Is Cpk a good measure of capability? There are several shortcomings of Cpk

[Tim Folkerts]

Looking back at various posts about capability indices, I note there are several shortcomings for cpk.

• There is no provision for asymmetric tolerance limits. For example, if the specs are 100 +5/-1, the best cpk is obtained by centering on 102, not 100. But this is clearly not what the customer wants.
  
• cpk = 0 occurs whenever the mean is equal to the spec limit – no matter what the spread in data. Presumably, less spread would be better in reality, but the cpk doesn’t change.
  
• The whole process is predicated on a “go/no-go” mentality, rather than a Taguchi-type “closer is better” mentality. A set of data tightly clustered just inside the spec limits will generate a good cpk, but all of the parts will be on the verge of being out of spec. A set of data clustered just outside the spec limits will work just about as well, but will have a terrible (negative) cpk.
  
• For non-normal data, some advocate going ahead with the calculations with no concern for the distribution. Others advocate transforming/manipulating the data into something closer to normal behavior. Which to choose?
  

Does anyone else care about these difficulties? Is there anything else I left out?


And then, is there any value in looking at a different capability index to address some of these issues, or is cpk so firmly ingrained that a system that offers some small (or even moderate) improvements is a waste of effort?

Tim F

 

[Darius]

Excelent post Tim

Does anyone else care about these difficulties? Is there anything else I left out?

I think that there is something else.

Wrong specs and the famous value of 1.33, 1.66, or whatever else that some guys think can achive no matter the reality of the specs. Not all specs are customer specs, but internal (specially with attributes like "taste", "smell"), wich are set by the company according to bibliographic references extrapolated to levels that can't be detected by the customers (if low is good nothing is better).

 

[Steve Prevette]

My answer is the same as over in the ASQ Discussion Boards, I don't do CpK, and I recommend to anybody who doesn't "have to", don't do it. Pay attention to the SPC chart itself. Plot the specification limits on the SPC chart as a reference, and you can visually see what is going on. Cpk, as a single number, can give you a false sense of security versus what the control chart can tell you in the same instance.

 

[Bill Pflanz]

Process capability calculations have been around since at least the 1980's. Does anyone know the history of Cpk and where it was first used? I am no bigger fan of Cpk than Steve but it is a commonly accepted quality statistic. It is not uncommon for customers to require Cpk information but has anyone ever asked what they use the information for?

Bill Pflanz

 

[Bev D]

not sure where Cpk originated (I have it here somewhere!) but my vague recollections are that it came from Ford - at least that's my first introduction to it. I distrusted it then and I despise it now...that I know what bad decisions, actions and behaviors it has driven. Steve is right: how can a single number describe varaition? I truly believe that the Cpk index was 'invented' by someone who wa too lazy - or really didn't care - to plot the data and think about the data.

 

[Bill Pflanz]

Bev,

My recollection is that Motorola and GE were using Cpk in the early 1980's. I googled process capability and Ford to do some research on the subject and it appears that Ford was using it and pushed for it to be in the QS9000 requirements.

In reading over some of the published internet articles, Cpk was meant to be an easy to understand calculation and a single number to explain the process rather than using control charts. With all of the threads on calculating and interpreting Cpk, the calculated number has become more important than what is really happening in the process. They may have created an easy to report calculation but have reduced it to such a level that it no longer represents the original theory or intent.

When something like this happens, I always attribute it to "hacks teaching hacks". There is something to be said about learning from the masters.

Bill Pflanz

 

[Tim Folkerts]

Steve,

We seem to have an electronic echo going here, with sets of posts and replies in different venues. Hopefully you, me, and Bill aren't getting to much of a sense of deja vue.

I agree that looking at a single number gives a limited view. That is one of the eternal challenges of statistics. The more you summarize, the less you know about the original data, but the simpler it is to state and compare (and to report to the boss and/or customer who may not have a good head for numbers). The challenge is to choose the appropriate level of summarization that is simple enough but still complete enough.

For example, you can summarize 100 data points with one value - the mean. Sometimes that tells you enough about the data for your needs. Other times, you might want to know a bit more - perhaps the st dev, or the range, or the skewness, or ....

So one challenge is to decide how many numbers to use to summarize the data sufficiently for your needs.

The second challenge is to decide which numbers to use for the summary. Instead of mean, we could report the median. In both cases we have a one-number summary, but the two numbers tell you slightly different things.

Your main point seems to be that any one-number summary is insufficient to adequately describe capability. Point well taken.

My original point was (assuming that you want or need to give a one-number summary) is Cpk the best choice? I would argue that even given this somewhat artificial limitation of a one-number summary, Cpk is not the best choice.

Tim F.

 

[Steve Prevette]

Your main point seems to be that any one-number summary is insufficient to adequately describe capability. Point well taken.

My original point was (assuming that you want or need to give a one-number summary) is Cpk the best choice? I would argue that even given this somewhat artificial limitation of a one-number summary, Cpk is not the best choice.

Tim F.

Dr. Deming often stated - "It's so simple, just plot the dots". The chart is the visualization, and one number will never replace a chart.

 

[Darius]

it's a shame missing a good thread.
IMO Only the post Tim post add some knowledge, As far as I know I can not send a control chart with 1000 points (to say a number) to the general manager or in the case of 40 control charts. Agree that control charts show even some behabuir that the histogram don't shows, but as Tim said it's necesary to obtain some indicators.

I tested many capability and performance index, I am not agree the use of performace for "non stability of the process", why?, because the performance indicators are afected by outliers too much, and if the standard deviation estimate for control limits is good for control limits even when "non stable process", why are not good for an capability-performance index.

I like Taguchi loss function (not the Taguchi loss index or cpm), but I must add to the calculus the use of non parametrical, like median and a percentile estimate of deviation. The non parametrics work good even for non normal conditions and the Taguchi loss function doesn't has a magical target as 1.33 for cpm.

 

[The Taz!]

Hey gang. . . any Cr fans here? That is the index that Process/Manufacturing Engineering should be most interested in. After tat is as low as possible, adjust to a desired target. No one index tells the whole story. . . like Neither Juran. Deming, Crosby, or Shanin had the whole picture nailed. As Marc says, "One size does not fit all"