Exponentially weighted moving average (EWMA) statistic is a memory type statistic that used present and past information to estimate the population parameter. This study utilizes EWMA statistic to propose a ratio and product estimator for the surveys based on time scale. The usual ratio and product estimators consist of only current sample information, whereas the proposed estimators consist of current as well as past sample information. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. It is revealed from the results of simulation study that utilization of the past samples information excels the performance of estimator in terms of efficiency. Two real life examples are presented to demonstrate the use of proposed estimators.

Statistical process control (SPC) provides tools to monitor the production process in order to avoid losses of the producer. Literature provides many control charts to monitor moderate and small shifts in the process while sensitivity of the charts is increasing day by day due to increased efficiency. In this study, a control chart is proposed using an auxiliary variable for joint monitoring of the process mean and variance. The proposed control chart is proved efficient to minor shifts in mean and variance on the basis of average run lengths ( ) and standard deviation of run lengths ( ). An example is presented to illustrate the performance of proposed control chart.

The use of auxiliary variable is common at estimation stage in the form of ratio and product type estimators. All such estimators use the current sample information to estimate the population characteristics. In this study, we utilized the past samples information along with the current sample information in the form of hybrid exponentially weighted moving averages to construct memory type ratio and product estimators for time-based surveys. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. An extensive simulation study is conducted to examine the performance of the proposed estimators. It is revealed from the results that use of past sample information along with the current sample excels the performance of estimator in terms of efficiency. A real life example is given to demonstrate the use of proposed estimators.