Y=f(X) is a function which describes the relationship between the input variable, X and the output variable, Y.

Since Y is expressed as a function X, Y is therefore dependent on X. For this reason, Y is also known as the dependent variable while X is known as the independent variable.

In process improvement context, the following operational definitions would apply:

Terms |
Operational Definitions |

Y |
Response, effect, outcome or results of a process |

X |
Input(s), cause(s) or factor(s) required to run a process |

f |
Process which transforms the inputs (X) into desired outcome (Y) |

Table 1.0: Operational Definitions of Y=f(x)

There can be more than one X or factor which contribute to Y. In such circumstances, the Y=f(X) will be modified to the following equation below:

Where n is the number of factors involved.

For example, if Y is the Employee Competency Rating, then Xs would be factors which affect Y, such as Results of Competency Based Training (CBT), Number of Non-Conformances Recorded and Number of Excellence Award Nomination Received from Senior Management.

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