Reliability of an Attribute Inspection based on Historical Data

D

dhardiman

#1
Hi,
First up thanks in advance to anyone who spends any time helping me out with this.
I have an attribute inspection on a small scale production line that has successfully detected 3 reject parts out of a total of 250 parts. From further testing i have been able to confirm that the remaining 247 parts were 'good' parts. Based on the above can I calculate the reliability/confidence for my inspection? In particular I am interested in what the likelihood of the inspection missing a defective part is (false negative).
I am using Minitab 16 if that is any help.
Thanks,
Dave
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
I'm not sure I understand your situation: what was your sample size?
how many of the 250 parts were inspected to find the 3 bad parts?
 
D

dhardiman

#3
Sorry i should have explained that. The test is a functional test and is completed on 100% of the parts.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
Ah.
the reliability (and confidence) you mention is usually thought of in terms of the ability of a sample to detect a certain defect rate in the population.

since you are doign 100% testing, your real concern is related to the effectiveness of the test. (false positive/false negative or in medical terms, sensitivity and specificity)

It can be more complicated than this, but the general approach is to test each unit twice and create a 2X2 table to assess the amount of disagreement. See my attachecment on this subject (among other MSA topics) here.
 
D

dhardiman

#5
Thanks Bev for the replies and the attachment. I'll spend some time going through it tonight. i think I may need to give you more information though. I have some limited experience in variable and attribute Gauge R&Rs before and my problem here is that a) the test is destructive and b)we i cannot create a defective part as we don't fully understand what is causing it. What we do know (or at least think we know) is that the functional inspection (think a worst case mechanical manipulation of the part) has picked out the defective units each time in 3 units. From our testing, any part that passes the functional test is extremely robust to testing from that point on.
In my head (and I'm sure you may be duty bound to correct me) I was thinking that it could be looked at in two ways. First we have never had a failure in a finished device that has passed all of our testing/inspection (n=247). Based on that presumably I could draw a statement on how likely/unlikely it would be to produce a defective product just on probability. Secondly, could my data be used retrospectively in the manner of the above attribute GR&R?
Sorry for the essay and thanks again for any guidance.

Dave
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#7
Sounds like the bottom line is you declared 3 bad parts, and verified none of those were false negatives.

Now you need some way of determining if any of the 247 "good" parts were false positive. That means running some or all of the parts through a known process and determine if any are declared bad.

Another approach is take some known bad parts and mix them up with some known good parts and send them through the inspection process. Then see if the the known bad parts are determined to be bad.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
so is this analagous to bending a paperclip? (without reducing the overall strangth of the part of course). you manipulate the part up to a certain 'force' level. if the part is weak enough it will 'break' in some way (such that it can't actually be assembled or used in the end product) and if it's strong enough it gets assembled and used in the end product and so far none of these passign units have 'failed' in an assembly?
 
D

dhardiman

#9
Bev,
Yes essentially that is it. The part in question contains a small rivet which is held in place by the structure of the component. In the functional test we deform the full component well past the point it will see in functional use and if the part passes this without losing the rivet we have found that it is robust in all types of other functional tests.
Steve,
We have functionally tested the 247 parts (which passed) as part of daisy chained worst case design verification testing so I am very confident that if the unit passes the test it is a functional pass for use. So I believe that the 247 units are not false positives. However going forward I will not be able to test parts but want to use the inspection as a screen that catches the defective components. i.e.can I make a statement about the ability of my inspection to identify a reject unit (despite the fact that I have only tested it with 3 defects in total) and based on a sample size of 247 'good' parts.
Again thanks again as this is clearly beyond my level of statistics :)
Dave
 
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