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This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple random sampling-based counterpart. Moreover, a new EWMA chart based on the mean estimator within the MS scheme is proposed. The performance of the EWMA charts, derived from both simple random sampling (SRS) and MS schemes, is evaluated using the metrics of steady-state average run-length and average number of items-to-signal. The findings underscore the superiority of the EWMA-MS chart over the EWMA-SRS chart. Additionally, as the magnitude of ranking errors escalates, the behavior of the EWMA-MS chart converges toward that of the EWMA-SRS chart. The practical implementation of the newly introduced EWMA chart is demonstrated through an illustrative example.
Abdul Haq (Fri,) studied this question.