The nonparametric (NP) control charts are famous for detecting a shift in the process parameters (location and/or dispersion) when the underlying process characteristic does not follow the distributional assumptions. Similarly, when the cost of estimations is very high and the ranking of observational is relatively simple, the ranked set sampling (RSS) technique is preferred over the simple random sampling (SRS) technique. On the other hand, the NP triple exponentially weighted moving average (EWMA) control chart based on SRS is superior to the NP EWMA and NP double EWMA (NP DEWMA) based on the SRS technique to detect a shift in the process location. This study designed an advanced form of NP TEWMA Wilcoxon signed-rank based on RSS, denoted as TEWMA − SR RSS control chart to identify a shift in the process location parameter. The Monte Carlo simulation method is used to assess the performance of the proposed TEWMA − SR RSS control chart along with SRS-based NP TEWMA (TEWMA-SR), SRS-based NP TEWMA sign (TEWMA-SN), SRS-based TEWMA − X ¯ , and RSS-based NP DEWMA-SR DEWMA − SR RSS control charts. The study shows that the proposed TEWMA − SR RSS control chart is more efficient in identifying shifts (especially in small shifts) in the process location than the existing control charts. Finally, a real-life application is also provided for the practical implementation of the proposed TEWMA − SR RSS control chart.

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable $X_i$. However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators.

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.

This article introduces a new robust multivariate Hotelling T‐square (TS) control chart that incorporates an L‐Comoments covariance matrix into a multivariate statistical process control (MSPC) charting scheme to enhance its robustness and detection ability. However, among the most popular, conventional Hotelling TS charts are affected by outliers and based on the so‐called classical covariance matrix estimators, which in turn presuppose normality and independence. This sensitivity reduces their usefulness in complicated practical problems where skewness, heavy tails, and outliers are likely to appear. Using L‐Comoments as a basis of the new chart can overcome these limitations since L‐Comoments are not affected by outliers. The performance of the proposed Hotelling TS (HTS) chart is assessed using total and generalized variances. By comparing the effectiveness of the L‐Comoments‐based TS chart using simulated and renewable energy data, the new chart based on the proposed approach outperforms the traditional chart and robust charts based on powerful estimators such as the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD). Hence, the new approach enables the new exploration of robust and reliable multivariate quality control analysis for high‐dimension and complex datasets.

The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts.

Measurement error (M.E) can have a substantial impact on quality control applications, diminishing the sensitivity to detect changes in the mean or variance of quality characteristics. To monitor shifts in process mean and dispersion, Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts are commonly employed. In our research, we investigated the influence of M.E on the Triple Exponentially Weighted Moving Average (TEWMA) control chart. We assessed the performance of the control chart using Average Run Length (ARL) as the evaluation metric. To compute the ARL properties, we adopted the Monte-Carlo simulation method. A comparison section has been made to check the performance efficiency of the control chart with the existing EWMA control chart. The implementation of a control chart on a real data set is also presented.