We manufacture materials of various types and hence target thickness. This is a continuous process, and material is cut to specified lengths (often over 10, 000 meters) after production. To control the process during production, we take regular measurements of the thickness (Which is the key variable we want to control) throughout production and the machine automatically compensates. The data shows that the processes are very capable of making the material to required thickness, with CP and CPK of 4 or over. However I suspect that there is something that changes in the properties of the material after production which effects the thickness and want to take random samples to check. As these tests would be done by many different people from different locations, and as I suspect the number of samples from each material type would need to be quite high in order to accurately compare the means of the sample and process distributions, I thought of a different approach. My hypothesis is that if I take a number of random samples for the different material types, of say just a meter length, and measure the average thickness of the samples and compare them to the target value, I should see an equal number of thicknesses above and below the target thickness. So using Binomial probability I can work out that there is a very high probability of finding between 30 and 70 measurements over the specified thickness for a sample size of 100. (appx 0.999) So when I find that over 90 random samples are above the target thickness, I conclude that the sample thicknesses are very likely to be different from the thicknesses measured during the process. Is this a valid conclusion?