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Six Sigma Measurement. Yield and Defects. Probability. of Yield. Probability. of Defects. USL. LSL. Target. Value. The Normal Curve. s. s. s. s. s. s. m. s. s. s. s. s. s. +1. -6. -5. -4. -3. -2. -1. +2. +3. +4. +5. +6. s. s. 68,26 %. s. s. 2. 2. 95,46 %.

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Six Sigma Measurement


Yield and Defects

Probability

of Yield

Probability

of Defects

USL

LSL

Target

Value


The Normal Curve

s

s

s

s

s

s

m

s

s

s

s

s

s

+1

-6

-5

-4

-3

-2

-1

+2

+3

+4

+5

+6

s

s

68,26 %

s

s

2

2

95,46 %

s

s

3

3

99,73 %

s

s

4

4

99,9937 %

s

s

5

5

99,999943 %

s

s

6

6

99,9999998 %


Statistical interpretation of six sigma

Let “X” be the quality characteristic of interest and

(Length/Thickness/Temperature/Pressure etc.)

USL = Upper Specification Limit

LSL = Lower Specification Limit

T = Target Value

m = Process Average s = Process Standard Deviation

X = Estimate of m s = Estimate of s

Statistical Interpretation of Six Sigma


Calculation of sigma level when process is centered
Calculation of Sigma level - When Process is Centered

USL - T

SIGMA LEVEL (Z) =

s

OR

T - LSL

SIGMA LEVEL (Z) =

s

L

Mean = T

U


Calculation of sigma level
Calculation of Sigma level

When Process is Centered Closer To LSL

X - LSL

SIGMA LEVEL (Z) =

s

L

Mean

T

U


Calculation of sigma level1
Calculation of Sigma level

When Process is Centered Closer To USL

USL - X

SIGMA LEVEL (Z) =

s

L

T

Mean

U


Calculation of sigma level2
Calculation of Sigma level

There is only Upper Specification Limit (USL)

USL - X

SIGMA LEVEL (Z) =

s

Mean

U


Calculation of sigma level3
Calculation of Sigma level

There is only Lower Specification Limit (LSL)

X - LSL

SIGMA LEVEL (Z) =

s

L

Mean


The Normal Curve wit Different Sigma Levels

S = 2 (SIX SIGMA Quality Level)

S = 3 (FOUR SIGMA Quality Level)

S = 4 (THREE SIGMA Quality Level)

USL = 1322

1298 = LSL

USL = 1310


SIGMA (s) QUALITY LEVELS (DPMO)

SIGMA LEVEL DPMO

1 6,97,700

2 3,08,537

3 66,807

4 6,201

5 233

6 3.4



Opportunities for Defect

DPMO

  • MEANS DEFECTS PER MILLION

  • OPPORTUNITIES

  • IS TRANSLATED INTO A SIGMA

  • NUMBER


Defects/Opportunity & Defect/Million Opportunity

Number of Defects

Formula =

# of Units x # of opportunities

Example 319 Defects, 1150 Items, 15 defect opportunity

319 defects on joints

Formula =

1150 Units x 15 opportunities/joist

= 0.018 DPO

= 0.018 x 106 = 18,000 DPMO


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