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Glossary
This section is intended to provide a definition of terms used in QW as well as
information on the calculations and rules followed by QW 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 (non-null) are included in
calculations in QW.
- Application
- A group of related variables based on a common element, like Product size or
weight.
- Average - Represented by
- The mathematical average of all data points in a field.
 where n = number of points in the field
- Calculated Field
- A value for a variable where the number is calculated from other values. When
a field is defined as calculated (C), you must specify the equation for the
calculation as part of the field template.There are two types of calculated
variables in Quality Window: Calculated numeric or Lookup calculated text.
- Calculated PPM and Calculated % Out of Specification (C%OOL)
- This statistic uses a table to infer the theoretical %OOL. 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%OOL you need :
- the average ()
- the standard deviation (S) of the population
- the Upper Specification Limit (USL)
- the Lower Specification Limit (LSL)
- a Z-Table to find the proportion out (Pz).
Calculate  |
Calculate |
Look up  in the Z-Table |
Look up  in the Z-Table |
If < LSL then  |
If < LSL then  |
Calculate 
- Capability Clearance - represented by Cpk
- Requires two separate calculations and then you select the smaller of the two
results.
 AND 
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 perfectlycentered 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
DCp). Low Cr and high Cpk numbers are good.
- Capability Ratio - represented by Cr
- 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:
- Constant
- A fixed value used in a calculated field. For example, in the expression V8 + 16,
the constant is 16.
- Control Limits
-
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. They are
preferably symmetric. +/- 3S can be used for any chart with 98-100% confidence without
assumptions as to normality and control. Control Limits in Quality Window can be fixed,
blank or continuously calculated values. There is an Upper ControlLimit (UCL) and a Lower
Control Limit (LCL). These values are used in the program to set the values where color
changes occur in the Charts and Logsheets. In Quality Window the control limits are
relative to the target and specification limits and appear to be used to establish a
"warning track" inside the specification limits.
- Control Rules
- There are four rules typically used in Quality Window and they are highlighted in
the Summary screen as rule 1, 3, 3 and 7. As with the Control Limits, these are for
warning purposes to indicate that there is a probability of a change.
- Correlation Coefficient -R, R²
-
A statistical value that indicates the strength of a linear relationship between two
variables. A value of zero implies no relationship, a value of +1.0 implies
perfect direct relationship. A value of -1.0 implies a perfect inverse relationship.
The correlation coefficient is always between -1.0 and +1.0. Statistical significance
does not depend on the value of the correlation coefficient. The correlation coefficient
should not be used unless it is significant. The value shown on the screen is now R2 as a
percentage. This value can be used as the percent of variation that can be explained by
the relationship of the data.
Quality Window does a separate calculation known as the T-test to determine the
significance of the correlation.
Where there is a 95% confidence that the correlation is significant and |T| > 1.96 then
the correlation is highlighted on the Relationship screen.
- Failure Rate - represented by FR
- The Failure Rate is the rate at which failures occur in a certain time interval for
those devices surviving at the start of the interval.
Calculate where
| N1 = the number of failures surviving time t1 |
| N2 = the number of failures surviving time t2 |
 T = the time duration for the interval (t2 - t1) |
The Failure Rate Chart in Quality Window plots and displays these values for each of the
30 intervals (with lines connecting the points). If the curve-fit mathematical functions
over the first three plots on the Quality Window Reliability Chart, you would derive
three functions which we will describe by the classical designations:
f(t) = the probability of failing in a specific interval function
F(t) = the cumulative failure function
R(t) = the cumulative survival function
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Quality Window does not use the curve fitting method to derive FR(t)... it uses the
equation above, but understanding this alternative method provides additional
understanding to the creation and use of the reliability charts.
With these functions defined, the following equations are derived from the failure rate
equation defined above. These equations may help you better understand the mathematical
origin of these charts.
 where:
dR(t) / dt is the derivative of the cumulative survival function with respect to time.
R(t) is the integral (or area under the curve) of f(t).
Therefore
In other words, the Failure Rate Chart FR(t) is proportional to the derivative
(rate of change) of the Cumulative Failure F(t) and the Cumulative Survival R(t)
charts. The Failure Rate Chart displays the rate of change in these charts. This chart
is valuable since the rate of change can be used to infer the percentage of failures
attributable to each mode of failure (i.e. - control, design and maintenance). We can
make this inference when the chart looks like a bathtub curve, or at least half of one.
It is suggested that you have as many failures in your database as possible and have
an in-control time between failure control chart. This inference of failure mode is
valuable so that improvement teams and efforts can be more efficiently directed and
staffed.
- Green Zone
- This is the zone shown on the Control Chart, Histogram and table coding which is
colored green. It represents the GOOD or Go area. The zone is the half
the control region between the target and the control limit, on both sides of the
target. The color coding was selected to simplify the communication of the state of
control.
- Low Tz and Cr
- The report uses this term as a criteria of summary statistics. It represents the
number of variables
where:
- Maximum (Max) and Minimum (Min) Values
- The highest and lowest values for the data being used in a calculation
- Mean Time Between Events - (MTBE)
- Calculated by adding all Event Duration's and then dividing by (the total number of
events - 1).
Quality Window makes use of two different MTBE calculations, depending on how the
application is defined:
Mean Calendar Time Between Events - MCTBE = (event stop time-next event stop
time)
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The total time between all events divided by the total number of events.
In MCTBE Time Between Each Events =
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Mean Run Time Between Events - MRTBE
This is the total time between events minus Excluded Time. Quality Window has a
feature to allow you to identify Excluded Time, making MRTBE more useful to
maintenance and engineering personnel. It gives a more accurate accounting of
Events based in the actual running time of the equipment or process. Excluded Time
is the duration of time you wish to remove from the length of time between events.
This can be scheduled downtime such as weekends in five day operations or planned
maintenance.
In MRTBE Time Between Each Events = (event stop time-next event stop time) - Excluded Time
- Number (N)
- The number of non-null values found in the data selected.
- Number(#) of Defects / 100 Units
- This is a report summary statistic. It is the total number of defects that could be
expected in a sample of 100 units of product. It has been known as the Sum of the %OOL
of all variables. The Sum of %OOL can be greater than 100.
- Observed # and Observed % Out of Specification (O%OOL)
- O%OOL is the sum of the points in the white band of the Control Chart divided by the
total number of points then multiply the result by 100.
- Points
- A point is an individual value for a variable for a specific record. A point may
represent the value of a single sample or there may be several samples averaged to
create a point. The choice is designated when creating or editing a template in the
QWSETUP program.
- Record
- Each line on the Logsheet is one record. The Logsheet can contain up to 100 records
and each record can contain up to 99 variables with one value (point) per variable.
Each record has a Date and Time associated with it.
- Red Zone
- This is the zone shown on the Control Chart, Histogram and the table coding which is
colored red. It represents the STOP or out of control area. It is the
area outside the region as defined by the UCL and LCL.
- Relationship
- A variable is influenced by or has an influence on another variable other than a
calculated field. The fact that a relationship exists or possibly exists has to be
decided by the person setting up the templates. In the process of editing a field, any
known or probable relationships can be defined and then the program will examine the
validity of the relationship when the Relate command is in the Quality Window execute
program. The time to study a relationship is when one variable goes out of control ... use
the relationship to see what moved at the same time.
- Sampling
- Each template of multiple variables is created around a common base sampling plan.
Typical base common sampling plans are 1/shift, 1/day, 1/maintenance, 1/changeover,
etc. Preferably, the variables in each template have a common primary source of
variation. Important process variables that relate to product variables may be included
in the product variable template. Each variable can be individually reduced in sampling in
multiples of the base sampling plan via the "time of sample" feature: i.e.- every other
check, etc. This is done for variables as control performance: i.e.- Cr, Tz, %OOL, etc. is
improved.
Random sampling has the benefit of better representing what the consumer will see in terms
of product quality. Unfortunately, random sampling can be inefficient in the quality of
samples required to control the process.
Event based sampling (based on sources of variation and when they are most likely to occur)
can be more efficient and effective in control applications. For example,
should teams running the process at different setting be a primary source of
variation, checking 1/shift at the beginning of each shift may be as effective as 1/hour or
1/minute: particularly as the shiftly control chart would best reflect this source of
variation over time.
- Specification Limits
- There should be an upper specification limit (USL) and a lower specification limit (LCL). The values for these should come directly from the formula card, RMS, or other spec. Specifications can be fixed, blank or continuously calculated at Average +/- 4SD.
- Standard Deviation Points - Represented by S
- This is a measurement of variability around the average. The calculation for S is expressed as:
which means that we 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.
- Target
- 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 point control rules for certain variables. The target can be fixed, blank or continuously calculated.
- Target Deviation - Represented by
- In the statistics of Quality Window 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 plus or minus. On the Summary screen the target deviation is only considering the last point on
the Logsheet and what is the difference between the last point and target.
 where Tgt = the target value for the variable
The result will be positive or negative, depending on whether the process average is above or below target.
- Target Z - represented by Tgt Z or Tz
- In Quality Window, this is determined by dividing the standard deviation into the Target 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
Calculated by the expression:
You may recognize that the numerator of this expression is the expression for Target Deviation. If you divide the Target Deviation by the Standard Deviation samples you have a value for Tz. The value can be plus or minus, just as the Target Deviation is plus or minus.
- Upper and Lower Specification Limits
- 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.
- Variable / Field
- In Quality Window this is a single element of data that is to collected. It can be a weight, a pressure or a comment. A Quality Window application is made up of up to 99 variables or fields of which
Date and Time are always the first two. A field or variable is a single column on the Log screen.
- White Zone
- This is the OUT OF SPEC zone. You might think of this as white hot
- Yellow Control Bands (Warning Zones) and 3, 5 and 7 Point Rules
- They are enabled when the lines have the capability of adjusting the process average and there is a process/product need to do so. The yellow control bands visually indicate to the operators that the 3, 5 and 7 point rules are in effect. The 3, 5 and 7 control rules are also removed for distributions that, by definition, are non-normal. Charts that are not normal only due to a lack of control effort will be made to look more normal via the 3, 5 and 7 control rules.
- Yellow Zone
- This is the zone shown on the Control Chart, Histogram and table coding which is colored yellow. It represents the CAUTION area. It is the half of the control region as defined by the target and the
UCL/LCL, which is closer to the control limits than the target
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