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Many popular neighbor designs are used in serology, agriculture, and forestry which manifest neighbor effects very much. If every treatment appears as a neighbor with other (v-2) treatments once but emerges twice with only one treatment, such designs are called Quasi Rees neighbor designs (QRNDs) in k size of circular blocks. These designs were used for counterbalancing the neighboring effects for the cases for which minimal neighbor designs cannot be constructed. In this article, various generators are constructed to obtain circular binary NDs, using cyclic shifts.

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In this paper, we propose a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart based on a mixture ratio estimator of mean using a single auxiliary variable and a single auxiliary attribute (Moeen et al., [1]). We call it as Z- HEWMA control chart. The proposed control chart performance is evaluated using outof- control-Average Run Length (ARL1). The control limits of the proposed chart is based on estimator, its mean square errors. A simulated example is used to compare the proposed Z-HEWMA, traditional/simple EWMA chart and CUSUM control chart. From this study the fact is revealed that Z-HEWMA control chart shows more efficient results as compared to traditional/simple EWMA and CUSUM control charts. The Z-HEWMA chart can be used for efficient monitoring of the production process in manufacturing industries where auxiliary information about a numerical variable and an attribute is available.

Background of the Study. Statistical models have been extensively used in modeling and forecasting the different fields of agriculture, economics, social sciences, and medical sciences. The transmission of some diseases is a serious life threat around the globe; therefore, proper assessment and modeling need time. Malaria is one of the major life-threatening diseases in Pakistan, and some death cases due to this disease have been reported during the last decade. Methodology. The data have been collected from the Ministry of Health, Rahim Yar Khan, Pakistan, from January 2011 to March 2022. Data were analyzed by applying time series models for prediction purposes. Diagnostic measures such as RMSE, MAE, and MAPE were used to choose the best forecasting model. Results and Discussion. This study aims to forecast malaria cases by choosing the best forecast model. After comparison, it was concluded that the Holt–Winter multiplicative model outperformed the ARIMA and SARIMA models, with the lowest RMSE, MAPE, and MAE compared to other models. Malaria cases in the district Rahim Yar Khan were forecasted by the Holt–Winter multiplicative model, for the month of April 2022 to January 2023. From the forecasting results, the minimum number of cases was found to be 586.75 in June 2022 and the maximum number of cases was found to be 1281.93 in October 2022 among the next ten months. Based on the results, it is paramount for the GOP (Govt. of Pakistan) to enhance the vaccination policy to erase the impacts of malaria cases to flatten the curve.