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How do I use the Equation Builder and Table function?
Article Details

Last Updated
6th of November, 2018

Applies to
WinSPC 7.2, WinSPC 8.0, WinSPC 8.1, WinSPC 8.2, WinSPC 8.3, WinSPC 9.0

The Equation Builder is WinSPC's tool for creating equations. Equations are sometimes used to calculate values, limits and targets for a variable, and even can be used in user-defined tests and triggers.

Displaying the Equation Builder

You can use the Equation Builder to develop an equation for any of the following… 

  • URL, USL, Target, LSL, LRL – Open the Properties window for the variable that you would like to build the equation for.  Click on the Advance button.  Select the Equation radio button for the limit or target and click the Equation Builder icon beside that button. The Equation Builder icon consists simply of three dots. The Equation Builder icon consists simply of three dots […].
  • Calculate Variables - Open the Properties window for the variable that you would like to build the equation for.  Click on the Advance button.  Select the Settings tab.  Check the Calculated checkbox and then click the Equation button.
  • Sample Level Test - In the Administrator window, double-click on a User-Defined sample level test. When this is done, the name given to the dialog box that appears is Sample Level Test Setup. Other than this name, this dialog box is identical to the Equation Builder.
  • Trigger Setup - - In the Administrator window, double-click the Control Test Template and select a test in the left pane and click the green plus sign [+] near the upper right of the dialog box. When this is done, the name given to the dialog box that appears is Sample Level Test Setup. Other than this name, this dialog box is identical to the Equation Builder.  The following triggers have the equation builder option to choose from : Log, E-Mail, Message Box, Serial Message, File, Poke DDE Item, Set OLE Auto Property, and Write OPC Item.  After you have made one of the above selections, click on the Insert Equation… button.

Building an Equationequation_builder_main.jpg

  1. In the Equation Builder (see Figure 1), from the Functions, Operators, Statistics and Variables lists, double-click the function, operator, statistic or variable you want to appear first in the equation. This copies the function, operator, statistic or variable to the right of Result = in the Calculation Text area. If preferred, you may drag-and-drop a list item to the Calculation Text area or enter the equation using your keyboard. If you enter the equation using your keyboard, notice that, as the characters you type match list items, those items become highlighted. Once only one highlighted item remains, pressing the [Space Bar] auto-fills the remaining characters of that item into your equation.
  2. Double-click other functions, operators, statistics and variables as appropriate in the order in which you want them to appear in the equation.
  3. If desired, create an interpolation table by completing the Creating and using a Look-Up table procedure below.
  4. Click the OK.

Creating and using a Look-Up table

A look-up table is a table used to match an input value with a standard set Equation Builder Tableof predefined values.

  1. In the Equation Builder that is displayed, click the Table button (see Figure 2).
  2. In the Table Editor that is displayed, single-click the first cell in the A value of column and enter a value that, upon collection, will be replaced by a pre-defined value.
  3. Single-click the first cell of the Results in column and enter a value that which the variable value is to be replaced.
  4. Repeat the preceding two steps for other and pre-defined values as desired. Notice that, as you do, a curve is displayed and updated in the right half of the Table Editor.  If, at any point, you want to edit a previously entered value, single-click the cell and enter the new value. If, at any point, you want to delete an input value and its corresponding predefined value, single-click either value, and click the Delete button in the lower left corner.  If, at any point, you want to edit a previously entered value, single-click the cell and enter the new value. If, at any point, you want to delete an input value and its corresponding predefined value, single-click either value and click the Delete button in the lower left corner.
  5. Click the OK. The Table Editor closes and the value pairs you entered in the table are copied to the Calculation Text pane of the Equation Builder, the first item of the pair being the variable value and the second being the pre-defined value.
  6. Double-click on the function, from the Functions list, that you want to use with the look-up table. The applicable options are:     
  • Lookup: When a variable value is collected or calculated during Data Collection, this function scans the values in the extrapolation table's A value of column for that value. If a match is found, it returns the matching pre-defined value. If a match isn't found, it returns 0 (zero).
  • LookupNearest: This function works similarly to the Lookup function bEquation Table close up viewut returns the value nearest to the input value if a matching value isn't found.
  • LinearInterpolate: This method uses the intercept of straight lines between points defined in the Table Editor. Points beyond the start and end points will be in a straight line.
  • CubicInterpolate: This method use the intercept of a smooth curve (cubic spine interpolation) between points defined in the Table Editor. Points beyond the start and end points will be in a straight line.
  • IsExtrapolated: Returns 1 (True) if the result was extrapolated from the table.  It will return 0 (False) if it was not extrapolated from the table (Value was in the table).
  • IsInTable: Returns 1 (True) if the value is in the table, else it returns 0 (False) if it is not in the table.
  1. Double-click the opening parenthesis “(” from the Operators list. Alternately the opening parenthesis can be entered from the keyboard.
  2. Double-click the name of the variable, from the Variables list, to which the interpolation will be applied.
  3. Double-click the closing parenthesis “)” from the Operators list. Alternately the closing parenthesis can be entered from the keyboard.
  1. Click the OK button to exit the Equation Builder.

Understanding the Equation Builder Statistics

FUNCTIONS LIST:

The mathematical functions that can be selected and used in an equation.  The following table lists and explains the available functions.

Function

Explanation

Abs

Absolute value of a variable.

ACos

Arc Cosine

ASin

Arc Sine

ATan

Arc Tangent

Cos

Cosine

CubicInterpolate

Creates a smooth curve between points defined in the Interpolation Table Editor.  Points extrapolated beyond the start and end points will be in a straight line.

Do

Conditional branching  Do While…..

Else

Conditional branching  If… Then… Else

End

Halts execution of calculation.

Exp

Exponent.

False

Logical operator

If

Condition operator  If…Then…Else…Endif

IsExtrapolated

Returns a value of 1 (True) if a value is extrapolated from data in an Interpolation Table, otherwise it returns a value 0 (False).

IsInTable

Returns a value of 1 (True) if value is contained in an Interpolation Table, otherwise it returns a value 0 (False).

Let

Assigns a variable.

LinearInterpolate

Creates a straight line between points defined in the Interpolation Table Editor.  Points extrapolated beyond the start and end points will be in a straight line.

Ln

Natural logarithm (base e) of x.

Log

Logarithm (base 10) of x.

Lookup

Looks up the value at a specified location within a table.

LookupNearest

Checks a table to see if the value is listed.  If not, it then extrapolates a value based on the last two values at the appropriate end of the table.

Mod

MOD returns the remainder when the first parameter is divided by the second parameter.

Pi

Mathematical constant = 3.1415926...

Result

Define the result of the calculation.

Sign

Returns –1 for numbers less than 0, 0 for 0, and 1 for numbers greater than 0.

Sin

Trig function Sine

Table

Creates a table containing the listed data

Tan

Trig function Tangent.

Then

Condition operator.  If…Then…Else…Endif

True

Logical operator.

Violation

Defines the terms of the Test.

Wend

Conditional operator  Do while….. Wend



OPERATORS LIST:

The mathematical operators that can be selected and used in an equation.  The following table lists and explains the available operators.

Operator

Explanation

-

Subtraction.

(

Opening parenthesis.

)

Closing parenthesis.

*

Multiplication.

.

Must be followed by a stat name (i.e. x.mean).

.Bar

Used to find the average value of a stat (i.e.  x.R.Bar).

Previous[]

Used to find the value of a stat of a previous subgroup (i.e. Previous[2].R = R from 2 subgroups back).

.Product

Used to find the value of a stat of an associated variable (i.e. x.Product.Mean {where x is a characteristic}).

/

Division.

And

Logical operator.

Not

Logical operator.

Or

Logical operator.

[

Opening bracket.

]

Closing bracket.

^

Exponential (to the power of)

|

Alternate for absolute value (i.e. abs(x) or |x|).

+

Addition.

<

Less Than.

<=

Less Than Or Equal To.

<>

Not Equal To.

=

Equal To.

>

Greater Than.

>=

Greater Than Or Equal To.

 

 

 

 

STATISTICS LIST:  

The SPC-related statistics that can be selected and used in an equation.  The following table lists and explains the available statistics.

Statistics

Explanation

Avg

Average of all of the individual values.

Cm

Machine capability 

Cp

Process Capability

Cpk

Process Capability Index

Cpkm

Process Capability Index (Adjusting)

Cpl

Process Capability Index Lower

Cpm

Process Capability (Adjusting)

Cpu

Process Capability Index Upper

Cr

Process Capability ratio

CuSum

Cumulative Sum Slope

Diff

Difference between X and Target for subgroup size of 1 for short run statistics

DiffMR

Moving Range of the Diff statistic and depends on the SubRangeSize for short run stats

Diff-bar

Difference between XBar and Target for subgroup size of greater than 1 for short run statistics

Diff-barR

Range of the Diff bar statistic for short run statistics

EWMA

Exponentially Weighted Moving Average

EWMS

Exponentially Weighted Mean Square

EWMV  

Exponentially Weighted Moving Variance

EWRMS

Exponentially Weighted Root Mean Square

IndW

W statistic for individuals

IndWStar

WStar statistic for individuals

Kurtosis

Peakedness of the probability distribution

Lambda

The exponential weighting factor used by all of the exponentially weighted charts as set in Variable Setup

LCL

Lower Control Limit

LotSize

Fixed Lot Size setting for an attribute

LRL

Lower Reasonable Limit

LSL

Lower Specification Limit

Max

Maximum value in a subgroup

Mean

Average of the samples in the current subgroup

Median

Middle value

Min

Minimum value in a subgroup

MR

Moving Range

Mu

Population Mean

NumSigma

s  value set in the Variable Setup   (Default = 3)

Pm

Machine Performance

Pp

Process Performance

Ppk

Process Performance Index

Ppkm

Process Performance Index (Adjusting)

Ppl

Process Performance Index Lower

Ppm

Process Performance (Adjusting)

Ppu

Process Performance Index Upper

Pr

Process Ratio

PriCL

Primary Chart Center Line

PriLCL

Primary Chart Lower Control Limit

PriUCL

Primary Chart Upper Control Limit

PZI

[ Average - Lower Spec Limit ] / Standard Deviation in a Subgroup

PZMin

The minimum between PZl or Pzu

PZu

[ Upper Spec Limit - Average ] / Standard Deviation in a Subgroup

R

Range in a subgroup

S

Standard Deviation in a subgroup

SecCL

Secondary Chart Center Line

SecLCL

Secondary Chart Lower Control Limit

SecUCL

Secondary Chart Upper Control Limit

Sigma

Process variability based on a control chart

Skew

Skewness - measure of the asymmetry of the probability distribution

SpecType

Specification Type in Variable Setup  0=Bilateral, 1=Unilateral Upper, 2=Unilateral Lower

SSquared

S2 - Squared deviations around the mean 

StationSubGroupNumber

Sub-group Number for data collection station

StdDev

Standard Deviation

SubGroupSize

Sub-group Size

SubRangeSize

Sub-range Size

SystemSubGroupNumber

Sub-group Number in database

Target

Nominal value

UCL

Upper control limit.

URL

Upper reasonable limit.

USL

Upper specification limit.

W

Range divided by Sigma

WStar

Range divided by R Bar

Z

Z score (or standard normal distribution) 

ZI

Z distribution Lower

ZMin

Z distribution Minimum

ZStar

Z distribution Star

ZStar-bar

Z distribution Star-bar

Zu

Z distribution Upper

Z-bar

Z distribution Average

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