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Lean Six Sigma projects strive to characterize project performance through the creation of a process formula. This formula allows the team to determine controllable factors and predict and optimize process performance.

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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 understanding. 

“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. These 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 the formula 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 and 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 than expensive testing with actual products or systems.
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  • 00:04 Hi, this is Ray Sheen.
  • 00:05 Well, we can't avoid some math if we're going to do Lean Six Sigma projects.
  • 00:10 Let's start with a discussion about the fundamental process formula that's used
  • 00:14 throughout, the DMAIC process.
  • 00:16 Throughout a Lean Six Sigma project, you're likely to hear and
  • 00:21 see the first Phrase, Y=F(x).
  • 00:24 Within Lean Six Sigma, this formula represents or
  • 00:27 models the process performance.
  • 00:29 In fact, the Lean Six Sigma project attempts to determine exactly how
  • 00:34 this formula works so that the process can be optimized.
  • 00:38 Let's look at each of the terms in the formula.
  • 00:40 The first is the Y, which represents the output from the process.
  • 00:44 Now you could make the case that a process actually has several formulas and
  • 00:49 several Y's.
  • 00:49 There could be one for how many items are produced in the process, or
  • 00:53 how well the items perform.
  • 00:55 There could be a Y for process timing or for process quality.
  • 01:00 A phrase often used at the beginning of a Lean Six Sigma project is the Y.
  • 01:05 This is the most important of those categories of the Y's and
  • 01:09 is often related to the primary justification for doing the project.
  • 01:14 Another element of the formula is x, this represents all the inputs and
  • 01:18 controls on the process.
  • 01:20 These are the items that the process designer, operator, or
  • 01:24 supervisor can control and thereby affect the resulting Y.
  • 01:28 These can usually be identified by examining the process map or
  • 01:32 value stream map.
  • 01:33 And finally, there is the F.
  • 01:36 This represents the function or another way of saying it is that this describes
  • 01:41 how all the x factors are combined so that they can give us the Y output.
  • 01:46 If I understand the F function and I control the x factors,
  • 01:51 I can predict and therefore control the Y output.
  • 01:55 And that is why we want to understand this formula.
  • 01:58 I can control the x inputs such as material, processes, equipment,
  • 02:02 the process operators, the process work instructions, and possibly other factors.
  • 02:08 All those are combined in the process represented by the box labeled F.
  • 02:12 The result is the Y output, which should meet the customer requirements CTQs.
  • 02:18 Incidentally, this type of flow is a characteristic of all processes.
  • 02:23 They take inputs and convert them to outputs.
  • 02:27 When you understand the formula,
  • 02:28 you can accurately predict the process performance.
  • 02:31 That allows a process operator to control the output of the process to meet
  • 02:36 the customer and business demands.
  • 02:39 That also allows the process designer to tune the process in such a way that it's
  • 02:44 less susceptible to common problems or issues.
  • 02:47 Knowing the formula allows the process designer to calibrate the process and
  • 02:52 set its area of normal operation in a zone where there is
  • 02:56 a minimum of process variation and waste.
  • 02:58 Let's look at how we worked out with the formula throughout
  • 03:02 the Lean Six Sigma project.
  • 03:03 In the define phase, the customer and stakeholders determine which
  • 03:09 Y is most important and will often set the target value for the Y performance.
  • 03:14 During the measure phase, the team collects data about both the Y and
  • 03:19 the various x's.
  • 03:20 They need to gather enough data to allow the team to move to the next phase.
  • 03:25 In the analyze phase, the team works with the data from the Y's and
  • 03:30 x's to discover the function, the F.
  • 03:32 The goal of this phase is to determine with a high degree of
  • 03:37 accuracy the Y=F(x) formula for the current process.
  • 03:42 On to the improve phase.
  • 03:43 Now, based upon this formula, the team can either tweak and tune the current
  • 03:49 formula for best performance, or they may need to make a major redesign.
  • 03:54 They might need to add some inputs, remove some inputs, or
  • 03:57 change the way the various x's are integrated in order to create a new
  • 04:02 formula that will be able to consistently deliver the desired Y performance.
  • 04:06 In the control phase, the new process with new formula is implemented and
  • 04:12 the organization is trained and provided with the tools to manage
  • 04:17 the x factors in order to achieve the desired Y output.
  • 04:21 Y = F(x) is the mathematical model for the real-world process.
  • 04:27 Once we understand that model, we can efficiently manage the process for
  • 04:31 success.

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