From: Stan Hilliard
Date: 02 Dec 1999
Time: 00:14:40
Greetings,
Here are some ideas for sampling plans for process control and product acceptance.
I assume that your data is measured variables data like thickness, strength, etc.? If so, I think that a sampling plan for the mean of the variable(s) would work for end-of-roll samples having three, five, or more crossweb measurements.
Operating strategy: Since the sample is not taken randomly within the web, any changes to operating conditions could be made just prior to ending the roll. Then pull the film back to before the change. This will provide a sample that represents the "steady" conditions before the change - internal to the roll.
To develop a sampling plan for the mean based on end-of-roll samples, you need a "known" downweb standard deviation. This is to take into account the within-roll variability. You can estimate this downweb standard deviation by calculating the standard deviation of differences of end-of-roll averages of adjacent rolls from a sequence of rolls. (Each data point in the calculation of the standard deviation is a difference: [xbar1-xbar2]).
You can use the same end-of-roll data for process control and product acceptance. However, you will probably want to have different decision limits for those two purposes.
The process plan should be a targeted (two-sided) plan. The product acceptance plan would have wider limits. This way, adjustments can be made while accepting the product. Combining a one-sided lower limit plan with a one-sided upper limit plan produces the wider limits. I recommend using alpha=0.05 and beta=0.05 for both the process and product plans. The software program TP414 designs both of these types of plan. See these pages:
www.samplingplans.com/programtp414.htm
www.samplingplans.com/outputvariablesmean.htm
www.samplingplans.com/modern3.htm
An additional sampling plan may be needed to establish limits for crossweb variability. A plan for the crossweb range (max-min) should work for this. Program TP414 will generate a plan for the range based on an alpha risk of 0.05 (5%).
Sincerely, Stan Hilliard