In the service and manufacturing industry, memory‐type control charts are extensively applied for monitoring the production process. These types of charts have the ability to efficiently detect disturbances, especially of smaller amount, in the process mean and/or dispersion. Recently, a new homogeneously weighted moving average (HWMA) chart has been proposed for efficient monitoring of smaller shifts. In this study, we have proposed a new double HWMA (DHWMA) chart to monitor the changes in the process mean. The run length profile of the proposed DHWMA chart is evaluated and compared with some existing control charts. The outcomes reveal that the DHWMA chart shows better performance over its competitor charts. The effect of non‐normality (in terms of robustness) and the estimation of the unknown parameters on the performance of the DHWMA chart are also investigated as a part of this study. Finally, a real‐life industrial application is offered to demonstrate the proposal for practical considerations.
To maintain and improve the quality of the processes, control charts play an important role for reduction of variation. To detect large shifts in the process parameters, Shewhart control charts are commonly applied but for small shifts, exponentially weighted moving averages (EWMA), cumulative sum (CUSUM), double exponentially weighted moving average (DEWMA), double CUSUM, moving average (MA), double moving average (DMA), and progressive mean (PM) control charts, are used. This study proposes double progressive mean (DPM) and optimal DPM control charts to enhance the performance of the PM chart. As the proposed DPM control charts use information sequentially, hence their performance is compared with natural competitors EWMA, CUSUM, DEWMA, double CUSUM, MA, DMA, and PM control charts. Run length and its different properties are evaluated to compare the performance of the proposed charts and counterparts. Results reveal that proposed optimal DPM outperforms the other charts. An example related to voltage on fixed capacitance level is also provided to illustrate the proposed charts.
<p>Conventional measures of location are commonly used to develop ratio estimators. However, in this article, we attempt to use some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, and mid-range of the auxiliary variable for this purpose. To enhance the efficiency of the proposed mean ratio estimators, population correlation coefficient, coefficient of variation and the linear combinations of auxiliary variable have also been exploited. The properties associated with the proposed estimators are evaluated through bias and mean square errors. We also provide an empirical study for illustration and verification.</p>
In recent times, it is common to the make use of auxiliary information to increase the precision of estimators in sample surveys. In this study, we propose some new modified linear regression type ratio estimators for estimating population mean by some non-conventional dispersion measures such as: Gini's mean difference, Downton's method and probability weighted moments with linear combination of population correlation coefficient and population coefficient of variation. Expressions for the bias and the mean squared error are derived and are compared with those of the usual ratio estimator and the existing ratio type estimators in literature. Conditions are determined for which the proposed estimators perform better than the existing estimators. Both theoretical and empirical findings show the soundness of the proposed procedure for estimation of population mean.
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