Interval estimation for statistical control

In order to develop meaningful statistical control limits when applicable based upon the normal distribution, the mean and the standard deviation of a population must be known. In cases when an accurate approximation of the standard deviation is not known, the calculation of reasonable statistical control limits can be performed by using the Student's t-distribution. The Student's t-value for n-1 degrees of freedom (n is the sample size) and the confidence intervals that correspond to 20 and 30 (95.45% and 99.73% respectively) is used to determine control limits from a relatively small data set. The control limits with this method are obtained by multiplying the calculated standard deviation of the data set by the appropriate t-value for the specified confidence level and degrees of freedom While the t-distribution method is needed primarily for a small sample size (n <30), it approaches the normal distribution with increasing n, and hence can be used for any size sample.