000 61.8% 1.8 337 99.966% 4.9345,000 65.5% 1.9 233 99.9767% 5.0309,000 69.1% 2.0 159 99.9841% 5.1274,000 72.6% 2.1 108 99.9892% 5.2242,000 75.8% 2.2 72 99.9928% 5.3212,000 78.8% 2.3 48 99.9952% 5.4184,000 81.6% 2.4 32 99.9968% 5.5159,000 84.1% 2.5 21 99.9979% 5.6136,000 86.4% 2.6 13 99.9987% 5.7115,000 88.5% 2.7 9 99.9991% 5.896,800 90.32% 2.8 5 99.9995% 5.980,800 91.92% 2.9 3.4 99.99966% 6.066,800 93.32% 3.0

EXAMPLE: Calculate Sigma Level

Calculate the Sigma Level and DPMO of a telecom network had 500 minutes of downtime in 2005. Product: Network (Connectivity) CTQ: Up time / Down time CTQ Measure: Minutes CTQ Specs: no downtime Defect measure: One minute of Network down Opportunity/Unit: 1 Total Defects in 2005: 500 minutes Total Time (Minutes): 365days X 24hours X 60min. =

525,600

DPU = 500/525,600 = 0.000951 DPO = 500 / (525600 X 1) = 0.000951 DPMO= 0.000951 X 106 = 951 Yield = 1 – DPO = 1 – 0.000951 = 0.999049 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 4.6σ


A manufacturer of computer hard drives wants to measure their Six Sigma level. Over a given period of time, the manufacturer creates 83,934 hard drives. The manufacturer performs 8 individual checks to test quality of the drives. During testing 3,432 are rejected.

# of Defects = 3432 # of Units = 83934 # of Defect Opportunities per Unit = 8

DPU = 3432/83934 = 0.041 DPO = 3432/(83934 X 8) = 0.0051 DPMO= DPO X 106 = 5111 Yield = 1 – DPO = 1 – 0.0051 = 0.9949 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 4.07σ


A project is focused on a billing process. The team wants to have correct bills sent to the customer. They have defined one opportunity for this process - either the bill is correct or not. All of the bills produced are the same in terms of complexity. The team took a sample of 250 bills and found 60 defects.

# of Defects = 60 # of Units = 250 # of Defect Opportunities per Unit = 1

DPU = 6/250 = 0.24 DPO = 6/(250 X 1) = 0.24 DPMO= DPO X 106 = 240,000 Yield = 1 – DPO = 1 – 0.24 = 0.76 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 2.21σ


If you have a total of 500 delivery orders and you find out that 41 of those were delivered late, and 17 were incorrect orders.

# of Defects = 41+17 = 58 # of Units = 500 # of Defect Opportunities per Unit = 2

(delivery time and correct order)


EXAMPLE: Calculate Sigma LevelA telecom service provider complies the defects of one year from the

inspection of 100 sites. The severity of each defect is classified in the following:

i. Criticalii. Majoriii. Minoriv. Trivial

The complete checklist comprises of 50 types of defects. The data of 2005 of 100 sites reveals the following figures:

Total # of Critical Defects: 5Total # of Major Defects: 20Total # of Minor Defects: 120Total # of Trivial Defects: 155

Calculate the Sigma Value and the DPMO for the year 2005. # of Defects = 5 + 20 + 120 + 155 = 300 # of Units (Opportunities) = 100 # of Defect Opportunities per Unit = 50


SIGMA TABLE

SIGMA

LEVEL

SHORT TERM (PROCESS NOT

SHIFTED)

LONG TERM (PROCESS SHIFTED 1.5

SIGMA)

Yield (OK)%

RejectPPM

Yield (OK)%

RejectPPM

1σ 68.27 317,300 30.23 697,700

2σ 95.45 45,500 69.13 308,700

3σ 99.73 2,700 93.32 66,810

4σ 99.9937 63 99.3790 6,210

5σ 99.999943 0.53 99.97670 233

6σ 99.9999998

0.002 99.999660 3.4

SIX SIGMA: Metrics (Cont…) Final Yield (FY)

Final Yield represents the acceptable pieces at the end of the process divided by the pieces started. The FY excludes scrap.

FY = (Total Unit Passed) / (Total Unit Tested)

Calculation from above example: The unit of measure must be the same for the numerator and denominator throughout the calculation.

Process 1 Yield: 46 passed / 50 entered = 92.0% Process 2 Yield (itself): 46 passed / 46 passed = 100% Yield AFTER Process 2: 46 passed / 50 entered: 92.0% Process 3 Yield (itself): 37 passed / 46 entered = 80.4% Yield AFTER Process 3 (also the same as the final yield of entire process): 37

passed / 50 entered = Final Yield = 74%

Process 3 has the lowest yield and probably the most cost associated since all the material, labor, and overhead costs are already in the pieces from the previous processes.


Throughput Yield (TPY): Also called:

FIRST PASS YIELD or FIRST TIME YIELD (FTY)

Throughput Yield (TPY) is the number of acceptable pieces at the end of a process divided by the number of starting pieces excluding scrap and rework.

TPY is the traditional quality metric for yield Unfortunately, it does not account for any

necessary rework


Throughput Yield (TPY): Also called FIRST PASS YIELD (FIRST TIME YIELD)

Calculation (assuming all rework only takes one time to correct): Process 1 TPY: 40 of the 50 pieces that entered Process 1 went through Process 1 correctly the first time. Therefore Process 1 TPY = 40 / 50 = 80.0% Process 2 TPY: 34 of the 46 pieces that entered into Process 2 went through Process 2 correctly the first time through. Therefore Process 2 TPY = 34 / 46 = 73.9% Process 3 TPY: 37 of the 46 pieces that entered Process 3 went through Process 3 correctly the first time. Therefore Process 3 TPY = 37/46 = 80.4%

There is another method to calculate TPY for a single process. If the DPU or defects and units are known then:


Rolled Throughput Yield (RTY): Rolled Throughput Yield is the probability of the entire process

producing zero defects. RTY is more important as a metric to use where the process has excessive rework.

Calculation from above example: RTY = Process 1 TPY * Process 2 TPY * Process 3 TPY RTY = 0.800 * 0.739 * 0.804 RTY = 0.475 = 47.5% There is a 47.5% of the entire process producing zero defects.

Another method to estimate RTY if the defects per unit or defects and units are known:

SIX SIGMA TOOLS

Q

• QFD• FMEA• SPC• QC

TOOLS• New

Management Tools

S

• Control Charts

• Capability

Analysis

• Probability

Distribution

• Sampling

• Confidence

Interval

• Regression

Analysis

M

• Project Management

• Organizationa

l Behavi

or• Human

Resource

Management

• Knowledge

Management

SIX SIGMA TOOLS1. Quality Tools2. Statistical Tools3. Management Tools

Every tool is a JUNK unless used appropriately

SIX SIGMA FRAMEWORKS

SIX SIGMA Lean Six Sigma DFSS

VARIATIONDefects

Cost of Poor Quality

WASTE / SPEEDCycle Time, Delivery

Cost of Operation

RELIABILITY & ROBUSTNESS

Design Features

DMAIC DMAIC DMADV

SIPOC, CTQ, SPC, FMEA, DOE, QFD,

CoQ, ANOVA, Hypothesis, Regression, MSA (R & R)

5S, Value Mapping, Time

Study, TPM,Cellular Prod.,Supply Chain,

Takt Time,Poke Yoke

VOC, QFD, FMEA, CTQ, Gage R & R, DOE, Reliability Analysis, SPC,

Systems Engineering

Program

Focus / Theme

Methodology

Tools

QUESTIONS

22

2. intro. to six sigma

Business

measure of sigma

sigma level

sigma methodology

sigma expert

defects unit

sigma shift theory

defects opportunity

sigma defined ina narrow