Introduction to Y=f(X) Model

SigmaXL Version 5 is a powerful but easy to use Excel Add-In that will enable you to Measure, Analyze and Control your service, transactional, and manufacturing processes.  This is the perfect tool for Six Sigma® Green Belts, Quality and Business Professionals, Engineers, and Managers.

SigmaXL will help you in your problem solving and process improvement efforts by enabling you to easily slice and dice your data, quickly separating the “vital few” factors from the “trivial many”.  This tool will also help you to identify and validate root causes and sources of variation, which then helps to ensure that you develop permanent corrective actions and/or improvements.

The Y=f(X) Model

SigmaXL utilizes the “Y=f(X)” model in its dialog boxes.  Y denotes a key process output metric; X denotes a key process input metric.  This process is shown pictorially as:

The mathematical expression Y = f(X) denotes that the variable Y is a function of X.   Y represents the key process output metric(s), X denotes the key process input metric(s). Another way to view this is that Y is the effect of interest, and X is the cause. Examples of Y are Yield, Customer Satisfaction, and Order to Delivery Time.  Examples of X are Raw Material Type, Responsiveness to Calls, and Location.  The key is to figure out which X’s from among many possible are the key X’s and to what extent do they impact the Y’s of interest.  Solutions and improvements then focus on those key X’s.

Data Types: Continuous Versus Discrete

X and Y metrics can each be continuous or discrete.   A continuous measure will have readings on a continuous scale where a mid-point has meaning.  For example, in a customer satisfaction survey using a 1 to 5 score, the value 3.5 has meaning.  Other examples of continuous measures include cycle time, thickness, and weight.  A discrete measure is categorical in nature.  If we have Customer Types 1, 2, and 3, customer type 1.5 has no meaning.  Other examples of discrete measures include defect counts and number of customer complaints.

It is possible to have various combinations of discrete/continuous X’s and discrete/continuous Y’s.   Some examples are given below:

Examples of Discrete X and Discrete Y

• X = Customer Type, Y = Number of Complaints
  
   
• X = Product Type, Y = Number of Defects
  
   
• X = Day Shift vs. Night Shift, Y = Proportion of Defective Units

Examples of Discrete X and Continuous Y

• X = Customer Type, Y = Customer Satisfaction (1-5)
  
   
• X = Before Improvement vs. After Improvement, Y = Customer Satisfaction (1-5)
  
   
• X = Location, Y = Order to Delivery Time

Examples of Continuous X and Discrete Y

• X = Responsiveness to Calls (1-5), Y = Number of Complaints

• X = Process Temperature, Y = Number of Defects

Examples of Continuous X and Continuous Y

• X = Responsiveness to Calls (1-5), Y = Customer Satisfaction (1-5)

• X = Amount of Loan ($), Y = Cycle Time (Loan Application to Approval)

Note that in SigmaXL, a discrete X can be text or numeric, but a continuous X must be numeric.  Y’s must be numeric. If Y is discrete, count data will be required.  If the data of interest is discrete text, it should be referenced as X1 and SigmaXL will automatically search through the text data to obtain a count (see Pareto and EZ-Pivot tools).