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In observational studies, the probability of selection of sampling units is not always equal. The recorded observations are biased in this scenario. The unweighted distributions in such situations are not useful until the inclusion probability of each item is same. The theory of weighted distributions offers a unifying approach for these types of conditions because it considers the adjustment bias. Failure to comply with such adjustment may lead to inappropriate results. In this article, an efficient mentoring scheme (Weighted-TBE chart) for time between events (TBE) using weighted exponential distribution has been proposed based on weighted variance (WV) method. A comparison has been established between CC based on weighted and unweighted probability distributions. The performance measure ARL has been calculated using Monte Carlo simulations. The Weighted-TBE chart has provided least values of ARL in the presence of unwanted process variations and proved to be more effective than the existing scheme. Further the proposed control chart has been applied to time between failures data to show its practical applicability.