From 100% Inspection to No Inspection – How Many Batches to Test Post-improvement?

Brian May 30, 2012Comments Off

This topic has 6 voices, contains 8 replies, and was last updated by M. D. Colley 352 days ago.

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May 30, 2012 at 2:11 pm #182577
Brian @wiencbok Reputation - 24 Rank - Aluminum	Hi, There is a process where we have manufactured 40 batches of product over the past year, we have been performing 100% inspection on these batches, the batch fails if one or more of the containers fails the test. 15 of these previous 40 batches have failed (1,2 or 3 failing containers in each case). We have since implemented an improvement and I am trying to use a statistical test that can tell me how many batches we need to continue to 100% inspect before we can reduce the rate of inspection or eliminate inspection entirely. I have been looking at sample size for comparison tests of attribute data and fear that we may need to test a high number of batches before we can say with any great confidence that the inspection can be reduced or eliminated. Any advice would be much appreciated.
May 31, 2012 at 5:49 am #182636
Robert Butler @rbutler Reputation - 2146 Rank - Silver	If we assume that 1 failure is the same as 2 or 3 so that the problem is reduced to a simple pass fail and if we assume your sample failure rate 15/40 is an accurate estimate of the current failure rate then the number of samples you will need to state with 80% power (and alpha < .05) that you have shifted from a failure rate of 37.5% is going to depend on the reduction in the failure rate. For example if you are going from 37.5% to 30% then you are looking at 262 samples. On the other hand, if you are going from 37.5% to 10% then you are looking at 18 samples. In each case the problem is framed as follows: 37.5% is the null and the new level is 30%, 10%, etc. and the number of samples is the number of tests needed to reject the null when, in fact, the new level is 30% or 10% or whatever.
May 31, 2012 at 7:00 am #182638
Mike86	Robert, I usually enjoy your answers to questions here. I’m wondering if I understand your answer to this question. If I’m understanding Brian, he has a batch process that generates multiple containers per lot. A fail in any container is considered a fail for the batch. He doesn’t say how many containers are in a typical lot, but since he’s using a plural I’m assuming it’s more than one. Brian is also asking for when they can stop 100% container inspection. Your answer is in relation to the number of failing batches per year, which is very high at 37.5%. Certainly, as you indicate, the impact of the improvement will be easier to measure if the change has made a radical shift in the process mean. My question is on whether this answers the original question or if you were making the point that many lots and much more additional data will be needed before that question can be answered. Brian’s problem will also be made considerably worse if the number of containers per lot is high.
May 31, 2012 at 1:21 pm #182670
Brian @wiencbok Reputation - 24 Rank - Aluminum	Robert and Mike, thanks for both your responses. Mike yours is an accurate account of my current situation. The batch size of each lot is approximately 134 containers, no containers are allowed to fail the test, if one container fails the whole batch is failed. The previous failures have involved 1, 2 or maximum of 3 failing containers in the failing batch of approx 134 containers. Batches are 100 % inspected. There does not appear to be a pattern to the 15 failures in the last 40 batches. We believe that the fix we have implememted will eliminate the need for inspection however we will continue to 100% inspect each batch my question is, given that we have had a 37.5% failure rate from our last 40 batches how many batches do we need to make without failure post improvement before we can eliminate the 100% inspection or at least reduce the rate of inspection? Is thre a formula i can use to determine a sample size (i.e. number of passing batches) that will allow me to be 95 % confident in reducing or eliminating the 100% inspection?
June 1, 2012 at 6:14 am #182719
Robert Butler @rbutler Reputation - 2146 Rank - Silver	Mike, I’m sure you understood my post, however, I will have to agree it is a tad too terse to be of much value to anyone. Let’s try again. There are two separate questions in the initial OP: 1. How big a sample is needed to detect a change in a percent defective? 2. How many samples are needed before one can make a decision concerning test frequency? I sort of provided the answer to the first but, given the additional information, I don’t think the answer is of much value. While the problem is phrased in terms of batch failure the real issue is frequency of container failure. What we need to know is the percent failure of the containers. Given that you have 40 batches and that 15 of them have failed then the lowest actual percent failure would be 15 containers out of a total population of 5360 which would be a minimum failure rate of .28%. If every batch that failed had a total of 3 bad containers each then the maximum failure rate would be .84% Either way, the actual failure rate is very small and the number of containers you would need to test to even be sure that you had reduced the failure rate by 50% would be betwen about a half a year and one and a half year’s worth of production(.84 to .42 = 2604 and ,.28 to .14 = 7847). None of the above addresses the issue of reduction of sampling. I’ll have to think about this some more. Since the smallest unit for sampling (and for failure determination) is the container and not the batch the issue of sampling frequency will be driven by the probabilites of having a single failure in 134 containers.
June 1, 2012 at 6:48 am #182720
Chris Seider @cseider Reputation - 3008 Rank - Titanium	@wiencbok It sounds like you might have an MSA problem if only some containers out of the batch are out of specification. You might argue that the batches aren’t uniformly homogeneous but then how can you ever be sure the individual containers aren’t in spec without testing or HIGHLY altering your process capability. Maybe your problem is actually a lack of uniformity within the batch being split up OR your MSA needs to look how the sampling is affecting the results. Just some thoughts…
June 1, 2012 at 6:52 am #182721
MBBinWI @MBBinWI Reputation - 2593 Rank - Titanium	@wiencbok – If I understand the original request, you are looking at a sampling rate to demonstrate that there are zero defects (correct?). And once zero defects are demonstrated, then eliminate testing entirely. In the first place, unless you change the actual process such that it is impossible to make defects, you will never achieve your objective. The typical approach is to identify what the customer population defect level is acceptable and to work backwards from there by gathering the current defect production rate and with this you can design a sampling plan to ensure that you do not release more than the acceptable population defect level. But you cannot bring to zero without 100% inspection (and then, only if you’ve got a capable measurement system with redundancy). Zero is a difficult standard and needs to be applied to truly critical products/processes. Are you sure that is what is required? Or is something low, but not quite zero, acceptable? It will make a huge difference in your approach to achieving the real objective.
June 4, 2012 at 3:33 am #182800
Safak Tan Ozkan @shafak Reputation - 29 Rank - Aluminum	@wiencbok As far as I understand you already made an improvement which will eliminte the failed bathes entirely. You want to make sure that the defect rate is consumed down to zero so that you can eliminate the costly %100 inspection process. I suggest using an i-chart. You mentioned you have the data for the last 40 runs.(asuming you have minitab) set them for phase 1 stage. then set a stage for the phase 2 where the improvements are introduced to the system. perfom all tests. you should expect to see significant drop on both control limits and the mean. You can also use a P chart which is a good tool to follow your process. Looking at these charts you should be able to tell if your process is under control therefore you can start inspect on sampling or completely eliminate inspection at all. hope this helps with your question.
January 29, 2013 at 1:07 am #189134
M. D. Colley	Hi Brian I think I am experiencing what you went through last year. I have exactly the same sort of problem on a turning operation, but with much larger batches and similar to lower reject proportions. We have implemented the fix for the special cause and have now witnessed two batches without the error via 100% inspection, in addition we measure the length of the bar end, which indicates if we have produced some rejects. I wondered where you ended, what stratergy you chose to follow, have you eliminated the extra inspection entirely, and on what basis did you do this ?

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