The Formula tab is used to define a calculation which will be applied to raw data. Formulas based on a single Characteristic may be applied to that Characteristic from the Formula tab in the Define Characteristic dialog box. Formulas based on two or more Characteristics may also be defined for Analyses or Work Sets (if real-time option purchased).
Note: When a formula is applied to a single Characteristic from the Define Characteristic dialog box, other properties (including specification limits (USL, LSL), data validation and alerting applied to specification limits, and short run standardization) should be entered relative to the calculated values. The statistics will be calculated and displayed relative to the calculated values. Only the Show Data option’s spreadsheet, as well as the Data Form when in add or edit mode, will display the raw values.
Formula Equation: Enter the calculation into this field using the keyboard, and/or the number and symbol pad provided. The equation must begin with an equals (=) sign.
The following operations are available in the Symbol Pad:
Addition (+)
Subtraction (-)
Multiplication (*)
Division (/)
Exponentiation (**)
The Symbol Pad also includes left bracket "(" and right bracket ")" for controlling the order of operations. The Delete (del) key deletes the rightmost entry in the Formula Equation field.
The Clear (clr) key deletes all the entries in the Formula Equation field.
Beneath the Symbol Pad is a list box of Characteristics (including previously created Formulas) in the Analysis. The Characteristics are listed by their Name, followed by an equal sign and an alphanumeric label. This label refers to their database location, and must be used in the equation. For this reason, it may be most useful to double-click on the Characteristic Name in the list box to add the Characteristic to the new Formula Equation. In so doing, the Characteristic is always added to the Equation using its database label, and is always added as the rightmost set of characters in the Equation. You can also type the database label for the Characteristic into the Equation.
Additional operators for single Characteristics include the following. For example, to calculate the square root of the data in the Length column, enter the following into the Formula Equation textbox:
=SQRT(C28)
where C28 is the database label for the Characteristic named Length:
ABS(C28): the absolute value of the quantity.
ACOS(C28): the arc cosine of the quantity (reported only for quantities between -1 and 1).
ASIN(C28): the arc sine of the quantity (reported only for quantities between -1 and 1).
ATAN(C28): the arc tangent of the quantity.
CEIL(C28): the smallest integer greater than or equal to the quantity.
COS(C28): the cosine of the quantity
COSH(C28): the hyperbolic cosine of the quantity.
DEGREES(C28): converts the quantity (in radians) to degrees (=180x/ð).
EXP(C28): e raised to the power of the quantity.
FLOOR(C28): the largest integer less than or equal to the quantity.
INT(C28): the integer portion of the quantity.
LN(C28): the natural log (base e) of the quantity.
LOG(C28): the log (base 10) of the quantity.
LOG2(C28): the log (base 2) of the quantity.
PI: the value of Pi (3.14159...)
RADIANS(C28): converts the quantity (in degrees) to radians (=ðx/180).
SIN(C28): the sine of the quantity
SINH(C28): the hyperbolic sine of the quantity
SQRT(C28): the square root of the quantity.
TAN(C28): the tangent of the quantity of the quantity.
TANH(C28): the hyperbolic tangent of the quantity
The following operators are applied to single or multiple Characteristics.
AVG: the average of two or more Characteristics (when more than one Characteristic specified) or the subgroup average (when one Characteristic specified).
COUNT: the count of the values
For example, to calculate the average of the data in the Length column and the data in the TIR column, enter the following into the Formula Equation textbox:
=AVG(C28,C29)
where C28 is the database label for the Characteristic named Length, and C29 is the database label for the Characteristic named TIR.
Notes for formulas based on multiple characteristics:
1. When the Characteristics have different subgroup sizes, the formula will be applied for each sample up to the lowest subgroup size. For instance, if the AVG function is applied to Characteristic A (with a subgroup size of three), and Characteristic B (with a subgroup size of five), then the average function will be calculated for the first three samples in each subgroup.
2. The Date, Traceability fields, and User information shown in the Data Form will correspond to those associated with the first characteristic specified in the formula.
3. When Characteristics have different number of subgroups, the formula is applied starting at the most recent subgroup for each Characteristic. For example, in the formula C = A + B, if A has 10 subgroups and B has 7 subgroups, the formula result will have 7 subgroups (i.e. the minimum number of subgroups for the Characteristics; the first three subgroups in B will not be used.
· Charts for each Characteristic included in the Formula may be quickly accessed from this tab by clicking on the characteristic’s name in the formula tab’s Data Form.
Note for users of the real-time options: If the data entry Characteristics used in the Formula all have subgroup size of one (or are attributes counts data), then the Visible field in the Define Work Set dialog box’s General tab may be used to restrict data entry to the Formula tab by hiding the raw data entry characteristics’ tabs. For an example of the output from these settings, see: Entering Multiple Characteristic Data in Formula Tabs .