The filed of nonparametric function estimation has broadened its appeal in recent years with an array of new tools for statistical analysis. In particular, theoretical and applied research on the filed of wavelets has had noticeable influence on statistical topics such as survival function estimation, nonparametric regression, nonparametric density estimation and many other related topics. Let be a stationary sequence of random variables with survival function . A wavelet linear survival function based on is proposed as an estimator for . We establish the rate of convergence for introduced estimator. Also strong consistency and pointwise as well as uniform of are discussed. These results are useful in the study of kernel-type density and failure rate estimators of the unknown density and failure rate function. Some preliminaries of the linear wavelet estimator of a survival function is given in section 2 and section 3 provides its asymptotic properties.

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