From: Bobbi
Date: 02 Dec 2003
Time: 23:17:14
In Juran's Quality Handbook, 5th Ed., it appears as Chart S in the appendix, page AII.33
The title of the chart is "Size of Sample for Arithmetic Mean When Sigma is Unknown." Within the text, Juran describes the method depicted in the chart. Basically, he states that confidence limits can be used to determine the sample size required to estimate a product characteristic within a specified precision. He gives this example: suppose it is desired to estimate the true mean life of a battery. The estimate must be within 2.0 hours of the true mean if the estimate is to be of any value. The variability is known as sigma = 10.0. A 95% confidence level is desired on the confidence statement. Two hours is the desired confidence interval half-width, so:
2.0 = [(1.96)(10)]/ [sq.rt. of n] solving for n, we get 96 pieces.
A sample of 96 batteries will provide a mean that is within 2.0 hours of the true mean (with 95% confidence). Simple, right? And Chart S is just a quick reference for these calculations. But here's my question: in a high-risk situation, such as with space craft or medical devices, you don't just pick the 2.0 hours out of the air. There must be a valid, documented justification for the 2 hour precision value. I could whip up a justification based on industry practice, but I'd feel much more comfortable if I could cite a published reference that states, for example, that the error (E) should be, say, twice the standard deviation (s), or something to that effect. Can you help?