LetX_{i,j} (1leq ileq k,1leq j leq n_i) be independent random variables and for a fixed i, X_{i,j}s, (1<=j<=n_i) be identically distributed random variables with survival function bar{F}_i={bar{F}}^{alpha_i}, where alpha_i denote the maximum and minimum of the i-th sample. This paper investigates the nonparametric confidence intervals for an arbitrary quantile of the distribution F and tolerance limits based on these statistics. Various cases have been studied and in each case, the nonparametric confidence intervals are obtained and exact expressions for the confidence coefficients of these confidence intervals are derived. A data set representing the time of successive failures of the air condition system on Boeing 720 jet aircraft is used to illustrate the results.

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