Lot to lot sampling Issues and Resolution using Predictive Metrics

Lot to Lot Sampling Results can be Deceiving – An Alternative that Provides a Projection of the Future

Question: I am doing Lot to Lot measurement on parts where there were to be 10 pieces from each lot x 5 collection samples. Should I have taken 30 pieces from each lot for the 95% confidence level? I thought that the 50 piece sample sequentially would have given me a good confidence level, but wanted to check with you.

Response: What is desired is to have a random process sample of the future so that you can make a good non-conformance, best-estimate-statement; however, that is not possible. However, we could do something different and take a stab at making this estimate – if we do things a little different from the norm?

When a process is very good, we don’t need many samples to feel confident that the process is good. Similarly, if we have a very bad process, we don’t need many samples to feel confident that the process is bad. The close-to-process-specification situations require more samples – keeping in mind that we really want a random sample of the population of interest; i.e., the future. The random sample of the population of interest is a very important point that is often not address when people try to get the sample size that a computer program tells them that they should have.

There are two kinds of variability for your situation. One variability source is within lot, while another is between lots. The customer (maybe next assembly) of your process experiences both components of variability. In general, processes tend to experience more variability between lots than within lots; i.e., more things can change between lots than within lots. When there is more variability between lots than within lots and we have many more samples within lots than evaluated lots, we can get a very optimistic answer if we simply lump the data together. Hence, in general I prefer to have more lots and fewer samples within lots. A variance components analysis, as described in Chapter 24, Volume 3 can provide insight to evaluating/sizing the component source of process variability.

When need to remember that we typically would like to make a statement about the process from which the samples are taken. Hence, we first need to assess whether the process is predictable and then if there is no reason to believe that the process is not predictable, we can make a prediction statement.

When the time sequence of the lots is known, calculate the mean and log of the standard deviation of each lot and plot these values on an individuals chart. There will be only five values for each chart. I would rather have more but we do the best we can with what we have. If the process is predictable from this assessment, we can plot all the data on a probability plot and determine the percentage non-conformance. We could use the total variability from the variance components model described above to make an assessment, considering also if the overall mean is skewed or not from the nominal specification.

A probability plot can give you a non-conformance best-estimate. There is a way also get the confidence interval around a specification value; i.e., the 95% confidence level of the percentage expected to fail at the specification limit. This is different from simply examining the vertical distance off a normal probability plot at the specification limits – statistical programs, such as Minitab, have a procedure for doing this.

More information about metric reporting issues and resolution can be found in the article “Creation of Effective Organizational Predictive Metrics that Lead to the 3 Rs of Business“