# Calculating Capability of a process when data is skewed in the upper range

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#### Kenwatch

I will start first by thanking everybody who spends their time here trying to solve issues or answer questions. I come here often to find answers to my questions and I have to recognize that this is one of the best sites I could find.
This time, I have an issue where I need your expertize.
I have a process where I collect torque values on a regularly basis (every 2 hours, on a daily basis). I have a value of the torque of 20Nm +/-5Nm. The subject of torque are nuts installed with an air torque gun. This air torque gun gets worn in time and the torque capability decreases in time.
In order for me to get the best out of this gun, I adjust the torque value at the very top of the range and I can use it until it reaches the bottom of the range. If I try to center it from the beginning, the life span is half.
My question is: what would be the correct way to calculate the Cp and Cpk for this process.
I have a colleague who proposes to use an "Upper Cp" and a "Lower Cp" to determine if my data is still OK. I find this weird and I do not think it is the right thing to do. Would you be able to give me some advice?
Thank you,

D

#### Darius

I have a colleague who proposes to use an "Upper Cp" and a "Lower Cp" to determine if my data is still OK. I find this weird and I do not think it is the right thing to do. Would you be able to give me some advice?
Thank you,
Weir indeed, a big NO, could be the answer, if as the text of the topic the issue is skewness, the common way is to use non parametric capability indexes or to transform (box, johnson, etc).

This air torque gun gets worn in time and the torque capability decreases in time. In order for me to get the best out of this gun, I adjust the torque value at the very top of the range and I can use it until it reaches the bottom of the range. If I try to center it from the beginning, the life span is half.
If this is the case, the topic should be sort of "capability indexes for process target that change with worn machinery". I wouldn't use transformations nor non parametric CI's. INHO the way is to calculate a value at a given time using regression analysis (to say at the end of the life span - a standarized value-) and calculate the Cp or Cpk at such "condition". Donald Wheeler put something like that (with SPC) in one of his site's articles, I readed it 10 years ago but it was something about sales and to show that there was not a change on them.

D

#### dickgent

Moving Range Average sounds right to me. Search for Moving Range Average Control Charts. Anyone Else?

all Quality Problems are Communication Problems...

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
This is a classis tool wear situation. none of the traditional approaches are useful.

For calculating a Cpk value the most straightforward way is to treat the distribution as uniform and simply divide the range of observed values by the tolerance. no fancy statistics or modeling necessary. first of all there is no real 'tail' to this distribution so need to 'predict what may be out there' using some statistical model. Secondly even if there were a model it wouldn't include the categorical defects related to not torquing, broken bolts/nuts, etc.

There is a statistical model for the uniform distribution Ppk calculation and I have attached that.

For trending/SPC:
Wheeler's use of regression is OK. the article was published in 1999 in teh free magazine Quality. I have attached it and another article below
You can check out Dr. Wheeler's current offerings at www.spcpress.com

You may find Bob Doering's approach useful. not statistical but it WORKS.

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#### bobdoering

Trusted Information Resource
I would totally avoid the trend chart approach. It doesn't matter to me who wrote about it. It skips the main, significant variation (that which is causing the trend - see total variation equation) and goes to lower level variations (generally measurement error, not process variation). I recommend charting that looks at the actual effect of the trend and reacts to it first!

I prefer not to use the terms Pp and Ppk for a uniform distribution, since they are truly for normal distributions. Also, Ppk is specifically designed to determine of the mean is centered, which is always the case in the uniform distribution. Using Ppu and Ppl alone does not determine centering of the mean, just distance from the spec - which is an entirely different question, not related to the intent of Ppk. Just because you can calculate it doesn't mean it has any value. Besides, for a uniform distribution they are the same. Not only that, the mean has no meaning in a uniform distribution, only the endpoints. A better calculation of capability is (USL-LSL)/(UCL-LCL), where the control limits are the values the process is adjusted between.

My approach is statistical, just different statistics from the Shewhart chart. That is because two very specific statistical limitations of the Shewhart charts are not met with tool wear or drift: randomness and independence. That is why they are not slightly erroneous, but entirely wrong for such applications. In fact, I have data that shows attempting to use X-bar/R or IMR charts for tool wear shows the exact opposite of the true process condition! That not a good tool.

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