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					                       Basic Statistics




DFSS Basic Staistics      2004-09-27   1   EAB/JN Stefan Andresen
       Cornerstones of a successful use of 6

                             Results




                           World Class
                       Business Performance



       Methodology                         Change Management



DFSS Basic Staistics      2004-09-27   2             EAB/JN Stefan Andresen
                         Lower                        Upper
Yield                    Tolerance                Tolerance
                         Limit                         Limit



                                          Yield


                                    Defects
                       Yield = Pass / Trials
                       p(d) = (1- Yield)/100

DFSS Basic Staistics         2004-09-27   4                    EAB/JN Stefan Andresen
          Discrete data - First Time Right (First Time Yield)
                        Measures the units that avoid the hidden costs.

                                 Yes                                   Yes
Step A                 Good?             Step B               Good?           Ship It!

                           No                                 No




                                 No                     No
                       Fix It?           SCRAP               Fix It?
                           Yes                               Yes

                       Rework                                Rework

          COPQ




DFSS Basic Staistics                   2004-09-27   5                        EAB/JN Stefan Andresen
                          Discrete data - Rolled Thru Yield
 Most processes are complex interrelationships of many sub-processes.
 The overall performance is usually of interest to us.
                                                                     Rolled yield is a realistic
                                                                assessment of the cumulative
                                FTY
                                                                      effect of sub-processes
 First Process             First Process
                                99%         Rework

                                                 FTY
                             Second
                                            Second Process
                             Process                          Rework
                                                 89%

                                                                    FTY
First pass yield or rolled through            Third Process    Third Process
                                                                   95%            Rework
yield for these three
processes is
0.99 x 0.89 x 0.95 = .837,                                      Terminator
almost 84%


   DFSS Basic Staistics                    2004-09-27   6                      EAB/JN Stefan Andresen
                                   YIELD
                             (process yield)no of operations

Yield \No of op.        3          10                  100        1000            10000
0,8                     0,512000   0,107374            0,000000   0,000000        0,000000
0,95                    0,857375   0,214639            0,005921   0,000000        0,000000
0,9999                  0,999700   0,999000            0,990049   0,904833        0,367861
0,999997                0,999991   0,999970            0,999700   0,997004        0,970445




      DFSS Basic Staistics            2004-09-27   7                    EAB/JN Stefan Andresen
Is it fair to compare processes and products that have different levels of complexity?

      DPO                   • DPO - Defects Per Opportunity


                                 DPO 
                                               defects
                                          opportunities
     DPMO                   • DPMO - Defects Per Million Opportunities

                                                  defects
                                DPMO                         *1 000 000
                                            opportunit ies

  Opportunity                Measurable
                             The number of opportunities for a defect to occur, is
                              related to the complexity involved.

     DFSS Basic Staistics                 2004-09-27   8                   EAB/JN Stefan Andresen
                         Yeild to DPMO?

                          Y=e(-dpu)

                          dpu=-lnY
dpu = defects per unit = DPMO*(opportunities/unit)/1 000 000

  DFSS Basic Staistics       2004-09-27   9               EAB/JN Stefan Andresen
      Product yield vs dpmo


                       100000 opp.     10000 opp.                          1000 opp. 100 opp.

    100




                                                The Design & supply wall




                                                                                      The automation wall
      50




        0

                  0     1       10             100                         1000    10000                      100000
                                              dpm o
                       6                     5                                  4 3
DFSS Basic Staistics             2004-09-27    10                                                           EAB/JN Stefan Andresen
Variation
                                                       Standard deviation
                                                           (std, s, )
                        Special cause
                          variation
Output power                                                                  Average, Mean-value
                                                                                 (x, m or µ, M)




                                        Common cause
                                          variation


                                                              Measurement no



 DFSS Basic Staistics        2004-09-27     12                              EAB/JN Stefan Andresen
Every Normal Curve can be defined by two numbers:
•Mean: a measure of the center
•Standard deviation: a measure of spread




                                                



                                       

   DFSS Basic Staistics   2004-09-27       15       EAB/JN Stefan Andresen
                                                                        Observation   value




                                       
                                                                          X1          0,4
     6                                                                    X2          0,3
                                                                          X3          0,4
      4                                                                   X4          0,6


                                                      
                                                                          X5          0,5
                                                                          X6          0,4
                                                                          X7          0,2
      2                                                                   X8          0,3
                                                                          X9          0,5
                                                                          X10         0,4
      0
                        0,1   0,2   0,3 0,4   0,5     0,6   0,7   0,8




                 x-m)2
                                                                                       The range method:
                                              sample = n-1                            N<10: Range/3
                                                population = n                          N>10 Range/4
                 n-1
 DFSS Basic Staistics                               2004-09-27    16                          EAB/JN Stefan Andresen
Exercise
Calculate Range, Variance and Standard deviation. Draw a normal
probability plot of the result.

Formulas                                               Data
                                                                                    2
                                                       Value (xi-x)        (xi-x)
 R = X max  X min                                         5
                                                           6
                                                           5


                                    
                                                           7
        1                2
            i 1 xi  x
             n
s2                                                        6

       n 1
                                                           9
                                                           7
                                                           8
                                                           6


                                
                                                           8
                         2
            i 1 xi  x
             n                                                 Sum
 s                                                            n-1
                n 1                                           Variance
                                                               Std. dev.

  DFSS Basic Staistics                   2004-09-27   19                      EAB/JN Stefan Andresen
              Average, Range &                                                                            Diagram 1


              Spread                                                                     20
                                                                                         18
                                                                                         16

              Each diagram has an average of                                             14
                                                                                         12




                                                                                Faults
              10, range of 18 and a variation                                            10
                                                                                          8
              of approx. 5,8. Imagine only                                                6
                                                                                          4
              looking at the result and not on                                            2

              the graphs.
                                                                                          0
                                                                                              0   2   4     6            8     10     12     14
                                                                                                                Number



                                         Diagram 2                                                        Diagram 3

         20                                                                              20
         18                                                                              18
         16                                                                              16
         14                                                                              14
         12                                                                              12
Faults




                                                                               Faults
         10                                                                              10
          8                                                                               8
          6                                                                               6
          4                                                                               4
          2                                                                               2
          0                                                                               0
              0        2        4          6            8   10   12     14                    0   2   4     6            8     10     12     14
                                               Number                                                           Number



                  DFSS Basic Staistics                            2004-09-27   20                                        EAB/JN Stefan Andresen
The normal distribution                                                   



                                                                              




                 -6      -5      -4      -3      -2      -1         0       1      2      3      4      5      6   
                                                                       68.27%
                                                                       95.45%
                                                                       99.73%
                                                                99.9937%
                                                               99.999943%
                                                              99.9999998%



   DFSS Basic Staistics                                        2004-09-27         21                                              EAB/JN Stefan Andresen
The Z-table

                                      Area under the normal curve
                                      is equal to the probability (p,
                                     also named dpo) of getting an
                                       observation beyond Z (see
                                               the Z-table)



                        Z



 DFSS Basic Staistics   2004-09-27   22                 EAB/JN Stefan Andresen
Normalizing standard deviations

          The expected probability of having a specific value


           Observed value - Mean Value
                                                         = Z-value
                       Standard deviation
                                                                     ( the Z-table gives the
                                                                     probability occurrence)
            |x-M|
              std          =Z




DFSS Basic Staistics                   2004-09-27   23                                EAB/JN Stefan Andresen
 Z-VALUES AND PROBABILITIES


68,3%                   -1 +1


95,4%
                        -2 +2


99,7%
                        -3 +3



                        -6 +6
99,999997%

 DFSS Basic Staistics    2004-09-27   24   EAB/JN Stefan Andresen
                   Z – Table                                                                     Area


 Z         0            0.01       0.02        0.03       0.04         0.05       0.06       0.07         0.08       0.09
0.0     5.00E-01      4.96E-01   4.92E-01    4.88E-01   4.84E-01     4.80E-01   4.76E-01   4.72E-01     4.68E-01   4.64E-01
0.1     4.60E-01      4.56E-01   4.52E-01    4.48E-01   4.44E-01     4.40E-01   4.36E-01   4.33E-01     4.29E-01   4.25E-01
0.2     4.21E-01      4.17E-01   4.13E-01    4.09E-01   4.05E-01     4.01E-01   3.97E-01   3.94E-01     3.90E-01   3.86E-01
0.3     3.82E-01      3.78E-01   3.75E-01    3.71E-01   3.67E-01     3.63E-01   3.59E-01   3.56E-01     3.52E-01   3.48E-01
0.4     3.45E-01      3.41E-01   3.37E-01    3.34E-01   3.30E-01     3.26E-01   3.23E-01   3.19E-01     3.16E-01   3.12E-01
0.5     3.09E-01      3.05E-01   3.02E-01    2.98E-01   2.95E-01     2.91E-01   2.88E-01   2.84E-01     2.81E-01   2.78E-01
0.6     2.74E-01      2.71E-01   2.68E-01    2.64E-01   2.61E-01     2.58E-01   2.55E-01   2.51E-01     2.48E-01   2.45E-01
0.7     2.42E-01      2.39E-01   2.36E-01    2.33E-01   2.30E-01     2.27E-01   2.24E-01   2.21E-01     2.18E-01   2.15E-01
0.8     2.12E-01      2.09E-01   2.06E-01    2.03E-01   2.01E-01     1.98E-01   1.95E-01   1.92E-01     1.89E-01   1.87E-01
0.9     1.84E-01      1.81E-01   1.79E-01    1.76E-01   1.74E-01     1.71E-01   1.69E-01   1.66E-01     1.64E-01   1.61E-01
1.0     1.59E-01      1.56E-01   1.5 39E01   1.52E-01   1.49E-01     1.47E-01   1.45E-01   1.42E-01     1.40E-01   1.38E-01
1.1     1.36E-01      1.34E-01    1.31E-01   1.29E-01   1.27E-01     1.25E-01   1.23E-01   1.21E-01     1.19E-01   1.17E-01
1.2     1.15E-01      1.13E-01    1.11E-01   1.09E-01   1.08E-01     1.06E-01   1.04E-01   1.02E-01     1.00E-01   9.85E-02
1.3     9.68E-02      9.51E-02    9.34E-02   9.18E-02   9.01E-02     8.85E-02   8.69E-02   8.53E-02     8.38E-02   8.23E-02
1.4     8.08E-02      7.93E-02    7.78E-02   7.64E-02   7.49E-02     7.35E-02   7.21E-02   7.08E-02     6.94E-02   6.81E-02
1.5     6.68E-02      6.55E-02    6.43E-02   6.30E-02   6.18E-02     6.06E-02   5.94E-02   5.82E-02     5.71E-02   5.59E-02
1.6     5.48E-02      5.37E-02    5.26E-02   5.16E-02   5.05E-02     4.95E-02   4.85E-02   4.75E-02     4.65E-02   4.55E-02
1.7     4.46E-02      4.36E-02    4.27E-02   4.18E-02   4.09E-02     4.01E-02   3.92E-02   3.84E-02     3.75E-02   3.67E-02
1.8     3.59E-02      3.52E-02    3.44E-02   3.36E-02   3.29E-02     3.22E-02   3.14E-02   3.07E-02     3.01E-02   2.94E-02
1.9     2.87E-02      2.81E-02    2.74E-02   2.68E-02   2.62E-02     2.56E-02   2.50E-02   2.44E-02     2.39E-02   2.33E-02
2.0     2.28E-02      2.22E-02   2.17E-02    2.12E-02   2.07E-02     2.02E-02   1.97E-02   1.92E-02     1.88E-02   1.83E-02
2.1     1.79E-02      1.74E-02   1.70E-02    1.66E-02   1.62E-02     1.58E-02   1.54E-02   1.50E-02     1.46E-02   1.43E-02
2.2     1.39E-02      1.36E-02   1.32E-02    1.29E-02   1.26E-02     1.22E-02   1.19E-02   1.16E-02     1.13E-02   1.10E-02
2.3     1.07E-02      1.04E-02   1.02E-02    9.90E-03   9.64E-03     9.39E-03   9.14E-03   8.89E-03     8.66E-03   8.42E-03
2.4     8.20E-03      7.98E-03   7.76E-03    7.55E-03   7.34E-03     7.14E-03   6.95E-03   6.76E-03     6.57E-03   6.39E-03
2.5     6.21E-03      6.04E-03   5.87E-03    5.70E-03   5.54E-03     5.39E-03   5.23E-03   5.09E-03     4.94E-03   4.80E-03
2.6     4.66E-03      4.53E-03   4.40E-03    4.27E-03   4.15E-03     4.02E-03   3.91E-03   3.79E-03     3.68E-03   3.57E-03
2.7     3.47E-03      3.36E-03   3.26E-03    3.17E-03   3.07E-03     2.98E-03   2.89E-03   2.80E-03     2.72E-03   2.64E-03
2.8     2.56E-03      2.48E-03   2.40E-03    2.33E-03   2.26E-03     2.19E-03   2.12E-03   2.05E-03     1.99E-03   1.93E-03
2.9     1.87E-03      1.81E-03   1.75E-03    1.70E-03   1.64E-03     1.59E-03   1.54E-03   1.49E-03     1.44E-03   1.40E-03


      DFSS Basic Staistics                         2004-09-27   25                                    EAB/JN Stefan Andresen
                  Z – Table                                                                        Area


 Z         0           0.01       0.02       0.03       0.04        0.05       0.06       0.07       0.08       0.09
3.0     1.35E-03     1.31E-03   1.26E-03   1.22E-03   1.18E-03    1.14E-03   1.11E-03   1.07E-03   1.04E-03   1.00E-03
3.1     9.68E-04     9.35E-04   9.04E-04   8.74E-04   8.45E-04    8.16E-04   7.89E-04   7.62E-04   7.36E-04   7.11E-04
3.2     6.87E-04     6.64E-04   6.41E-04   6.19E-04   5.98E-04    5.77E-04   5.57E-04   5.38E-04   5.19E-04   5.01E-04
3.3     4.84E-04     4.67E-04   4.50E-04   4.34E-04   4.19E-04    4.04E-04   3.90E-04   3.76E-04   3.63E-04   3.50E-04
3.4     3.37E-04     3.25E-04   3.13E-04   3.02E-04   2.91E-04    2.80E-04   2.70E-04   2.60E-04   2.51E-04   2.42E-04
3.5     2.33E-04     2.24E-04   2.16E-04   2.08E-04   2.00E-04    1.93E-04   1.86E-04   1.79E-04   1.72E-04   1.66E-04
3.6     1.59E-04     1.53E-04   1.47E-04   1.42E-04   1.36E-04    1.31E-04   1.26E-04   1.21E-04   1.17E-04   1.12E-04
3.7     1.08E-04     1.04E-04   9.97E-05   9.59E-05   9.21E-05    8.86E-05   8.51E-05   8.18E-05   7.85E-05   7.55E-05
3.8     7.25E-05     6.96E-05   6.69E-05   6.42E-05   6.17E-05    5.92E-05   5.68E-05   5.46E-05   5.24E-05   5.03E-05
3.9     4.82E-05     4.63E-05   4.44E-05   4.26E-05   4.09E-05    3.92E-05   3.76E-05   3.61E-05   3.46E-05   3.32E-05
4.0     3.18E-05     3.05E-05   2.92E-05   2.80E-05   2.68E-05    2.57E-05   2.47E-05   2.36E-05   2.26E-05   2.17E-05
4.1     2.08E-05     1.99E-05   1.91E-05   1.82E-05   1.75E-05    1.67E-05   1.60E-05   1.53E-05   1.47E-05   1.40E-05
4.2     1.34E-05     1.29E-05   1.23E-05   1.18E-05   1.13E-05    1.08E-05   1.03E-05   9.86E-06   9.43E-06   9.01E-06
4.3     8.62E-06     8.24E-06   7.88E-06   7.53E-06   7.20E-06    6.88E-06   6.57E-06   6.28E-06   6.00E-06   5.73E-06
4.4     5.48E-06     5.23E-06   5.00E-06   4.77E-06   4.56E-06    4.35E-06   4.16E-06   3.97E-06   3.79E-06   3.62E-06
4.5     3.45E-06     3.29E-06   3.14E-06   3.00E-06   2.86E-06    2.73E-06   2.60E-06   2.48E-06   2.37E-06   2.26E-06
4.6     2.15E-06     2.05E-06   1.96E-06   1.87E-06   1.78E-06    1.70E-06   1.62E-06   1.54E-06   1.47E-06   1.40E-06
4.7     1.33E-06     1.27E-06   1.21E-06   1.15E-06   1.10E-06    1.05E-06   9.96E-07   9.48E-07   9.03E-07   8.59E-07
4.8     8.18E-07     7.79E-07   7.41E-07   7.05E-07   6.71E-07    6.39E-07   6.08E-07   5.78E-07   5.50E-07   5.23E-07
4.9     4.98E-07     4.73E-07   4.50E-07   4.28E-07   4.07E-07    3.87E-07   3.68E-07   3.50E-07   3.32E-07   3.16E-07
5.0     3.00E-07     2.85E-07   2.71E-07   2.58E-07   2.45E-07    2.32E-07   2.21E-07   2.10E-07   1.99E-07   1.89E-07
5.1     1.80E-07     1.71E-07   1.62E-07   1.54E-07   1.46E-07    1.39E-07   1.31E-07   1.25E-07   1.18E-07   1.12E-07
5.2     1.07E-07     1.01E-07   9.59E-08   9.10E-08   8.63E-08    8.18E-08   7.76E-08   7.36E-08   6.98E-08   6.62E-08
5.3     6.27E-08     5.95E-08   5.64E-08   5.34E-08   5.06E-08    4.80E-08   4.55E-08   4.31E-08   4.08E-08   3.87E-08
5.4     3.66E-08     3.47E-08   3.29E-08   3.11E-08   2.95E-08    2.79E-08   2.64E-08   2.50E-08   2.37E-08   2.24E-08
5.5     2.12E-08     2.01E-08   1.90E-08   1.80E-08   1.70E-08    1.61E-08   1.53E-08   1.44E-08   1.37E-08   1.29E-08
5.6     1.22E-08     1.16E-08   1.09E-08   1.03E-08   9.78E-09    9.24E-09   8.74E-09   8.26E-09   7.81E-09   7.39E-09
5.7     6.98E-09     6.60E-09   6.24E-09   5.89E-09   5.57E-09    5.26E-09   4.97E-09   4.70E-09   4.44E-09   4.19E-09
5.8     3.96E-09     3.74E-09   3.53E-09   3.34E-09   3.15E-09    2.97E-09   2.81E-09   2.65E-09   2.50E-09   2.36E-09
5.9     2.23E-09     2.11E-09   1.99E-09   1.88E-09   1.77E-09    1.67E-09   1.58E-09   1.49E-09   1.40E-09   1.32E-09
6.0     1.25E-09     1.18E-09   1.11E-09   1.05E-09   9.88E-10    9.31E-10   8.78E-10   8.28E-10   7.81E-10   7.36E-10

      DFSS Basic Staistics                        2004-09-27     26                                 EAB/JN Stefan Andresen
Capability

  CP Tolerance width divided by 6 times the standard deviation. A CP value
  greater than 2 is good (thumb rule)

                                                    Tolerance width



                  TÖ - TU                                
             CP = -----------
                             6

                                                    *6
      DFSS Basic Staistics        2004-09-27   27                EAB/JN Stefan Andresen
Capability

     Cpk Difference between nearest tolerance limit and average,
     divided by 3 times the standard deviation. A Cpk value
     greater than 1,5 is good (thumb rule)
                                       TU                               TÖ


              Min(TÖ alt.  TU)
    CPK      = ----------------------                    
                             3


                                                    *3
      DFSS Basic Staistics        2004-09-27   28            EAB/JN Stefan Andresen
Continuous data and possible Pitfalls
   Can be divided in to two types of variation
          Common cause                           (e.g. within batch variation)
          Special cause             -The shift between      and        (e.g. batch variation)
                                     -Outliers or non-rare occasions will appear and may ruin the analyze


                                                             Output power

                            22

                            20

                            18
             Effect (dBm)




                            16

                            14

                            12

                            10
                                 0           5             10              15              20         25          30
                                                                        Number


    DFSS Basic Staistics                                   2004-09-27     29                                EAB/JN Stefan Andresen
                                                                 Short-Term
„Shift Happens“                                                  Capabilities
                                                                (within group
                                                                  variation)

                          Time 1


  (between                Time 2

    group                 Time 3
  variation)              Time 4




                                                                 Long-Term
                                                                 Capability
                                                                (all variation)


                                   LSL           Target   USL
   DFSS Basic Staistics             2004-09-27    30                   EAB/JN Stefan Andresen
Z long term and Z short term
                                            Tol  
                        Z _ long _ term                      Single  sided 
                                            
                                           Tol  T
                        Z _ Short _ term                     Single  Sided 
                                              s
                        p  overall  Z B
  The sample and the population sigma are often almost the same, but the average will probably
  differ. Therefore is zST (zB ) and shift & drift preferably used to estimate the “true” fault rate.

                            Shift & Drift = Zshort term - Zlong term

       What will the long term fault rate be in exercise 5 with
       a S&D of 1.5?
     DFSS Basic Staistics                   2004-09-27   31                     EAB/JN Stefan Andresen
ZB                     Lower                        Upper
                       Tolerance                Tolerance
                       Limit                         Limit




                           Ptot=Pupper+Plower

                       ZB – From table with Ptot

                                                             Rev C Peter Häyhänen 9805
DFSS Basic Staistics          2004-09-27   32                  EAB/JN Stefan Andresen
                  Is Six Sigma corresponding to a defect level of 3,4ppm?

            LSL                                                                                                      USL
                                                                   1.5




                                                            Short-term
                                                              Short-term




             -6       -5      -4      -3      -2        -1        0    1      2      3      4      5        6   

                                                  99.9999998% or 0.002 ppm

                                                                        99.99966% or 3.4 ppm


                        Yes, with a S&D of 1,5!!
DFSS Basic Staistics                                       2004-09-27       33                                         EAB/JN Stefan Andresen
         Shift & Drift

                a typical process 4,02 (based on
Z short term inProcess Capability Analysis for Z-short term approx. 30 values).
                               LSL
      Process Data
USL                        *                                                                                     ST
Target                     *                                                                                     LT
LSL             10,0000
Mean            12,5804
Sample N             25
StDev (ST)     0,641863
StDev (LT)     0,641863


Potential (ST) Capability
Cp                      *
CPU                        *
CPL                  1,34
Cpk                  1,34
Cpm                     *
                               10              11           12           13            14               15

 Overall (LT) Capability            Observed Performance     Expected ST Performance        Expected LT Performance
Pp                         *    PPM < LSL            0,00    PPM < LSL         29,08        PPM < LSL         29,08
PPU                        *    PPM > USL               *    PPM > USL             *        PPM > USL             *
PPL                  1,34       PPM Total            0,00    PPM Total         29,08        PPM Total         29,08
Ppk                  1,34



   DFSS Basic Staistics                                     2004-09-27   34                                           EAB/JN Stefan Andresen
       Shift & Drift

                 typical process 3,03 (measurments from one and a
Z long term in a Process Capability Analysis for Z-long term
half year of production, “all values”)
                                LSL
       Process Data
 USL                        *                                                                                      ST
 Target                     *                                                                                      LT
 LSL             10,0000
 Mean            12,2222
 Sample N            161
 StDev (ST)     0,732048
 StDev (LT)     0,732048


 Potential (ST) Capability
 Cp                      *
 CPU                        *
 CPL                  1,01
 Cpk                  1,01
 Cpm                     *
                                10                11                12                13           14

  Overall (LT) Capability            Observed Performance          Expected ST Performance    Expected LT Performance
 Pp                         *    PPM < LSL             0,00        PPM < LSL        1200,46   PPM < LSL      1200,46
 PPU                        *    PPM > USL                *        PPM > USL              *   PPM > USL            *
 PPL                  1,01       PPM Total             0,00        PPM Total        1200,46   PPM Total      1200,46
 Ppk                  1,01




 DFSS Basic Staistics                                         2004-09-27       35                                   EAB/JN Stefan Andresen
Shift & Drift


                       Poverall = 1200ppm  Z = 3,03

                       Psample = 29ppm                Z = 4,02

                       Shift & Drift = Zshort term - Zlong term

                          Shift & Drift = 4,02 - 3,03

                              Shift & Drift = 0,99



DFSS Basic Staistics               2004-09-27   36                 EAB/JN Stefan Andresen
Minitab Capability Output




DFSS Basic Staistics   2004-09-27   37   EAB/JN Stefan Andresen
    Nomenclature
dpmo - defects per million opportunities
Yield        - % of the number of approved units divided by the total number of units

p(d)         - probability for defects (1-Yield)

Fty          - First time yield, the yield when the units are tested for the first time

TpY          - Throughput yield, the yield in every unique process step

Yrt          - Yield rolled through, multiplied throughput yield

DPU          - Defects per units

DPO          - Defects per opportunity

Opp          - Opportunity, measurable opportunity for defect

 DFSS Basic Staistics                  2004-09-27   38                         EAB/JN Stefan Andresen
     Nomenclature
Zst          - Single side short term capability, calculated with the help of the target
Zb           - An estimate of the overall short term capability, used to calculate Zlt

Zlt          - A rating of the long term capability, normally based on S&D & Zb

pl           - Probability for defect beneath lower specification limit

pu           - Probability for defect above upper specification limit

p            - Summarized probability for defect, pl + pu

S&D          - An approximation of the drift in average, fundamentally 1,5

LSL          - Lower specification limit

USL          - Upper specification limit

 DFSS Basic Staistics                 2004-09-27   39                        EAB/JN Stefan Andresen

				
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