By David Drain (auth.)
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Additional info for Statistical Methods for Industrial Process Control
For any given precision, Table 1-4 shows the sample size necessary to produce an interval with that precision about 90% of the time. Individual interval widths will vary from the predicted precision. To use the table, convert the desired precision (half the width of the confidence interval) to a number of population standard deviations. This is accomplished by dividing the desired precision by a preestimate of the population standard deviation. 12 Sample Size Determination for Confidence Interval About the Mean of a Normal Random Variable A two-sided 99% confidence interval for mean LTO thickness with 5 A precision is desired.
The curve with the highest peak is the pdf of the standard normal, and the curve with the lowest peak is the pdf of a t-distribution with two degrees of freedom. The intermediate curve is the pdf of a t-distribution with 10 degrees of freedom. See Table 1-3 for a listing of important t-percentiles. As the number of degrees of freedom approaches infinity, the t-distribution approaches the normal distribution. For this reason, Table 1-3 lists percentiles only for up to 120 degrees of freedom; the normal percentiles are a sufficient approximation for degrees of freedom greater than this.
Intelligent filtering algorithms are very helpful in excluding truly wrong measurements, but schemes that filter data on the basis of arbitrary limits (such as specification limits) hide the true nature of the popUlation. • Aggregated data (means rather than individual measurements, for example) are convenient, but raw data contain more information about the population-wherever possible, take raw data and perform any aggregation after the preliminary data examination. One of the main reasons for preliminary data examination is to detect outliers.