Abstract: he equations for confidence limit curves of a normal distribution are established. The formulas for confidence limits of percentiles and percentages and tolerance limits of a normal distribution are given by means of the noncentral t-distribution. The one-sided confidence limits and two-sided confidence intervals of percentiles and percentages can be obtained,and the one-sided tolerance limits and two-sided tolerance intervals of a normal distribution may be cal- culated by these formulas.They are applicable to the complete,the incomplete and the zero-fail ure data.Amethod of combining sample means or sample variances is also presented to make full use of previous data and reduce the number of specimens.The formulas are simple and con- venient for application in engineering.

Key words: normal density functions, confidence limits, reliability analysis