This requires some thought and perhaps even an iterative approach. For us to help you we really will need to understand two things to begin with. As Steve asked, we need to understand this ‘standard value’. We also need to understand if you have any reason to believe that teh standard deviation of the test sample will be different than the historical value.
You will need to base your sample size calculation on the estimate of the standard deviation. There are formulas for this. (The sample size will be larger than one for a mean estimate…)
You will then need to PLOT the individual values against the historical data. The historical data can be plotted in time series if you have it in that form. (You should). If not you can use a sample of data produced under the current conditions as a “control”. The complicating factor here is that you will have variation in the individual values as well as variation between the averages of the process if the process is non-homogenous. Whihc is why we are typically better off with multiple independent small samples than one larger sample from a single run.
Look at the plot of data. Is the mean of the test data far enough away from the standard value that the standard deviation of the test result will guarantee that the lower tail of individual values will be above the standard value? This will help tell you if you need a second larger larger sample or a series of samples.
If you run the test and return here with the data we can help you further. I do understand that in some industries your regulatory statistician may require that you determine the sample size and receive approval of the approach before running any tests. If that is your case you can return here and provide us some of your historical data and we can provide a specific approach.
Hi Bev, thanks for your comment!
The continuous variable in question is tensile peak force (in Newtons) for a joint for a medical device. There is no upper specification however the lowest it can be is 5N. This requirement/specification comes from an ISO standard depending upon the outer diameter of the tubing.
There is no "historical data". I don't know what the mean and std dev will be. The first step would be to determine the sample size to collect data for verification.
I need to figure out what kind of hypothesis testing to apply (if any) and determine statistically valid sample size. As I mentioned in my original post, it's for verification of the design. If for N number of samples, the peak tensile force is above 5N, then we would consider the design verified.