Statistics In QW5
QW5 Help Files
This section is intended to provide a definition of terms used in QW 5 as well as information on the calculations and rules followed by QW 5 in developing the statistics that appear when a graph of a variable is displayed.
These calculations are based on having a fixed USL, LSL and Target.
Only entered values (nonnull) are included in calculations in QW 5.
Please note the following changes with the release of Quality Window version 5.0.0.783:
Cpk and Cp are still reported.
Calculating Statistics in QW 5
How to use this table
1. Match the combination of fixed limits you have with the Fixed Limits column.
2. Go right to the column of the statistic you want to calculate.

O % OOL 
C % OOL 
Cr 
Tz 
(replaced by Ppk) 
(replaces Cpk calculations) 
Fixed USL Fixed Target Fixed LSL 
Use both Limits Out Upper Out Lower 
Use both Limits Z Upper Z Lower 
6S / (USL  LSL) 
(AVG  TGT) / S 
Lesser of (USL  AVG) / )/(3*SD MR) and (AVG  LSL) / (3*SD MR) 
Lesser of (USL  AVG) / (3*SD Pop) and (AVG  LSL) / (3*SD Pop)

Fixed USL Fixed Target Fixed LSL

Use USL Only 
Use USL Only Z Upper 
3S / (USL  TGT) 
(AVG  TGT) / S 
(USL  AVG) / (3*SD MR) 
(USL  AVG) / (3*SD Pop) 
Fixed Target Fixed LSL

USe LSL Only 
Use USL Only Z Lower 
3S / (TGT  LSL) 
(AVG  TGT) / S 
(AVG  LSL) / (3*SD MR) 
(AVG  LSL) / (3*SD Pop) 
Fixed Target

N/A 
N/A 
N/A 
(AVG  TGT) / S 
N/A 
N/A 
Fixed USL 
Use USL Only 
Use USL Only Z Upper

3S / (USL  AVG) 
N/A 
(USL  AVG) / (3*SD MR) 
(USL  AVG) / (3*SD Pop) 
Fixed LSL 
Use LSL Only 
Use USL Only Z Lower

3S / (AVG  LSL) 
N/A 
(AVG  LSL) / (3*SD MR) 
(AVG  LSL) / (3*SD Pop) 
Fixed USL Fixed LSL 
Use USL & LSL 
Use both Limits Z Upper Z Lower 
6S / (USL  LSL) 
N/A 
Lesser of (USL  AVG) / (3*SD MR) and (AVG  LSL) / (3*SD MR) 
Lesser of (USL  AVG) / (3*SD Pop) and (AVG  LSL) / (3*SD Pop) 
Example
If you have fixed Target and LSL values and want to calculate Cr, the calculation would be 3S/(Tgt  LSL). (Divide 3 standard deviations by the difference between the target and the lower spec limit.)

Definitions of Statistics used in QW 5
Average represented by Avg
The mathematical average of all data points in a field. Also known as the Arithmetic Mean
where n = number of points in the field
Calc % above TGT represented by C%>TGT
Calculated percent above target.
Calc % above UCL represented by C%>UCL
Calculated percent above upper control limit.
Calc % above USL represented by C%>USL
Calculated percent above upper specification limit.
Calc % above UWL represented by C%>UWL
Calculated percent above upper warning limit.
Calc % below LCL represented by C%<LCL
Calculated percent below lower control limit.
Calc % below LSL represented by C%<LSL
Calculated percent below upper specification limit.
Calc % below LWL represented by C%<LWL
Calculated percent below lower warning limit.
Calc % below TGT represented by C%<TGT
Calculated percent below target.
Calc % OSL represented by C%OSL
This statistic uses a table to infer the theoretical %OSL. The table assumes normality, control and the right number of samples so that the Average and SD are representative of the true population. Unless these assumptions hold true, the number will be inaccurate. When you have calculated quantities and no observed quantities, first suspect the assumptions above have been violated ... particularly with large sample sizes. It is calculated as the value of the percentage (or parts per million) of a normal distribution curve that will fall outside the specification limits (points in the white band of the chart) if a large number of samples are taken. This value is theoretical and is accurate only if the variable is in statistical control and the data is normally distributed.
To calculate the C%OSL you need :
 the average (Avg)
 the standard deviation (Std Dev  pop) of the population
 the Upper Specification Limit (USL)
 the Lower Specification Limit (LSL)
 a ZTable to find the proportion out (Pz).
Calc N above TGT represented by Cn>TGT
Calculated number above target.
Calc N above UCL represented by Cn>UCL
Calculated number above upper control limit.
Calc N above USL represented by Cn>USL
Calculated number above upper specification limit.
Calc N above UWL represented by Cn>UWL
Calculated number above upper warning limit.
Calc N below LCL represented by Cn<LCL
Calculated number below upper control limit.
Calc N below LSL represented by Cn<LSL
Calculated number below lower specification limit.
Calc N below LWL represented by Cn<LWL
Calculated number below lower warning limit.
Calc N below TGT represented by Cn<TGT
Calculated number below target.
Calc N OSL represented by CnOSL
Calc ppm above TGT represented by Cppm>TGT
Calculated parts per million above target.
Calc ppm above UCL represented by Cppm>UCL
Calculated parts per million above upper control limit.
Calc ppm above USL represented by Cppm>USL
Calculated parts per million above upper specification limit.
Calc ppm above UWL represented by Cppm>UWL
Calculated parts per million above upper warning limit.
Calc ppm below LCL represented by Cppm<LCL
Calculated parts per million below lower control limit.
Calc ppm below LSL represented by Cppm<LSL
Calculated parts per million below lower specification limit.
Calc ppm below LWL represented by Cppm<LWL
Calculated parts per million below lower warning limit.
Calc ppm below TGT represented by Cppm<TGT
Calculated parts per million below target.
Calc ppm OSL represented by CppmOSL
Calculated parts per million out of specification limits.
Calc ppm UCI represented by CppmUCI
The Calculated parts per million Upper Confidence Interval is an adjustment to the defect estimate to account for sampling error using the normal distribution theory.
The UCI ppm values are defect estimates that represent the worst case scenario of the actual defect level since it takes into account the potential error associated with low sample size. The larger the sample size, the lower the UCI ppm value. For example, if random samples were repeatedly taken from the same population and used to determine the defect estimate in ppm, the 95% UCI ppm would represent the ppm number that 95% of the samples estimates would fall below and 5% would fall above.
Calc Lower Warning Limit represented by CLWL
Calculated lower warning limit.
Calc Upper Warning Limit represented by CUWL
Calculated upper warning limit.
Clearance see Ppk
Coefficient Variation represented by %CV
The absolute value of (the standard deviation divided by the average) multiplied by 100
Control Limits
Upper Control Limit represented by UCL
Lowerer Control Limit represented by LCL
Control limits reflect target +/ 3S based on the historical performance of each line in question. Choosing a best time (absence of special causes) for basing the historical performance on is preferred as long as special causes can be eliminated or corrected. Control limits are based on the best capability of each line are preferably symmetric. +/ 3S can be used for any chart with 98100% confidence without assumptions as to normality and control. Control Limits in QW 5.0 can be fixed, blank or continuously calculated values. These values are used in the program to set the values where color changes occur in the Charts. In QW 5.0 the control limits are relative to the target and specification limits and establish a "warning track" inside the specification limits.
Correlation Coefficient
All Null values within
variable X are filled with extrapolated values
All Null values within variable Y are filled with extrapolated values
All leading and trailing pairs of X, Y data are removed if either X or Y are null.
Determine R (Correlation Coefficient)
If R > 1 then R = 1
If R < 1 then R = 1
Determine T (Significance Test)
Determine if Significant.
If  T  > 1.96 highlight the value (95% significant)
Display Correlation Coefficient as
Current Average represented by Avgcurrent
Current Standard Deviation represented by Scurrent
fcalc
Tests whether the Variation of two populations are different.
Last Value represented by Last Value
Lower Capability Limit represented by Cpl
(AVG  LSL) / ) / (3*SD MR)
Lower Control Limit represented by LCL
Lower Performance Limit represented by Ppl
(AVG  LSL) / ) / (3*SD Pop)
Lower Process Capability (3S) represented by Avg3S
Lower Process Capability (4S) represented by Avg4S
Lower Spec. Limit represented by LSL
Lower Warning Limit represented by LWL
Maximum Value represented by Max
The highest value found in the data selected.
Median represented by M
The median is a measure of control tendency derived from taking the middlemost or most central point in a set of sorted points. Half of the points will lie above the median, and the other half will lie below the median. If the number of points is odd the middle point is the median. If there is an even number of points the median is the average of the middle points.
Minimum Value represented by Min Value
The lowest value found in the data selected.
Moving Range Average represented by
The Moving Range Average is based on succesive differences between individual values.
Moving Range Upper Control Limit represented by MRUCL
Is the Moving Range Upper Control Limit
Number of Points represented by N
The number of nonnull values found in the data selected.
Obs % above TGT represented by O%>TGT
Observed percent above target.
Obs % above UCL represented by O%>UCL
Observed percent above upper control limit.
Obs % above USL represented by O%>USL
Observed percent above upper specification limit.
Obs % above UWL represented by O%>UWL
Observed percent above upper warning limit.
Obs % below LCL represented by O%<LCL
Obs % below LSL represented by O%<LSL
Obs % below LWL represented by O%<LWL
Obs % below TGT represented by O%<TGT
Obs % on TGT represented by O%=TGT
Obs % OSL represented by O%OSL
Obs N above TGT represented by On>TGT
Obs N above UCL represented by On>UCL
Obs N above USL represented by On>USL
Obs N above UWL represented by On>UWL
Obs N below LCL represented by On<LCL
Obs N below LSL represented by On<LSL
Obs N below LWL represented by On<LWL
Obs N below TGT represented by On<TGT
Obs N on TGT represented by On=TGT
Obs N OSL represented by OnOSL
Obs ppm above TGT represented by Oppm>TGT
Obs ppm above UCL represented by Oppm>UCL
Obs ppm above USL represented by Oppm>USL
Obs ppm above UWL represented by Oppm>UWL
Obs ppm below LCL represented by Oppm<LCL
Obs ppm below LSL represented by Oppm<LSL
Obs ppm below LWL represented by Oppm<LWL
Obs ppm below TGT represented by Oppm<TGT
Obs ppm on TGT represented by Oppm=TGT
Obs ppm OSL represented by OppmOSL
Obs ppm UCI represented by OppmUCI
The Observed parts per million Upper Confidence Interval is an adjustment to the defect estimate to account for sampling error using the binomial distribution theory.
The UCI ppm values are defect estimates that represent the worst case scenario of the actual defect level since it takes into account the potential error associated with low sample size. The larger the sample size, the lower the UCI ppm value. For example, if random samples were repeatedly taken from the same population and used to determine the defect estimate in ppm, the 95% UCI ppm would represent the ppm number that 95% of the samples estimates would fall below and 5% would fall above.
Point
The value of each cell in a data collection.
Process Capability Index represented by Cpk
Requires two separate calculations and then you select the smaller of the two results.
These equations describe the clearance between the process distribution curve and the specification limits in terms of standard deviation. The concern would be on whichever end of the distribution curve is closest to the specification limit (could be equal if the process is perfectly centered within the specification limits). A value of 1.33 or greater is considered good. A value of 1.33 would mean that the process average is four deviations away from the nearest specification limit. Compare Cr with Cpk. The process variation is in the numerator of Cr, and the denominator of Cpk (also Cp). Low Cr and high Cpk numbers are good.
Process Capability Rate represented by Cp
The inverse of Capability Ratio.
Process Performance Index represented by Ppk
Requires two separate calculations and then you select the smaller of the two results.
These equations describe the clearance between the process distribution curve and the specification limits in terms of standard deviation. The concern would be on whichever end of the distribution curve is closest to the specification limit (could be equal if the process is perfectly centered within the specification limits). A value of 1.33 or greater is considered good. A value of 1.33 would mean that the process average is four deviations away from the nearest specification limit. Compare Cr with Ppk. The process variation is in the numerator of Cr, and the denominator of Ppk (also Pp). Low Cr and high Ppk numbers are good.
Process Performance Rate represented by Pp
The inverse of Capability Ratio.
Range AVG represented by RAVG
Range LWL represented by RLWL
Range UCL represented by RUCL
Range UWL represented by RUWL
Rule Violation represented by Rule
SD Low
SD Low is defined as the lowest standard deviation of a consecutive group of m points with a population of n points.
m is determined by multiplying n by 20%
if the result is < 10 then m = 10
if the result is > 100 then m = 100
Sigma represented by Sigma
Specification Limits
Upper Spec. Limit represented by USL
Lowerer Spec.Limit represented by LSL
Fixed specification limits must be outside fixed control limits and the target. They reflect a shutdown scenario or a high probability that a real process or product problem exists that must be corrected immediately. They are defined via product and process research. All lines have the process capability to run within specifications with a margin that allows for control charts to provide their intended benefit of early warning. A Cr of < .75 and Tz of < .5 is preferred to allow early warning. avoid overadjustment and reactive operation. Specifications should not be calculated based on lead line capability. This will be a dilution of the quality system in terms of real meaning to the business.
Std Dev  mr represented by Smr
The standard deviation of the Moving Range Average.
Std Dev  pop represented by Spop
The measurement of variability around the average
Take each individual data point and calculate the deviation of that point from the average, square the deviation (multiply it by itself), add up all the results, divide the total by one less than the number of points, then take the square root of the result.
Sum represented by Sum
tcalc
Tests whether the Average of two populations are different.
Target represented by TGT
The target should reflect the optimum place to average the process relative to product and process research. The process should have the capability to average a target. If not, the 3, 5 and 7 point rules cannot be used without creating overadjustment. Each lines' capability may require a unique target in order to use 3, 5 and 7 point control rules for certain variables. The target can be fixed, blank or continuously calculated.
Target Deviation represented by TDev
In the statistics of QW 5 it is the separation between the process average and the Target value of the variable. The value shown is in units of measure of the variable and can be positive or negative, depending on whether the process average is above or below target.
TDev = Avg  TGT
where TGT = the target value for the variable
Targeting represented by Tz
In QW 5 this is determined by dividing the Target Deviation by the Standard Deviation
This produces a number that measures how well the process is centered on target in standard deviations. A good process should be less than 0.5 away from target (can be plus or minus). A good Target Z does not necessarily mean the process is always in specification.
If Cr .5 then Tz is calculated depending on the type of spec. limits and calculated Average.
If TGT and both spec. limits are fixed the Avg is compared against Tgt +/ 4.2% of the spec. range.
If TGT and only one spec. limits are fixed the Avg is compared against Tgt +/ 8.4% of Tgt to spec. range.
If AVG is within these limits then Tz = 0.
If AVG is greater than these limits then Tz = +1.
If AVG is less than these limits then Tz = 1.
Upper Capability Limit represented by Cpu
(USL  AVG) / )/(3*SD MR)
Upper Performance Limit represented by Ppu
(USL  AVG) / )/(3*SD Pop)
Upper Process Capability (+3S) represented by Avg +3S
Upper Process Capability (+4S) represented by Avg +4S
Upper Spec Limit represented by USL
Upper Warning Limit represented by UWL
A term that describes the size of the process variability relative to the size of the specification range. It does not consider where the process is centered so a good value for capability ratio does not mean that all the values are within specification.
When both specifications are fixed Quality Window calculates CR as