# Capability Studies - Fewest Number of Parts for a Capability Study

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#### ivo

For my traineeship, I have to improve a production process. I have done an FMEA and now I want to do a capability study. But at school I learned that the least amount of products you should produce (to test) is 50.
But the products that I have to produce are about 13 meters long and 100 kg. Is there a way to reduce the number of products? Please let me know..........

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#### Mike525

ivo:

I'm not a statisticion, but I believe the fewest number of parts one can use for a capability study, and still be statistically correct, is 31 - has something to do with the distribution under a normal curve based on the Standard Normal (z) Table and Sample (t) Table. Two good books to reference are "Introduction to Statistical Quality Control" 2nd ed. by Douglas Montgomery, and "Understanding Statistical Process Control" 2nd ed., by Donald Wheeler and David Chambers. Hope this helps.

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#### Qualiman

ivo:

As a normal rule you cannot make a capability study unless you have already demonstrated the stability of your process, and you need at least 30 data if you use average lectures and more than 100 for individual moving range charts.
However,(I declare : I am not an expert in this field) you can run some short time period (or preliminary)studies to have an idea of your process capability using let us say.. 7 lectures, but in this case you must close your gap and instead of using 3 sigma you have to use 4, I think to "compensate" of using few points.

What other folks think ?

Qualiman

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#### Batman

One should always plan the attack before going into the field. If one is charged with improving a process, one would plan the attack, which would include the "after" sampling, along with the comparison to the "before" stuff.

That said, in this instance, based on the description of the product there are few parts made per day, them how about just adding the new data onto the old in a run chart of some sort. I assume that there was historical data that suggested the need for improvement, so take some "after" parts (seperate enough from the "before" parts - maybe a "purge" of the process) and add the sample data to a run chart of the prior data - Average and moving range, for example. If the large size is an indication of being able to run only a few per hour or day, then I think only a few could be necessary. The improvement (or lack thereof) should be obvious. IF there is an improvement, continue to run more parts, enough to see expected variation over some time, then calculate capability.

I think the first step is to determine if the change was a real improvement.

#### Marc

##### Fully vaccinated are you?
ivo said:
For my traineeship, I have to improve a production process. I have done an FMEA and now I want to do a capability study. But at school I learned that the least amount of products you should produce (to test) is 50.
But the products that I have to produce are about 13 meters long and 100 kg. Is there a way to reduce the number of products? Please let me know..........
Can anyone clarify the minimum number of parts required for a capability study and the reasoning behind the number?

Anyone know where Mike525 might have gotten the number 31?

#### Jim Wynne

Marc said:
Can anyone clarify the minimum number of parts required for a capability study and the reasoning behind the number?

Anyone know where Mike525 might have gotten the number 31?

Generally speaking, in a normally distributed population, the sample and population standard deviations should be nearly identical after ~30 pieces. Generally. There are some problems (among others) with the idea of so-called 30-piece capability studies:
• If the sampling isn't really random (i.e., each individual has an equal chance of being selected each time), all bets are off.
• Unless the chronological order of production is preserved in the samples, an important and oft-overlookes component of capability study is lost.

J

#### jrubio

Here is what I think, if I am wrong I will be pleased to know it.

-Ppk the procces is cronic none stable. (Minimum 100 parts)
-Cpk the process is stable. (MSA third edition page 7)

---------------------------------

-Preliminary.

Short term.

According to MSA Do not included the effect of people, raw material, method, machine, gages, enviroment).

For new process or revised proccess

3-5 parts > 20 subgroup = 100 parts (According to Ford Design Institute. Page 5 Control Process Course)

and According to PPAP Thied Edition (Sorry but I am not in Automobile Arena).

Need to produce a minimum of 300 parts produced minimum 1 hour to 8 hours.( Page 2) for these 300 parts need to select (according to PPAP thierd Editiion Page 6) Minimum 25 subgrops with total amount of 100 readings of a significant production batch. These samples could be changed to long term if Customer request.

Long term.

According to PPAP

included the effect of people, raw material, method, machine, gages, enviroment). Minimum 100 parts splited during some change in our process.

Therefore with that info I consider that minimum 100 parts.

Therefore 100 parts is the number minimum to calculate the capability.

#### Jim Wynne

jrubio said:
Therefore 100 parts is the number minimum to calculate the capability.

You are correct with regard to AIAG requirements, but I think the question pertains to a statistical justification for a minimum number.

#### Miner

##### Forum Moderator
Marc said:
Can anyone clarify the minimum number of parts required for a capability study and the reasoning behind the number?

Anyone know where Mike525 might have gotten the number 31?

In the early 80's the Big 3 specified 30 as the minimum sample size. This was probably based on the fact that the confidence intervals about the mean tighten rapidly as you approach n=30, then become asymptotic as n increases.

In the mid 80's the big three increased the minimum sample size to 50, and ultimately to 100. At this point it becomes less of a matter of the width of the confidence interval and more a matter of verifying a stable process and incorporating long term variation into the study.

J

#### jrubio

In my opinion 5 parts (But no source available).

Minimum 3, to obtain average and sigma

And 5 parts to know if the curve is normal.

Which is the number for pre-production control.
If you start a machine if these 5 parts (Short Term) have a capability less than 1.65 the machine must be stopped.

I used to take 5 parts in order to calculate the PPk index, and when the index become Stable and minimum more than 100 parts.

therefore every 5 parts I calculated the ppk.

ppk1,ppk2... to ppk20. I in ppk20 the process is stable I used to pass to Cpk.

(Before I calculated the cpk aggregating all the 100 points (Short Term)).