A procedure ts discussed for interval estimation of the mean O of a correlated binary (0, 1) sequence The proposed method can be applied to sunulation data that are not intrinsically bmary m nature The method assumes that the sequence ts strictly stauonary and that a particular stnng of m bmary digits is a recurrent event m the sequence, where m _> 1 is unknown Of the 2 m choices for the possible recurrent events, the strmgs of all zeros and of all ones are exammed For each m = l, 2,. the sequence is demarcated by entrance to the recurrent event.The subsequences between the demarcation points thus form mdependent epochs by assumption Classical techniques then yield variance estimates for the number of ones and zeros m the epoch as well as an estimate of the covanance of the ones and zeros.A quadratic equation m O is solved to obtain an mterval estimate.Each string of all ones or all zeros examined yields a 1 -ct confidence mterval The intervals are intersected to obtain shorter mtervals with confidence greater than 1 -2c~ Since each m = 1, 2, yields an mterval, a conservative rule is developed to determme the m whose mterval is fmally used.This rule is based upon the empirical run lengths in the binary sequence.The procedure is then apphed to interval estunation of the waitmg time dlstnbution m a simulation of the M/M/I queue with activity level 0.9.For O = 0.l and 0.5 the proposed method worked well For O = 0.9 results showed some degradauon.An error analysis led to a set of recommendations for keepmg performance m practice close to the desired theoretical levels An appendLx describes algorithms for computing the crmcal quantmes upon which the proposed method rehes