1. Basic Statistics

2. Cornerstones of a successful use of 6
EAB/JN Stefan Andresen
Cornerstones of a successful use of 6
Results
World Class
Business Performance
Where in six sigma do we use statistics?
Used for:
-Validating results, ideas etc.
-Understanding differences, root causes etc.
-Gives a mathematic as well as a graphical view of a problem
Methodology
Change Management
DFSS Basic Staistics

3. Different types of data
EAB/JN Stefan Andresen
Different types of data
Continuous Data
Often obtained by use of a measuring system e.g. dB, Watts, volts etc.
The usefulness of the data depends on the quality of the measurement system
Discrete Data
Includes percentages, attribute & counts
Percentages: The proportion of items with a given characteristic; need to be able to count both occurrences and and non-occurrences, e.g. Yield
Attribute data Gives only conforming or non conforming information, such as Pass/Fail, Red/Green, 1 / 0, etc.
Counts Number of events per hour, per shift or other delimitations
Occurrences must be independent
Being continuous means that the data can always be expressed in a smaller unit of measure: e.g.,
Amperes ®mA ® mA
months ® weeks ® days ® hours ® minutes
With continuous data, the reliability of the measurement instrument is extremely important. With count data, its important to know the area of opportunity: the boundaries that define when you’ll start and stop the count. This can be a given time period, a fixed area of product etc.
The occurrences must be relatively rare compared to a relatively large area of opportunity
Independence is also important for all data. It means that any given measurement or occurrence is not influenced by another measurement or occurrence.
DFSS Basic Staistics

4. EAB/JN Stefan Andresen
Lower
Tolerance
Limit
Upper
Tolerance
Limit
Yield
Yield
Defects
Yield = Pass / Trials
p(d) = (1- Yield)/100
DFSS Basic Staistics

5. 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
Fix It? No
SCRAP No
Fix It?
Yes
Yes
Rework
Rework
COPQ
DFSS Basic Staistics

6. Discrete data - Rolled Thru Yield
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
effect of sub-processes
FTY
First Process
99%
First Process
Rework
FTY
Second Process
89%
Second
Process
Rework
FTY
Third Process
95%
Third Process
Rework
First pass yield or rolled through
yield for these three
processes is
0.99 x 0.89 x 0.95 = .837,
almost 84%
Terminator
DFSS Basic Staistics

7. EAB/JN Stefan Andresen
YIELD
(process yield)no of operations
Yield \No of op
0,8 0, , , , ,000000
0,95 0, , , , ,000000
0, , , , , ,367861
0, , , , , ,970445
DFSS Basic Staistics

8. EAB/JN Stefan Andresen
Is it fair to compare processes and products that have different levels of complexity?
DPO
DPO - Defects Per Opportunity
DPMO
DPMO - Defects Per Million Opportunities
Opportunity
Measurable
The number of opportunities for a defect to occur, is related to the complexity involved.
DFSS Basic Staistics

9. Y=e(-dpu) dpu=-lnY Yeild to DPMO?
dpu = defects per unit = DPMO*(opportunities/unit)/

10. EAB/JN Stefan Andresen
Product yield vs dpmo
opp.
10000 opp.
1000 opp.
100 opp.
The Design & supply wall
The automation wall
Den ökade komplexiteten medför att vi måste ha bättre processer. Detta accentureras av att vi ser en ytterligare ökad komplexitet i våra framtida produkter.
En ökad yield minskar vårt omarbete och ökar vår lönsamhet.
Vi har även konkurrenter som är bättre än oss
Vi kan inte överleva om vi iinte förbättrar oss.
En del konkurrenter (Motorola) säger sig ha en felkvot på under 10 ppm. 6s 5s 4s 3s
DFSS Basic Staistics

11. EAB/JN Stefan Andresen
The Normal Curve
Context
The normal distribution provides the basis for many statistical tools and techniques.
Definition
A probability distribution where the most frequently occurring value is in the middle and other probabilities tail off symmetrically in both directions. This shape is sometimes called a bell-shaped curve.
Characteristics
Curve theoretically does not reach zero; thus the sum of all finite areas total less than 100%
Curve is symmetric on either side of the most frequently occurring value
The peak of the curve represents the center, or average, of the process
For all practical purposes, the area under the curve represents virtually 100% of the product the process is capable of producing
DFSS Basic Staistics

12. EAB/JN Stefan Andresen
Variation
Standard deviation
(std, s, )
Special cause
variation
Output power
Measurement no
Average, Mean-value
(x, m or µ, M)
Common cause
variation
DFSS Basic Staistics 23

13. 6:th
Sum 1:6 5 21 3 6 2 22 24 20 4 . 1 18 19 n
1:st 1 2 4 3 5 6 7 8 9 . 97 98 99
100
2:nd 5 1 6 3 2 .
Sum 1:2 7 9 10 8 4
3:rd
Sum 1:3 1 8 5 10 3 12 4 13 6 14 2 7 . 9
4:th
Sum 1:4 4 12 5 16 1 14 6 19 17 2 11 3 10 . 13 7 8
5:th
Sum 1:5 4 16 2 18 1 15 21 20 5 6 17 14 3 . 13

14. EAB/JN Stefan Andresen
Calculations
Arithmetic Mean Average
For a Sample
For the whole Population
Median
Middle value, so that half of the data are above and half of the data are below the median.
= Average of entire population or “true” mean
= (x bar) Average of sample or “best estimate” for mean
N = Number of observations in entire population
n = Number of observations in the sample
= Value of measurement x at position i
DFSS Basic Staistics

15. 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  
A copy of the Z-table is located at the back of this module in their manuals.
Plus Minitab can do it for them.
DFSS Basic Staistics

16. EAB/JN Stefan Andresen
Observation value
X1 0,4
X2 0,3
X3 0,4
X4 0,6
X5 0,5
X6 0,4
X7 0,2
X8 0,3
X9 0,5
X10 0,4 6  4  2
0, , ,3 0,4 0,5 0,6 0,7 0,8
x-m)2

n-1
The range method:
N<10: Range/3
N>10 Range/4
sample = n-1
population = n
DFSS Basic Staistics 28

17. Parameters to describe the spread (variability)
EAB/JN Stefan Andresen
Parameters to describe the spread (variability)
Range
Difference between highest and lowest value of the distribution
Influenced by Outliers
Variance (s2)
Average squared difference of data point from the average
Standard Deviation
Square root of the variance
Commonly used parameter for variability
DFSS Basic Staistics

18. EAB/JN Stefan Andresen
How to calculate
Range
Sample
Population
Variance (s2)
Standard Deviation
s2 = Variance of entire population, or “true” variance
S2 = Variance of sample, or “best estimate” for s2
s = Standard deviation of entire population, or “true” standard deviation.
S = Standard deviation of sample, or “best estimate” for s
DFSS Basic Staistics

19. EAB/JN Stefan Andresen
Exercise Calculate Range, Variance and Standard deviation. Draw a normal probability plot of the result.
Formulas
Data
R =
The same data set as before are used:
Range = 4
Variance = 1.78
Minitab gives
So Standard deviation = sqrt =
Variance - Why divide by (N-1)?
Because you’ve only taken a sample – and it will underestimate the variance by a small amount – and therefore to compensate by a slightly smaller number.
N-1 is the degrees of freedom
Calculate
106 (101, 102, 104, 105)
DFSS Basic Staistics

20. EAB/JN Stefan Andresen
Average, Range & Spread
Each diagram has an average of 10, range of 18 and a variation of approx. 5,8. Imagine only looking at the result and not on the graphs.
DFSS Basic Staistics

21. The normal distribution
EAB/JN Stefan Andresen
The normal distribution m s
-6s -5s -4s -3s s -1s s 2s 3s s 5s 6s
68.27%
95.45%
As you can see, the curve is divided into a series of equal increments, each representing one standard deviation from the mean.
The area under the curve represented by the first standard deviation out from the center in either direction represents approximately 34% of the total area.
Together, the area represented within one standard deviation of the center is about 68% of the total area. In other words, given a data set that is normally
distributed, approximately 68% of the data values should fall within one standard deviation of the center.
Going out plus or minus two standard deviations represents approximately 95% of the total area; go out 3 standard deviations in either direction and you’ve accounted for more than 99% of the area.
Tables have been developed that contain these listed areas, plus many more.
Thus by knowing a normal curve’s mean and standard deviation, we can figure out the yields within specified “zones.”
99.73% % % %
DFSS Basic Staistics

22. 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
A copy of the Z-table is located at the back of this module in their manuals.
The Z-value is the number of stdev between average/Target and specification limit
DFSS Basic Staistics

23. Normalizing standard deviations
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

24. Z-VALUES AND PROBABILITIES
EAB/JN Stefan Andresen
Z-VALUES AND PROBABILITIES
68,3%
-1+1
95,4%
-2+2
99,7%
-3+3
99,999997%
-6+6
DFSS Basic Staistics

25. EAB/JN Stefan Andresen
Z – Table
Area Z
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
This table represents the p-value for z= 0 to 2,99
DFSS Basic Staistics

26. EAB/JN Stefan Andresen
Z – Table
Area
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 Z
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
This table represents the p-value for z= 3,0 to 6,09
DFSS Basic Staistics

27. 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 
Hur bra processen skulle kunna vara
* 6
DFSS Basic Staistics

28. 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  
Hur bra processen är
* 3
DFSS Basic Staistics

29. 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
DFSS Basic Staistics

30. EAB/JN Stefan Andresen
„Shift Happens“
Short-Term
Capabilities
(within group variation)
Time 1
(between group variation)
Time 2
Time 3
Time 4
Key Messages:
To this point we have been talking about process capability in a short-term sense. It has been demonstrated that means do shift over time.
Process center shifts can result in defects though the process is capable. This shifting over time is an indication of the process’ long-term capability. It is important to reduce variation to provide for these process mean shifts.
Your Notes:
Long-Term Capability
(all variation)
LSL
Target
USL
DFSS Basic Staistics

31. Z long term and Z short term
EAB/JN Stefan Andresen
Z long term and Z short term
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
Ptot = 0,1%  Zb = 3,12
Zlt =Zb-S&D = 3,14 -1,5 = 1,64  p = 0,0559  5,6%
Calculate
133, 131, (132, 134)
What will the long term fault rate be in exercise 5 with a S&D of 1.5?
DFSS Basic Staistics

32. EAB/JN Stefan Andresen ZB
Lower
Tolerance
Limit
Upper
Tolerance
Limit
Ptot=Pupper+Plower
ZB – From table with Ptot
Rev C Peter Häyhänen 9805
DFSS Basic Staistics

33. Is Six Sigma corresponding to a defect level of 3,4ppm?
EAB/JN Stefan Andresen
Is Six Sigma corresponding to a defect level of 3,4ppm?
USL
LSL
± 1.5s
Short-term
Short-term
-6s -5s s s s s s s s s s s
% or ppm
% or 3.4 ppm
Yes, with a S&D of 1,5!!
DFSS Basic Staistics

34. EAB/JN Stefan Andresen
Shift & Drift
Z short term in a typical process 4,02 (based on approx. 30 values).
DFSS Basic Staistics

35. EAB/JN Stefan Andresen
Shift & Drift
Z long term in a typical process 3,03 (measurments from one and a half year of production, “all values”)
DFSS Basic Staistics

36. EAB/JN Stefan Andresen
Shift & Drift
Poverall = 1200ppm Þ Z = 3,03s
Psample = 29ppm Þ Z = 4,02s
Shift & Drift = Zshort term - Zlong term
Shift & Drift = 4,02s - 3,03s
Shift & Drift = 0,99s
DFSS Basic Staistics

37. Minitab Capability Output
EAB/JN Stefan Andresen
Minitab Capability Output
Above is an example of how Minitab can help you to calculate Zlt and Zst, although Minitab uses average for calculating both Zlt and Zst
DFSS Basic Staistics

38. 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

39. 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