The mean residual life (MRL) is used in analyzing life time data for reliability engineering, survival analysis and other related applications. Consider X as a continuous nonnegative random variable describing duration of lifetime. If X has a survival function S(t) = P(X > t) at age t and a finite mean μ, then the MRL is defined as for t such that S(t) > 0. M(0) = μ, and since μ is finite, M(t) < ∞ (Ref. 1). The problem of estimating MRL based on a simple random sample is subjected to extensive studies. The article estimates MRL for ranked set sampling (RSS). This sampling scheme is adopted when measuring sample units is costly, time consuming or destructive. The alternative method used here is to rank them even when the sample size is small. In RSS, instead of measuring, the samples are ranked and the sample with rank 1 is selected for actual measurement. Again, a sample of the same size is drawn and ranked, and the sample with rank 2 is chosen for actual measurement. This continued until a unit with rank k is selected from a sample of size k is selected for actual measurement. The process is repeated m times to get a sample of size n = mk. Ranking is done based on judgement, and the ranking process is called perfect if the process of ranking is error-free. Detailed information about RSS and its applications is available in Wolfe (Ref. 2).
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