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#### AHartman

Hi all! I have had some college courses about SPC, control charts, statistics, etc, but haven't ever applied it in the real world. Well, I'm now tasked with developing a reduced inspection plan for one of our products. We currently do 100% inspection, and it's simply too great a drain on our resources to continue. I'm the only person in our company that comes close to a process or quality engineer, so I've got to find the solution on my own.

We've determined from customer feedback that if we ship product that is better than 90% conforming (or less than 10% non-conforming), they'll be happy. We also make less than 150 parts per day. So, I decided to try the MIL-STD-1916 and apply it to our process. I'd like to start out w/ Attribute sampling, just because it seems quicker to implement, but ultimately I'd like to use Variables sampling to set myself up for process improvements in the future. Two immediate problems came up:

1) Our data is very simple, and non-normal. Using inspection, we score our parts for roundness on a discrete scale of 1 to 5, with any parts scoring 3 or higher considered round enough to pass. Though this is a step up from our previous pass/fail inspections, it still doesn't give much information. However, this is the inspection we're stuck with for the time being as it's too difficult to get more detailed data in a quick and cost effective way. In addition, our data is not normally distributed. There are maybe 15% of parts scoring 3, about 30% scoring 4, and the remaining 55% are scored as 5. So, I'm not sure if it's even appropriate to use the MIL-STD-1916 procedures.

2) In the MIL-STD-1916 document, the Verification Level (VL) is always treated as a specification. The handbook that goes along with the standard gives the guideline that "for critical characteristics, a VL of VII is to be used". While the roundness score of our parts is indeed critical, I suspect that applying VL VII would be overkill for our 90% conforming requirement. I don't want to reject every lot simply because I'm using a too strict procedure. I can't find ANYWHERE that describes how the different VL's are calculated, or what each VL translates to in terms of a percentage of conforming parts. Also, I believe that I need to use an AQL (Acceptable Quality Level) type measurement, but did not find that in the MIL-STD-1916 document. The closest was the "k" value, which is called the acceptability criterion. And no information is presented as to how the "k" values are determined other than in reference to a specified VL. I need to be able to link it to how many conforming parts there are. The handbook provides OC, AFI, and AOQ charts, but these are still just given for each VL, and I'm not sure how to read them to get the % conforming translation.

Given all of this (and thanks to anyone who's are still reading this far into my epic post), I did some searching and found that the ANSI Z1.4 and Z1.9 standards are essentially similar to the MIL-STD-1916 standard. Also, I was able to find a few excerpted tables that seem to indicate that the ANSI standards have a very clear method of translating a desired percent conforming into an inspection test. I've not yet gotten a copy of the ANSI standards, but they seem like a better tool than the MIL-STD-1916 in this instance. The ANSI standard solves my #2 problem above, but I'm still not sure if it's kosher to apply it to a non-normal distribution.

I don't have access to MiniTab, so I can't use it's fancy tools to normalize the data, and I must confess that the few classes I've had never went beyond normal distributions other than to mention that other distributions were out there. I think that, in my understanding, the central limit theorem says that even if a population is not normally distributed, a random sample from that population will be more normal than the population itself, and that a cheap way of possibly "normalizing" the data would be average groups of sample measurements. That is, instead of 3 random samples from each of 6 machines giving n=18, I could average the samples from each machine for n=6. But, it seems to me that I would then only be saying that the original 18 samples should be accepted or rejected, not the larger lot from which they were drawn.

So, given that we've got small lot sizes to begin with, and the process is pretty heavily biased toward one end of our measurement scale, what's a good standard to use to know that we're shipping better than 90% conforming product? Can I use the Z1.4 and Z1.9 standards on non-normal distributions by using more samples and averaging? Do those ANSI standards still work pretty well for a 90% conforming requirement such that the non-normal distribution can be ignored? Is AQL the right way to conclude acceptance, or is a Lot Total Percent Defect (LTPD) measurement better?

I apologize for my almost utter lack of knowledge in this area, and hope that I'm not asking really dumb questions. As you can tell, our inspection requirements are not nearly as strict as large scale industrial production, but I'd still like to use an industry standard, both for customer satisfaction and for my own education, if possible. Our 100% inspection records clearly indicate that we're meeting or beating our 90% conforming requirement, so I'm hopeful that there's a reduced inspection process out there that can help me.

Thank any and all of you in advance for taking the time to pour over this huge post, and for any comments, advice, or suggestions you may have!

Adam Hartman

Mechanical Engineer

Zyvex Corporation

We've determined from customer feedback that if we ship product that is better than 90% conforming (or less than 10% non-conforming), they'll be happy. We also make less than 150 parts per day. So, I decided to try the MIL-STD-1916 and apply it to our process. I'd like to start out w/ Attribute sampling, just because it seems quicker to implement, but ultimately I'd like to use Variables sampling to set myself up for process improvements in the future. Two immediate problems came up:

1) Our data is very simple, and non-normal. Using inspection, we score our parts for roundness on a discrete scale of 1 to 5, with any parts scoring 3 or higher considered round enough to pass. Though this is a step up from our previous pass/fail inspections, it still doesn't give much information. However, this is the inspection we're stuck with for the time being as it's too difficult to get more detailed data in a quick and cost effective way. In addition, our data is not normally distributed. There are maybe 15% of parts scoring 3, about 30% scoring 4, and the remaining 55% are scored as 5. So, I'm not sure if it's even appropriate to use the MIL-STD-1916 procedures.

2) In the MIL-STD-1916 document, the Verification Level (VL) is always treated as a specification. The handbook that goes along with the standard gives the guideline that "for critical characteristics, a VL of VII is to be used". While the roundness score of our parts is indeed critical, I suspect that applying VL VII would be overkill for our 90% conforming requirement. I don't want to reject every lot simply because I'm using a too strict procedure. I can't find ANYWHERE that describes how the different VL's are calculated, or what each VL translates to in terms of a percentage of conforming parts. Also, I believe that I need to use an AQL (Acceptable Quality Level) type measurement, but did not find that in the MIL-STD-1916 document. The closest was the "k" value, which is called the acceptability criterion. And no information is presented as to how the "k" values are determined other than in reference to a specified VL. I need to be able to link it to how many conforming parts there are. The handbook provides OC, AFI, and AOQ charts, but these are still just given for each VL, and I'm not sure how to read them to get the % conforming translation.

Given all of this (and thanks to anyone who's are still reading this far into my epic post), I did some searching and found that the ANSI Z1.4 and Z1.9 standards are essentially similar to the MIL-STD-1916 standard. Also, I was able to find a few excerpted tables that seem to indicate that the ANSI standards have a very clear method of translating a desired percent conforming into an inspection test. I've not yet gotten a copy of the ANSI standards, but they seem like a better tool than the MIL-STD-1916 in this instance. The ANSI standard solves my #2 problem above, but I'm still not sure if it's kosher to apply it to a non-normal distribution.

I don't have access to MiniTab, so I can't use it's fancy tools to normalize the data, and I must confess that the few classes I've had never went beyond normal distributions other than to mention that other distributions were out there. I think that, in my understanding, the central limit theorem says that even if a population is not normally distributed, a random sample from that population will be more normal than the population itself, and that a cheap way of possibly "normalizing" the data would be average groups of sample measurements. That is, instead of 3 random samples from each of 6 machines giving n=18, I could average the samples from each machine for n=6. But, it seems to me that I would then only be saying that the original 18 samples should be accepted or rejected, not the larger lot from which they were drawn.

So, given that we've got small lot sizes to begin with, and the process is pretty heavily biased toward one end of our measurement scale, what's a good standard to use to know that we're shipping better than 90% conforming product? Can I use the Z1.4 and Z1.9 standards on non-normal distributions by using more samples and averaging? Do those ANSI standards still work pretty well for a 90% conforming requirement such that the non-normal distribution can be ignored? Is AQL the right way to conclude acceptance, or is a Lot Total Percent Defect (LTPD) measurement better?

I apologize for my almost utter lack of knowledge in this area, and hope that I'm not asking really dumb questions. As you can tell, our inspection requirements are not nearly as strict as large scale industrial production, but I'd still like to use an industry standard, both for customer satisfaction and for my own education, if possible. Our 100% inspection records clearly indicate that we're meeting or beating our 90% conforming requirement, so I'm hopeful that there's a reduced inspection process out there that can help me.

Thank any and all of you in advance for taking the time to pour over this huge post, and for any comments, advice, or suggestions you may have!

Adam Hartman

Mechanical Engineer

Zyvex Corporation

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