From: bart.debruyn@vlm.be
Date: 10 Sep 2001
Time: 09:09:29
greetings Stan,
> I SAID -- "The fact that we receive more than 10 deliveries for each project give us enough confidence that we do not accept an average quality less than the AQL." > YOU SAID -- "I have my doubts about this. When you look at the oc curves in 2859-1 or 8422, don't you find that lots with fractions defective higher than AQL can still have a high probability of acceptance? "
> REMARK -- The oc-curves give information on the probability of accepting a single lot with a certain percentage of non-conformities. The probability of accepting all lots in a series with a minor quality is very small (multiplication law of probabilities). As we apply i.e. the switching rule to tightened inspection, we "force" the contractor to deliver an AVERAGE quality less than the AQL. You are right that the consumers risk is still enormous if within the series of lots there is one single lot with a bad quality.
> I SAID --"The operating curves indicate that there is little chance to accept a quality less than the LQ. How can we have an idea of the quality those isolated lots really have?" > YOU SAID -- "For any specific lot, the best estimate of its fraction defective is fraction defective of the sample: p'=(X defectives)/(n sample size) The lower and upper confidence limits will show the interval of plausible fraction defective in the lot. That calculation is performed for the binomial and poisson distribution by software program TP105. www.samplingplans.com/software.htm "
> REMARK -- Does the software also contain decision rules taken into account the confidence limits ??? For example: Specification indicates that fraction f within lot: f > 97% result within sample: 96% +/- 3%
> I SAID -- "The AQL with the corresponding Operating curve gives just an indication. A contractor could always try to deliver an isolated lot with more errors than twice the AQL. Do you have a suggestion for this fact ????" > YOU SAID -- "The oc curve for individual lots tells you how the sampling plan will perform -- whether the lot is one of a kind or one in a series of lots. It cannot be used to estimate the quality of a lot. This is because the oc curve can only be read in one direction. That is, if you know the fraction defective (p') of a lot, you can determine with the oc curve the probability of the lot's acceptance (Pa). You cannot read an oc curve backwards (Pa to p') to estimate the quality."
> REMARK -- To determine a convenient quality level in production a contractor too can examine the OC-curves. Because of cost-efficiency reasons, he doesn't want to have to correct too many "rejected lots" afterwards. In case he has only one lot to deliver, he could take the risk to lower his production quality. For example: He could choose the quality level that has a Pa of 70%. In a small series of 3 consecutive lots he has only 34% (0.7 X 0.7 X 0.7) chance that all lots should be accepted.
> I SAID -- "Honestly I am alarmed there is little difference in the sample size we need in function of the lot size." > YOU SAID -- "It is because the standards are based on the binomial and poisson distributions, both of which assume infinite population. Lot size doesn't effect the statistical calculations. Infinite population is another name for sampling with replacement."
> REMARK -- There is a great difference between the 2 sub-norms (ISO 2859-1 and 2859-2 B). In ISO 2859-1 there are for all AQL-values 15 different and fixed code letters (A-->H) whereas in 2859-2B for most LQ-values only 4 ranges are provided. Despite your answer this is still very difficult to understand ! for example: N=300 items;n=50 items for ISO 2859-1; for ISO 2859-2 and LQ=2%: 200 items N=9900 items;n=200 items " ": " " " : 200 items
NEW QUESTIONS > Is there a software tool to calculate the acceptance criteria for sample sizes which are not provided with ISO 2859-1 ? For example N=300;n=70 instead of n=50 > What do you think about AQL-value as maximum p' in case of 100% sampling ? We have added this rule in our specifications. > Do you offer a tool to calculate the risk in treating an isolated lot as lot in a series of lots ? I am still convinced that the AQL-value just gives an indication of the quality that will be accepted in most cases (cfr supra).