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Variation leads to uncertainty in process performance which requires extra management and buffers elsewhere in the business environment. One of the primary goals of a Lean Six Sigma project is to identify sources of variation in process performance and eliminating or reducing those sources of variation.

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Quick reference

Variation

Variation leads to uncertainty in process performance which requires extra management and buffers elsewhere in the business environment. One of the primary goals of a Lean Six Sigma project is to identify sources of variation in process performance and eliminating or reducing those sources of variation.

When to use

All processes have variation. Every Lean Six Sigma project should be seeking to identify sources of variation and reduce or eliminate those sources. This is one of the fundamental purposes of a project.

Instructions

Since all processes have variation, an objective of Lean Six Sigma projects is to identify the variation and its sources so that these can be reduced or eliminated. Understanding the variation is part of understanding process stability. A process is considered stable if the variation is predictable. The process managers can then allow for the variation and optimize the overall system relative to the levels of variation in each of the process steps.

One of the techniques used to understand the impact of variation is the Taguchi Loss Function. Dr. Taguchi challenged the common approach to quality that was being used in the 1980s, which was that if the process result was within the allowable specification limits, the quality was good, and if it was outside the limits, the quality was bad. Dr. Taguchi believed that whenever the process performance was missing the ideal target, that losses in the system occurred. Those losses increased rapidly the further the deviation was from ideal process performance.

He created an equation to show this relationship:

Loss = k (y-m)2

  • Where Loss is the system loss of both actual failures and errors and the additional costs to the system that are needed to accommodate the uncertainty from large deviations
  • k is a factor that represents the cost structure of the system
  • y is the actual process output
  • m is the target process output

As you can see, this is the equation for a parabola. As the process output deviates from the target, the loss increases. This occurs regardless of where the upper and lower specification limits are located.

Dr. Taguchi would plot this function with the normal process output to show that if the variation was very small, there was little loss to the system, but as the variation grew, the losses grew, even if the process performance was within specification.

This illustrates the need for very little variation and demonstrates the power of the process sigma measurement. Sigma is a measure of the spread or variation within a process. Virtually all of the process output occurs between approximately minus 3 ½ sigma to plus 3 ½ sigma. The six sigma objective is to reduce the sigma value enough in order for the range from minus 6 sigma to plus 6 sigma to fit within the allowable specification limits.

Of course this has some implications. These include that the process is stable and predictable, that the process can be centered on the target value, and that the process can be controlled so that it does not drift.

Hints & tips

  • Variation is the enemy of stability. When analyzing a process, strive to identify all sources of variation – don’t assume some of them away.
  • A six sigma process can drift one or two sigma in either direction and still have virtually a 100% yield. If the sigma level is only about 3 to 3 ½, even a slight drift higher or lower will immediately start to create scrap or rework conditions.
  • Often the largest of the system losses described by Dr. Taguchi occur in downstream processes that must add inspections or design robustness to accommodate a wide range of inputs.
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  • 00:04 Hi, this is Ray Sheen, I've told you that one of the things
  • 00:08 Lean Six Sigma tries to control is process variation.
  • 00:13 Let's take a few minutes and explore why variation's such a big problem.
  • 00:18 It starts with the concept of process stability.
  • 00:22 Process stability sounds great, but
  • 00:23 the reality is that all processes have variation.
  • 00:26 In the real world,
  • 00:27 there is at least a little bit of uncertainty in everything we do.
  • 00:31 Stability depends upon whether we can tolerate this variation or not.
  • 00:35 There are ways to describe how a process is performing,
  • 00:38 that helps us understand the degree of stability or instability.
  • 00:43 A stable process is predictable, the center or
  • 00:45 average point doesn't change over time, and
  • 00:48 the actual values fall within some easily determine minimum and maximum values.
  • 00:53 Because these values are stable, they're predictable over time, and
  • 00:57 these values can be measured and empirically tested.
  • 01:00 When a process is stable,
  • 01:02 the predictable performance allows the the surrounding processes and
  • 01:05 systems to tune themselves to the level of variation in that original process.
  • 01:11 This tuning can lead to ideal or optimal process performance, and
  • 01:15 it shouldn't be a surprise that the lower the level of variability,
  • 01:18 the easier it is to tune the process for ideal performance.
  • 01:23 I'll illustrate this point using the Taguchi Loss Function.
  • 01:27 A typical view of quality requirements is that anything that
  • 01:30 is within the allowable specification limits is acceptable.
  • 01:34 But that means that a process output that is exactly centered within the limits as
  • 01:39 just as good as the output that is just barely within the limits.
  • 01:43 A good metaphor is thinking of scoring a goal in football.
  • 01:47 Whether the ball is exactly center between the left and right posts, or
  • 01:50 hits the right post and bounces through, the team gets the same number of points.
  • 01:55 Dr. Taguchi,
  • 01:57 one of the quality improvement gurus from Japan, had a different perspective.
  • 02:01 He believed that if the result deviated from the perfect,
  • 02:04 on-target condition, it reduced the efficiency of the overall system.
  • 02:09 There were several reasons for this.
  • 02:11 If the process results were close to the goal posts,
  • 02:14 they must be inspected to know if they were inside the goal or outside the goal.
  • 02:19 This adds cost to do the inspection, and slows down the process for
  • 02:23 the inspection, and sometimes the inspectors get it wrong.
  • 02:27 In addition, the rest of the system must be robust to accommodate a wider variation
  • 02:31 in the process outputs and still perform as it's expected to perform.
  • 02:36 This will usually add cost and complexity to the rest of the system.
  • 02:41 Doctor Taguchi expressed this idea with the equation below.
  • 02:44 This is a typical equation for a parabola, and
  • 02:46 you can see a visual graph of that equation on the right.
  • 02:50 The blue curved line represents the level of loss.
  • 02:53 The closer you get to the upper or
  • 02:55 lower specification limits, the greater the loss, and therefore the greater
  • 02:59 the cost to the rest of the system to accommodate that level of uncertainty.
  • 03:05 All of this is building up to the concept of Six Sigma quality,
  • 03:08 as we consider now variation and process performance.
  • 03:12 I said earlier that all processes have some inherent level of variation, and
  • 03:15 for this illustration, I'll be representing this variation using that
  • 03:19 bell-shaped curve that's in red on this slide.
  • 03:23 We know that Doctor Taguchi said that the farther the process result
  • 03:27 was from the target, the greater the loss of the system.
  • 03:30 And we can see that in these three graphs,
  • 03:32 in the first one on the left, there is very little variation.
  • 03:36 The width of the curve is much less than the range from the lower specification
  • 03:40 limit to the upper specification limit.
  • 03:42 Everything is considered good quality and there's very little of the bell shaped
  • 03:47 curve that is under Dr. Taguchi's blue loss function line.
  • 03:51 Now, look at the center graph, everything is still within specification, but
  • 03:56 now our bell shaped curve is coming right up to the edges of the allowable range.
  • 04:01 Using our earlier metaphor, we are hitting the goal posts and
  • 04:04 bouncing through the goal.
  • 04:06 Traditional quality control says that everything's acceptable, but
  • 04:09 there's a lot more of that bell shaped curve under the blue Taguchi loss line.
  • 04:15 And now when we look at the graph on the right, we see a major problem developing.
  • 04:19 Since the normal variation is wider than the allowable specification limits,
  • 04:23 we know we are actually creating some out of tolerance conditions,
  • 04:27 resulting in scrap or re-work.
  • 04:29 And we can see that there is a much larger portion of that process output that is
  • 04:33 under the loss function line, indicating more cost to the business.
  • 04:38 If we can reduce the amount of variation relative to the upper and
  • 04:41 lower specification limits, we can have a huge impact on system losses.
  • 04:46 This brings us to the term sigma, which is the Greek symbol used for
  • 04:49 standard deviation.
  • 04:51 I'll talk more about that in another module, but for our discussion right now,
  • 04:55 the sigma is a way of measuring how wide the bell shaped curve is,
  • 04:59 relative to the specification limits.
  • 05:02 Let's define Six Sigma variation, in this graph,
  • 05:06 we have a bell shaped curve for normal variation.
  • 05:09 For all intents and purposes, the curve is only about plus three and
  • 05:12 a half sigma to minus three and a half sigma wide.
  • 05:16 You can see that the fact that there is no more of the bell shaped curve
  • 05:19 visible beyond the four sigma marks on either side of the graph.
  • 05:23 Six Sigma quality control means that the sigma value is so small that the spread
  • 05:28 from the minus six sigma to the plus six sigma is still small enough to fit within
  • 05:33 the range from the lower specification to the upper specification limit.
  • 05:39 And for this to work,
  • 05:40 there are several implications, one implication is that the smaller the sigma,
  • 05:44 which is the width of the variation, the better for the process.
  • 05:48 Another implication is that the process performance must be predictable and
  • 05:51 that it's stable, not drifting or varying.
  • 05:54 And of course, that implies that by achieving Six Sigma performance,
  • 05:57 we should always be within specifications.
  • 06:01 But the process performance should be centered within the allowable range also.
  • 06:04 And one the benefits from centering is that, if the process was initially
  • 06:08 centered but then starts to drift a little bit, it won't
  • 06:11 immediately drift out of specification, which brings me to the last implication.
  • 06:16 The organization needs to apply some level of statistical process control
  • 06:20 on the output, so that they know if the process drifts or
  • 06:22 becomes unstable. Lean Six Sigma
  • 06:27 projects strive to reduce variation in order to reduce system losses.
  • 06:32 The sigma measure is an indication of how well the process is performing.

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