iSixSigma

How to Explain and Understand Process Capability

Have you tried to explain the concept of process capability to someone who then looks at you like you have two heads? Try using the following analogy to explain the subject more easily.

Driving in a Construction Area

Imagine you are driving on a highway that is undergoing construction. The width of your vehicle – and because you are a successful Six Sigma practitioner, you have many vehicles available to you – is the variability of your process (i.e., the ± 3 sigma from the mean in a normal distribution). The lines defining your driving lane are your specification limits.

Monday

On this day you are driving a motorcycle. You are greeted by one narrow lane with modular concrete barriers on both sides. Driving in the middle of your lane you have plenty of room on either side. You can even wander from side to side and still have room without getting too close to the barriers.

Tuesday

On Tuesday, you take your compact car. This time you do not have as much room between the barriers – only a couple of feet on either side of the vehicle. This is not a problem, but you do have to be a bit more careful of going into and beyond the barriers or, in process capability speak, out of specification.

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Wednesday 

Now the fun begins. On Wednesday you hop into an 18-wheeler for the same trip. This time you have hardly any room on either side of your vehicle. If you do not stay centered in your lane you run the risk of causing damage to you and your vehicle. Would you try to go the speed limit through these barriers or would you slow down? In process speak, if you are filling your tolerance zone with process variation even when your process is centered, might it also be a good idea to slow your process down?

Thursday

Just when you are feeling better about getting through Wednesday’s drive, you are asked to drive the same 18-wheeler, but this time you will be towing a manufactured home behind you! You are extremely nervous now – not only do you have almost no room on either side of your vehicle but you also must tow something that takes up more room than the entire driving lane. You are outside the lane (out of specification) before you start to drive. It’s clear now why the 18-wheeler will be accompanied by a vehicle with warning signs and lights on it – its job is not only to warn oncoming traffic, but also to help identify potential hazardous situations (like the barriers). Today you have to find an alternate route. Consider the warning vehicle to be a company’s quality department. It is looking out for both you and your customer.

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Friday

You take the day off to recover from all the stress of this week’s driving.

Process Potential – Cp

What you have experienced is varying degrees of capability, ranging from good capability (the motorcycle with room to roam inside the lane) to poor capability (18-wheeler towing a manufactured home taking up more room than is available).

Assume that the modular concrete barriers around you are 10 feet wide. The vehicles are average widths:

Vehicle TypeSpecification
Motorcycle3 feet
Compact car6 feet
18-wheeler9.5 feet
Manufactured home14 feet

All the vehicles are running straight down through the lane – your process is centered on nominal (the target value). This is equivalent to what is typically called Cp – your process potential – calculated as the width of your specification (the vehicle) divided by your variability (the barrier). Using the values previously noted, the vehicle capabilities are:

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Vehicle TypeSpecificationCapability
Motorcycle3 feet3.33
Compact car6 feet1.67
18-wheeler9.5 feet1.05
Manufactured home14 feet0.71

Which vehicle would you prefer to drive? The one with the highest capability – the motorcycle.

Process Performance – Cpk

Now consider a variation. In this example, you are running your vehicle (or process) off center, thereby getting closer to the barrier (specification limit) on one side. As you approach the barrier, your opportunity for success is lowered. This is your Cpk – process performance – the distance from the center of your vehicle to the closest barrier, divided by the distance from the center of your vehicle to the edge of the vehicle closest to that same barrier. The reason why you only use the closest side is that this is the only one in danger of being damaged.

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In this situation a motorcycle running 3 feet away from the barrier would have a capability of 2.0 while the compact car would have a capability of 1.0. You do not want to be that close – you may be scraping the paint off the side of your car. In a production environment, you are at risk of sending defective product to your customer.

With the 18-wheeler you do not have any wiggle room; the manufactured home would be ruined if you attempted to go through the barriers – intentionally or accidentally. If your process has a Cp of less than 1, even if your process is centered, you will make bad product. That leaves only two options:

  1. Move out the barriers – that is, widen the specification limits. Not many customers are willing to widen the specification limits; they are what you agreed to initially.
  2. Reduce your variation so that your process fits between the existing barriers. The manufactured home industry has figured out how to get around this dilemma – they ship the homes in sections, literally cutting their variation in half.
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Now you should be able to explain process capability to anyone who is new to the concept. And remember to center your processes, reduce your variation and increase your process capabilities.

Centered and Off-centered Performance

Centered and Off-centered Performance


This article was originally published in Quality Progress.

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Comments 9

  1. Chris Seider

    I’ve used similar examples when teaching process capability. This was well written in entertaining story style.

    However, I have a real problem with two statements.

    First, don’t get these guys judging Cp without looking at Cpk also. Take the example of a motorcycle driving in the same lane going in the opposite direction. The motorcycle I have described still has the same Cp as your motorcycle from Monday but is entirely out of specification (when taking into the driving rules of the road). Cp gives the process owner an idea of potential but doesn’t imply anything about what’s actually IN THE PROCESS which is why we need to look at Cpk also and graphical representations.

    Also, the statement of why to use Cpk is because we can only get damaged on the closest side implies you can’t get defects on the other side. I’m sorry but you have to look at the other side. You CAN be making no defects but often you will be depending on how much variation is in the process. I always tell my students to look at a histogram with the specs shown on it if they don’t have good statistical software like Minitab which gives them the Cp and Cpk.

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  2. Brooktrout007

    Good analogy, but I think use confused what the specification and variability are before your calculations. You wrote:

    All the vehicles are running straight down through the lane – your process is centered on nominal (the target value). This is equivalent to what is typically called Cp – your process potential – calculated as the width of your specification (the vehicle) divided by your variability (the barrier).

    Should that not be “the width of your specification (the barrier) divided by your variability (the vehicle)”?

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  3. Jon Otto

    You are correct. The specification is the barrier (10 feet) / Vehicle Process (14 feet) = .71 Cp.

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  4. Praveen

    I guess in the example, it should be movinf off-center by 2 Feet, and not 3 Feet. Please check, as only then the Cpk comes out to be 2.

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  5. kicab

    John, I’ve seen variations of this explanation (e.g., my clients’ Six Sigma materials). These “explanations” only illustrate graphically and analogously the formulas–not the meanings. It’s as if you “explained” Centigrade by telling me the formula to convert from Fahrenheit but never told me it was a temperature metric.

    All capability indices are just probabilities of meeting specifications. This is never said. IMO, it’s a significant omission.

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  6. John EVelyn

    John Evelyn • It’s a very nice first step, but I respectfully suggest maybe not a place to leave the customer. One consideration is that certainty (the fixed width of a truck) is not the same as probability or variance (how likely is it that I will be that “wide”). Process Capability means that no matter how wide you are most of the time, you’ll make it sometimes … perhaps after many, many tries.

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  7. Hoda El Shibiny

    Good analogy. I voice brook’s opinion to start with defining what is Process Specification and What is Process capability. Thank you for Sharing

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  8. Maninder

    the distance from the center of your vehicle to the closest barrier, divided by the distance from the center of your vehicle to the edge of the vehicle closest to that same barrier.

    In this situation a motorcycle running 3 feet away from the barrier would have a capability of 2.0 while the compact car would have a capability of 1.0.

    Please explain this with calculation.

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