# X-Y Matrix

The X-Y Matrix is a Six Sigma tool mostly used during the DMAIC measure phase and the DMADV measure phase to show the relationship between X and Y factors.

It may also be used to determine the objective of the FMEA (Failure Mode and Effects Analysis) study or determine the primary factors of a designed experiment like the DOE plan.

The XY Matrix table illustrates the correlation of process inputs to customer’s outputs. The table is illustrated using a group of columns and rows, with factor X (input) represented by the horizontal axis and factor Y (output) represented by the vertical axis.

This is also called the C&E Matrix or the Cause and Effect Matrix or the priority matrix. Most of the time a Process Map, which is the origin of related information, is used to rate the relation between two factors. Numerical ranking is created to identify which amongst the proposed plan is the most feasible and least expensive.

## Goal & Purposes

The objective of the XY Matrix is to numerically calculate the correlation of Y (output) which is equal to the frequency multiplied by X (input). This filters all possible scenarios and probable contributors to the problem at hand. The tool also studies and analyzes the relationship between what is being proposed in the process and what benefit the customer would get from it. The XY Matrix allows the group to determine areas of development and process gaps.

There are many purposes of the XY Matrix. Since the process uses numerical ranking the most obvious use of this method is to narrow down several lists of imaginable inputs (Xs) into a more controllable one.

XY Matrix is also an effective tool if the objective is to determine the few significant variables. XY Matrix quickens the identification of the most probable solution.

For example, if the process map pointed out fifty inputs that should be inspected by the project owner. The list is very lengthy and will eat up a lot of time. So instead of evaluating all fifty inputs using random picking, team members will use the XY Matrix to identify which amongst the fifty inputs should be prioritized during evaluation.

Another use of XY Matrix is during the process of collecting data. Not all data available gives value to the study. The prioritization scheme highlights information that is vital to the study. And since the process uses generic weights, team members’ varying hypothesis about the nature of the problem is neutralized.

Any Six Sigma tool used in any form of analysis has a basic requirement of first understanding the requirement of the product’s end user. Thus, a study on VOC is also helpful. Every opportunity for improvement can be regarded as valuable; there will always be those who will be more valuable than the others. The XY Matrix utilizes an uncomplicated output/input structure that regards both the vitality of the potential outputs and the involvement of inputs to the output. Aside from considering the voice of the customer, the voice of the business should also be regarded.

The top priority in using the XY Matrix should always be the voice of the customer.

Organizations may conduct a survey or conduct a sampling study as to what the customer would like the product or service to have and what it should not include. Once these outputs (check out SIPOC as well) are identified they will be drawn into the XY Matrix table and assigned a corresponding score on each output depending on the priority factor. To make the ranking easier and simpler use the scale of one to ten with one being the factor the customer is interested in the least and ten being the most important factor for the customer.

After assigning values on every output, the key input element should then be identified. This is can be done by getting information from the process map or by asking people who are affected by the process. Ranking how strongly related the inputs are with the outputs will be done after completing the two prior steps. The ranking is done using the one to ten scale that was explained earlier.

Another tip to make the ranking simpler is to limit the assigning of weights to five classifications. Assign ten to have the most impact, seven rating to have strong impact, five to have the marginal impact, three rating if the output provides minimal impact, and one if the proposed output gives no impact at all.

After assigning the weight of each input and scale of each output, these numerical representations will be multiplied to showcase the relationship of both factors and its gravity to the process. The table should be filled out during a brainstorming activity to identify and measure every team member’s opinion. The product of both factors will then be added and percentage will be generated to determine which amongst all possible output best address the current problem. The illustration below will explain how the XY Matrix works:

X-Y Matrix Table Example

The XY Matrix table shows that Action 2 has greater probability than Action 1.

The illustration only shows two inputs which make it seem simple. In reality it is seldom that a study will only have two inputs. Most of the time, the numbers of inputs are unimaginable that you will consider the XY Matrix your new best friend.

Keep in mind that the whole tool is based on opinions, therefore it’s imperative that a cross functional group is present to aid the analysis. Opinions of team members should be objective and not subjective. Biased opinions will not bring benefit to both the organization and its consumers. It will just be a waste of time, effort, and resources.

The scale used to rate outputs may also vary depending on what the project owners want to establish. The XY Matrix is very flexible in terms of assigning weights and determining ranks. Everything will depend on what the analysis team wants to uncover. What is important is that the proposed recommendation should be a result of unbiased deliberation which is done during the brainstorming activity. Team members must always keep their mind open to all possibilities to be able to come up with favorable outcome.