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Quick reference
Y=F(x)
Lean Six Sigma projects strive to characterize project performance through the creation of a process formula. This formula allows the team to predict and optimize process performance.
When to use
The Y = F(x) formula is developed during the first three phases of a DMAIC project and optimized during the final two.
Instructions
To improve a process it is very helpful to understand how it works and what it does. The Y=F(x) formula is the Lean Six Sigma shorthand for this approach.
“Y” is the process output. It could be quantity, quality, feature performance or any other attribute that is important to the customers and stakeholders. They identify what the “Y” should be and will often set targets for the “Y” performance. The “Y” is normally established as part of the Define phase activities.
The “x” in the equation represents the process inputs and controls. These are typically identified as the process map or value stream map is created and are both discovered and measured during the Measure phase of the project.
The “F” in the equation represents the functional combination of all the “x” inputs so as to achieve the “Y” output. This is determined both from the process map/value stream map and from analyzing data collected during the Measure phase and analyzed in the Analyze phase. The first three phases of the DMAIC build the formula and then analyze it to determine if the current process is able to achieve the desired “Y” output.
Based upon the analysis of the formula, the process is either redesigned with a different “F” and possibly different “x” factors, or the process is tuned and tweaked to get the desired performance from the existing process. This is occurring during the Improve phase.
Finally, when the new or improved process is put in place during the Control phase, a control plan is established that will allow the process operators to achieve and maintain the desired “Y” performance level. The operators can accurately predict the process performance given any set of “x” factors as inputs and controls.
Hints & tips
- You are seldom able to develop an absolutely perfect formula. However, if it is close it will still work well for process control.
- Once the formula is discovered, target values and tolerances can be set for all process parameters and inputs through simulation testing rather then expensive testing with actual products or systems.
- 00:04 Hi, this is Ray Sheen.
- 00:06 Well, we can't avoid some math if we are going to do Lean Six Sigma projects.
- 00:11 Let's start with a discussion about the fundamental process formula
- 00:14 that's used throughout the DMAIC process.
- 00:19 In a Lean Six Sigma project, you're likely to hear and
- 00:21 see the phrase Y equals a function of x.
- 00:23 Within Lean Six Sigma, this is a formula that represents or
- 00:27 models the process performance.
- 00:30 In fact, the Lean Six Sigma project attempts to determine exactly
- 00:33 how this formula works so that the process can be optimized.
- 00:37 Let's look at each of the terms in the formula.
- 00:39 The first is the Y which represents the outputs from the process.
- 00:44 Now, you can make the case that a process actually has several formulas and
- 00:48 several Ys.
- 00:49 There could be one for how many items are being produced in the process or
- 00:53 how well the items perform.
- 00:55 There could be a Y for the process time or the process quality
- 00:59 A phrase often used at the beginning of a Lean Six Sigma project is the Big Y.
- 01:04 This is the most important of those categories of the Y, and
- 01:07 is often related to the primary justification for doing the project.
- 01:12 Another element of the formula is the x.
- 01:14 This represents all the inputs and controls on the process.
- 01:18 These are the items that the process designers, operators, or
- 01:21 supervisors can control, and thereby affect the resulting Y.
- 01:26 These can usually be identified by examining the process map or
- 01:29 the value stream map.
- 01:31 And then, finally, there's the f.
- 01:33 This represents the function.
- 01:35 Or another way of saying it is this describes how
- 01:38 all the x factors are combined so as to give us the Y output.
- 01:43 If I understand the f function and I control the x factors,
- 01:47 I can predict accurately and control the Y output.
- 01:52 And this is why we want to understand this formula.
- 01:55 Y equals f of x is a mathematical description of the real world process.
- 02:00 In your Lean Six Sigma project, you seek to discover this formula.
- 02:04 Once it is known, you'll have a full and complete understanding of the process.
- 02:08 You'll know what would happen when an input is out of tolerance, or
- 02:11 a process control is setting correctly.
- 02:14 You can actually predict the process performance that allows the process
- 02:17 operators to control the output of the process to meet specific customer or
- 02:22 business demands.
- 02:23 That also allows the process designer to tune the process in such a way that
- 02:27 it is less susceptible to common problems or issues.
- 02:31 Knowing the formula allows the process designer to calibrate the process and
- 02:35 set the area of normal operation in the zone where there's a minimum of
- 02:40 process variation and waste.
- 02:42 Let's look at how we work with this
- 02:44 formula throughout a Lean Six Sigma project.
- 02:47 In the Define phase, the customers and stakeholders determine which
- 02:50 Y is most important, and will often set targets for the Y performance.
- 02:55 During the measure phase, the team collects data about both the Y and
- 02:59 the various xs.
- 03:00 They need to gather enough data to allow the team to move to the next phase.
- 03:05 In the analyze phase, the team works with the data from the Ys and
- 03:09 the Xs to discover the f, the function.
- 03:12 The goal of this phase is to be able to determine with a high degree of accuracy
- 03:16 the Y equals f(x) formula for the current process.
- 03:21 On to the Approve phase.
- 03:23 Now, based upon this formula, the team can either tweak and tune the current process
- 03:28 for the best performance, or they may need to make a major redesign to add some new
- 03:33 inputs or remove some existing inputs until they have a new formula that
- 03:37 will be able to consistently deliver the desired Y performance.
- 03:42 In the Control phase, the new process with the new formula is implemented, and
- 03:46 the organizations is trained and provided with the tools to manage the x factors
- 03:51 in order to achieve the desired Y output.
- 03:56 Y = F(x) is the mathematical model for the real world process.
- 04:02 Once we understand that model, we can officially manage the process for success.
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