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Are you capable?

I’d like to talk a little about capabilities. Don’t worry, not about your personal capabilities, which I have no doubt are excellent. We shall talk about your processes’ capabilities. Though, I must say, some find that even more frightening. However, I have found that some concepts which appear difficult and intimidating may become simple and straightforward, if we but look at them from a slightly different, a bit more familiar and less threatening an angle.

What is process capability and why do we need to measure it? Why does it even bother us at all?

Many people think: a process is a process, so how can its capability change? It doesn’t spend all day sitting in front of the computer, nor is it concerned with proper nutrition…

The truth is, this is not exactly so, and measuring the process capability may be critical to our process quality, the amount of non-conformance, the time and effort we invest in inefficient corrective actions, the team morale and the whole profitability of our organization. So, first thing, as usual, let’s get attuned about what process capability is. Define the concept.

Illustration: process-capability

What is process capability?

Process capability is the ability of the process to produce according to the specification. In other words, it is the ability of the process at each moment to satisfy the requirements.

Hold on, but we are manufacturing the product in some predefined process. Have the engineers not set the process properly from the beginning?

That’s the thing, not always, and even when they do – it’s not as if it is set in stone. Processes, as we know, need to be controlled, simply because they are ever-changing due to various noises.

Remember the noises from the article “Noise proof“? Every noise, as we have established, appears unexpectedly, continues for unknown period of time and with unpredictable force. And every noise affects the process, and thereby – its products. It affects the two process parameters: its average and its variability.

Therefore we must measure the process capability in two situations: (1) before turning it over to mass production, to ensure that the process is able to deliver the design requirements at all; (2) periodically, during the whole time of mass production, to ensure the process capability hasn’t changed significantly (for the worse, naturally, as we don’t mind it changing for the better, as long as it is a consistent, controlled and deliberate change).

Normal distribution
Normal distribution

Process capability indices

The index to measure process capability is C­p or Cpk, where the second takes into consideration the process average, as well, and allows us to inspect process capability at each end of the tolerance limits, separately.

So how shall we measure process capability? And how do we determine when the process is well capable and when it’s not that impressive?

Well, we need to understand how well the tolerance window fits to the range of manufacturing ability. In other words, how well the familiar Gaussian bell fits into the tolerance window.

The Gaussian bell, known formally as the normal distribution curve, is defined by two parameters:

  • its average, µ, or its highest point;
  • its standard deviation, σ, which reflects its variability, or how much the results vary.

Most, or 99.74% to be precise, of the products in a normal distribution fall between 3 times the standard deviation (3σ) in each direction, which leaves but two small “tails” to each side of the bell, of 0.13% each (2,600ppm in all).

Measuring and understanding process capability

We cannot determine the process’ curve without measuring its results, or products. And tolerance window is received from the specification, which is rigidly defined from the start and does not change, as long as the product requirements do not change.

As a matter of fact, when measuring process capability, we compare this range of 3σ in each direction to the tolerance window of specification requirements: does it fit into the tolerance window, and even more importantly – how it fits into it.

To demonstrate process capability measurement, let’s look at a car in a parking lot. In the drawing you may see a car (OK, not just a car, a Porsche Cayenne) which is required to park between two lantern posts, while the posts are placed at a distance precisely equal to the car width. In this situation our whole process (3σ in each direction) fits exactly between the tolerance limits on both sides.

Process capability equals 1
כושר תהליך שווה 1

Process capability equals 1

It is rather clear that no driver in the world could ever park our Porsche without scratching or damaging it, at least on one side. Ouch, that’s a shame!

So all of you who thought that process capability = 1 was good, do you think so still? Even if that were your Porsche?

Process capability lower than 1
Process capability lower than 1

Not just whether it fits in the tolerance window, but how it fits

I said that the Cpk index takes into consideration the process average, that is we separate it into Cpk-right and Cpk-left. In the above picture our (invisible) driver is such a pro that the car ends up centered precisely between the two lanterns, thus making both right- and left- Cpk indices equal, and generally Cpk=1.

But what about the next time? It is impossible to reproduce the results exactly, therefore when the driver gets home tomorrow, the Porsche would not be centered quite as precisely.

Process Capability CPK

And then we shall find that in spite of the lanterns being placed at just the same distance, exactly equal to the car width, the slight shift of the Porsche to the left (I am looking from the driver’s point of view, of course) will make him smash the left side completely into the post, while the right side would feel very comfortable with respect to the lantern there. In other words, Cpk-right less than 1, Cpk-left greater than 1.

When shall we have no problem? When the car and some additional space to allow for natural variation of its placement during parking, will fit completely in the distance between the two posts.

In our case – either the posts are to be spaced farther away from each other, or the car should be narrower. Well, one who has a Porsche can probably afford to widen his parking lot.

The lower limit for the Cpk index for each direction is 1.33, which means the distance of to each side of the normal distribution curve fits into the tolerance window, and the non-conformance are negligible (or to be precise, 64ppm).

Process capability greater than 1
Process capability greater than 1

Illustration: process-capability
Illustration: process-capability

But how is this reflected in our processes?

Measuring process capability before turning over to mass production is critical, as it allows us to clearly see the car width with respect to the parking lot size.

What we get here is what we may expect to get during the whole mass production period! If the normal distribution curve does not fit well into the tolerance window, it means we shall have non-conformance from day one, and for as long as the process remains as it is now. We can do nothing about it! It shall be designed into the process!

Widening the posts

Can we widen our “posts” (the tolerance window)? It is defined according to the customer requirements, set into the product specifications. However, the engineers often set up the window to be much tighter than the actual customer’s requirements, and then the measurement of process capability would show us what we can expect during the manufacturing stage, leading to a more realistic setting of specification tolerance window.

Slimming the car

Can we make our bell narrower? In the long run – we can, indeed, but usually for the long run. That will require a project for process improvement. So at this specific point of time, the answer is usually – not significantly. Though, naturally, there is always a place for immediate small changes, and every design or process improvement narrows its variability to some extent.

And yes, the worse the process capability, the more realistic should expectations be.

Narrow parking

What do you mean by realistic expectations?

It means that one cannot manufacture in a process with poor capability and measure the products on a 100% quality scale with respect to the requirements. One simply cannot! It would be absurd, as the process is incapable of ever doing it!

In the car example above, this would be akin to punishing the driver every time he hits the posts, in spite of them standing too close. Can one avoid hitting them? Clearly not! Then what is the point of punishing ourselves again and again because we have failed to avoid it???

Then what are we to do? It is costing us!

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That it is! We shall still have to repair, we shall still have to “swallow” all the non-conformance, and it would cost us money, time, material, workers… But – it would have cost us the same anyway. The difference here is that we shall no longer waste resources on failed attempts to analyze and make corrective actions where the non-conformance is designed into the process in the first place.

We are to set a performance ceiling at what the process is able to do, and not punish ourselves for poor performance we should have known about from the beginning. Instead and at the same time we should invest the resources we saved in process improvement, to solve the problems and lower those unnecessary costs.

And another point: if you are a sub-contractor, and the process and the requirements were defined by your customer, then process capability measurement will clearly and without emotions show them they must carry at least some of the costs, those ensuing from same requirements. And that is no small amount of resources. This would motivate the customer to take part in finding a solution for process improvement and invest in it, to eliminate the unnecessary costs to himself.

So far about the process capability before mass production.

Process Capability in mass production

All through the mass production period we must monitor our ongoing process capability in a standard, frequent, periodical manner. We have already established that it is constantly changing, due to noises, as well as due to the improvements we introduce in design and process. It is important that all these changes are monitored, to see what happens to the process capabilities and what we can expect from it at each given time, whether it can still satisfy the requirements. This follow-up can direct us to the actions we need to take, and lower otherwise hidden costs.

So are you ready to work on your capabilities?

Process capability chart is taken from the Six Sigma Community blog.

Narrow parking picture is taken from an article on parking in Japan at nihonshock blog.

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