Standard Deviation - Doubt and Clarification of my Understanding

K

KCIPOH

#21
Hello NC,

Agree and I think I get a better idea on the Cp issue up to this point. Will come back to you for reference if any doubt.

Thank You and good day :)
 
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K

KCIPOH

#22
Hello Cove members,

From the Cp and Cpk formula itself, it using 6xsigma and 3xsigma for the formula denominator respectively. Since the sigma signage is referred to Population Standard Deviation, so is it we are calculating the Cp and Cpk using Population Standard Deviation? or is it just an indication where it can be refer to either Population Standard Deviation or Samples Standard Deviation, depends to the case we want to measure?

Please help :confused:
 
N

NumberCruncher

#23
Hi KCIPOH

You will almost always use the sample standard deviation.


In practice there is not much difference between the two for any reasonable sized sample. If you work out the population standard deviation and the sample standard deviation for a sample of size 50, the numbers are almost the same.

I did this for a set of 50 numbers generated by Excel.
Sample standard deviation = 0.3408
Population standard deviation = 0.3374

So both numbers are about 0.34

If you have taken a sample from your output (30 samples out of 2000 for example) you would use the sample standard deviation.

You would only use the population standard deviation when you have used the entire output of your process as the sample, in this case 2000 items.

NC
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#24
KCIPOH - This is a typical point of confusion for capability indexes. Fortunately, this question has been answered many times and at great length in this forum. If you search for "Ppk Cpk standard deviation" or "Long term capability" or other variations you will find many helpful threads on this topic.

A great place to start is this thread wich contains link to other threads:
Ppk & Cpk

My response in the above thread provides a direct answer to your question:

"So that you understand why the answer we give is the correct one we must first understand the concepts of Cpk and Ppk.

The first concept is that Cpk and Ppk formulas were originally designed for ongoing processes and was conceived as an extension of SPC. Properly designed SPC charts are constructed using a series of small samples – or subgroups – taken over time. In general, when properly designed the parts within a subgroup are created under relatively the same conditions: same raw material, same operator, same equipment, same settings, same tool/fixture/equipment condition, same environmental conditions, etc. Each subgroup is taken far enough apart that some and eventually all of these conditions change so that all variation is captured.

Within subgroup variation therefore represents short term variation. Cpk uses the within subgroup standard deviation (the average of all of the subgroup Standard deviations)

The total variation (within subgroup plus subgroup to subgroup) is the long term variation. Ppk uses the standard deviation of all of the individual values.

(It is important to note that often people use the notation of Cpk as a generic term for a process capability index. They will specify Cpk when they really mean Ppk.)

When a product – or process – is new, there is often limited variation in the various inputs. So there is no way to determine the long term performance. Short term capability can be assessed. The units are all to be created using essentially the same conditions: same raw material, same operator, same equipment, same settings, same tool/fixture/equipment condition, same environmental conditions, etc. Only the sample size is much larger than one would take for an ongoing sampling of multiple subgroups. Typically, the sample size would be from 30-100 units. In this case since there aren’t multiple subgroups the standard deviation is just the single standard deviation on the individual values. The same standard deviation formula as for Ppk. So the short capability calculation for new products looks like the Ppk formula…"
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#25
NumberCruncher has hit the nail on the head. for real capability studies it doesnt' matter wether or not you use n-1 or n for the standard deviation formula. there is far more variation in the sample data you select for the study than will be introduced by your choice of the 'population' or 'sample' standard deviation...
 
K

KCIPOH

#26
Hello NC and BevD,

Appreciate very much for your explanation, I get better now, will come back for any further clarification.

Thank You :)
 

Statistical Steven

Statistician
Staff member
Super Moderator
#27
NumberCruncher has hit the nail on the head. for real capability studies it doesnt' matter wether or not you use n-1 or n for the standard deviation formula. there is far more variation in the sample data you select for the study than will be introduced by your choice of the 'population' or 'sample' standard deviation...
Bev, maybe I am a purist, but if you KNOW the population standard deviation, then you have no need to take a sample. We sample from the population because we desire to estimate the mean and standard deviation of a population. It is SUCH a minor point, but for some reason it gets my crow.


Sorry for the diversion!:bonk:
 

Jim Wynne

Staff member
Admin
#28
Bev, maybe I am a purist, but if you KNOW the population standard deviation, then you have no need to take a sample. We sample from the population because we desire to estimate the mean and standard deviation of a population. It is SUCH a minor point, but for some reason it gets my crow.


Sorry for the diversion!:bonk:
Along similar lines, we will often hear people referring to the population standard deviation as an estimate.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#29
Bev, maybe I am a purist, but if you KNOW the population standard deviation, then you have no need to take a sample. We sample from the population because we desire to estimate the mean and standard deviation of a population. It is SUCH a minor point, but for some reason it gets my crow.


Sorry for the diversion!:bonk:
yeah - I understand the frustration, on the other hand I run into so much fretting about the little innacuracies that the big thing gets lost. The point I drive home with my students is not about knowing the population standard deviation of course, it is directed at which formula you use to estimate the population standard deviation from a sample. While the n-1 formula is considered the correct one for estimating the total from a sample, for all practical purposes it hardly matters even when used with small sample sizes. my motto is that if additional precision in the answer doesn't change the action taken - why bother? Too often improper sampling (non-random sampling from a non-homogenous process) effects the accuracy so much that the innaccuracy from the precision is lost.

Of course I always use the n-1 formula anyway since the only times I have the total population are trivial examples.
 
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