This research article addresses an efficient separate and combined class of estimators for the population mean estimation based on stratified random sampling (StRS). The first order approximated expressions of bias and mean square error of the proposed separate and combined class of estimators are obtained. A comparative study is conducted to determine the efficiency conditions in which the suggested class of estimators outperforms the contemporary estimators. These efficiency conditions are examined through an extensive simulation study by employing a hypothetically drawn symmetrical and asymmetrical populations. The simulation results have shown that the suggested class of estimators is more effective than the other available estimators. In addition, an application of the proposed methods is also presented by examining a real data set.

A control chart is the most well-known statistical monitoring tecnique to address unfavourable process parameter (s) changes. Quality practitioners always desire a charting device that promptly identifies the undesired changes in the process. This study intends to design a sensitive homogeneously weighted moving average chart using two supplementary variables (hereafter, TAHWMA). The two supplementary variables are correlated with the study variable in the form of a regression estimator, which is an efficient and unbiased estimator for the process mean. The suggested TAHWMA charting structure is checked out and compared in terms of appearance and non-appearance of multicollinearity amidst the two additional variables. Average run length-related measures are taken as performance measures. It is observed that the proposed TAHWMA scheme performs effectively when the two supplementary variables have no collinearity. A comprehensive comparison between the proposed TAHWMA and existing charts is also carried out, showing the proposed’s supremacy over existing counterparts. For execution purposes, two illustrative examples, one belonging to carbon fibre manufacturing-related data and the other using a simulated dataset and where our simulated dataset belongs to symmetrical distribution, are also presented for the application of the recommended TAHWMA chart.

Estimation using a suboptimal method can lead to imprecise models, with cascading effects in complex models, such as climate change or pollution. The goal of this study is to compare the solutions supplied by different algorithms used to model ozone pollution. Using Box and Tiao (1975) study, we have predicted ozone concentration in Los Angeles with an ARIMA and an autoregressive process. We have solved the ARIMA process with three algorithms (i.e., maximum likelihood, like Box and Tiao, conditional least square and unconditional least square) and the autoregressive process with four algorithms (i.e., Yule–Walker, iterative Yule–Walker, maximum likelihood, and unconditional least square). Our study shows that Box and Tiao chose the appropriate algorithm according to the AIC but not according to the mean square error. Furthermore, Yule–Walker, which is the default algorithm in many software, has the least reliable results, suggesting that the method of solving complex models could alter the findings. Finally, the model selection depends on the technical details and on the applicability of the model, as the ARIMA model is suitable from the AIC perspective but an autoregressive model could be preferred from the mean square error viewpoint. Our study shows that time series analysis should consider not only the model shape but also the model estimation, to ensure valid results.