"Prasad" [EMAIL PROTECTED] writes: > > I need to come up with an upper specification limit (USL) and lower > specification limit (LSL) for a new process. I need to set the limits > such that the yield through that process step is > 99.73%. Due to cost > reasons, I am only allowed to make 30 samples using this new process > and come-up with the control limits. > > USL = mean + TINV(1-0.9973,30-1)*sigma = mean+3.28*sigma > LSL = mean - TINV(1-0.9973,30-1)*sigma = mean+3.28*sigma > > mean and sigma are calculated from the 30 samples. TINV is the inverse > of a t-distribution calculated in Excel for a 2-tail distribution.
There are important distinctions between control limits, specification limits, and natural process limits. The specification limits are set by the customer or by management on behalf of the customer. What you want, I think, is a natural process limit. Your formulas are close to what you want, but you need to estimate sigma differently, through a control chart. This is typically a multiple of the average range across subgroups, or a multiple of the average moving range if there are no subgroups. Just estimating sigma from the batch of 30 will confound short term and long term variation in the process and will often give a very bad answer. If you don't already have a good book on control charts, Donald Wheeler has some excellent ones. His introductory book, Understanding Variation, is outstanding. Try reading that book and see if it answers your questions. Wheeler, D. J. (1993). Understanding Variation: The Key to Managing Chaos. Knoxville, TN, SPC Press Inc. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. The STATS web page has moved to http://www.childrens-mercy.org/stats. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
