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Unlike other natural hazards, drought has severe consequences on numerous aspects of life. After the industrial revolution, drought is prevailing in most parts of the world. Likewise, global warming and climate change have increased the recurrent occurrences of extreme values and the short-distance variability in precipitation. Therefore, accurate and effective reporting of drought characteristics at the regional level is one of the most challenging tasks in hydrology. This research aims to improve the accuracy and quality of drought characterization and its continuous monitoring at the regional level. This article develops a new drought indicator by integrating unequal weights under an X-bar chart with the regional aggregation precipitation data. We called the new index– the Quality Boosted Regional Drought Index (QBRDI). In application, the northern region of Pakistan is considered to assess and evaluate QBRDI. In comparison, the study includes a pairwise comparison of QBRDI and Regional Standardized Precipitation Index (RSPI) using the Pearson correlation coefficient. Comparative to RSPI, a significantly low Coefficient of Variation between the correlations of QBRDI with other meteorological stations reveals that QBRDI has more regional characteristics than RSPI. These outcomes endorse the rationality of using QBRDI for regional drought analysis. In addition, the methodology of QBRDI provides a new way to minimize the impact of outliers and extreme values in the regional aggregation of precipitation data.

Vibration condition monitoring is a non-devastating technique that can be performed to detect tooth cracks propagating in gear systems. This paper proposes to apply a new methodology using time-domain analysis, frequency-domain analysis, and statistical process control charts (SPCC) for gear crack detection of a 10 DOF dynamic model of spiral bevel gear system (SBGS). The gear mesh stiffness effect used in the model has been studied analytically for different levels of crack faults. Adding Gaussian white noise is discussed as the first step to simulating the initial modeling signals of real-world conditions. Second, time-domain signal analysis was performed to identify periodic vibration pulses as failure components and calculate the statistical standard deviation (STD) feature as a fault-sensitive feature. Third, a fast Fourier transform (FFT) to time signals of the variable gear mesh stiffness was applied to determine the gear mesh frequency and sidebands to detect tooth cracks. Fourth, the SPCC was designed using the Shewhart X-bar chart and an exponentially weighted moving average (EWMA) chart based on the STD feature of the healthy gears. Finally, in the testing stage, the control charts are carried out with simulation signals under faulty conditions to detect the different levels of cracks. The results showed that the EWMA chart outperformed the time domain analysis, frequency domain analysis, and Shewhart X-bar chart in detecting all levels of cracks at an early stage.

In this article, an enhanced X-bar control chart using generalized multiple dependent state (GMDS) sampling under neutrosophic statistics is presented. The joint advantages of GMDS sampling and the neutrosophic statistics have been recycled for the efficient monitoring of the average quality characteristic of any production process. The efficiency of the proposed chart has been evaluated using the average run length values under different ranges of the parameters under study. The comparison of the proposed chart with the existing control chart has been discussed. The comparison shows that the proposed chart is better than the existing chart. Results reveal the superiority of the proposed neutrosophic-based GMDS sampling chart. In addition, an example has also been included for the practical implementation of the proposed methodology.

Introduced by Shewhart, the traditional variable control chart for mean (X-bar Chart) is an effective tool for controlling and monitoring processes. Notwithstanding, the main disadvantage of X-bar chart is that the population standard deviation is unknown though the sample mean is an unbiased estimator of the population mean. There are many approaches to estimating the unknown standard deviation with the expertise available with the researchers and practitioners that may lead to varying conclusions. In this paper, an innovative approach is introduced to estimate the population standard deviation from the perspective of Six Sigma quality for the construction of the proposed control chart for mean called Six Sigma-based X-bar control chart. Under the assumption that the process is normal, in the proposed chart the population mean and standard deviation are drawn from the process specification from the perspective of Six Sigma quality. After discussing the aspects of the traditional X-bar control chart, the procedure for the construction of the proposed new Six Sigma-based X-bar control chart is presented. The new chart is capable of maintaining the process mean close to the target by variance reduction resulting in quality improvement. Also, it may be noted that at a point of time, the process, though under statistical control, may be maintaining a particular sigma quality level only while the goal is Six Sigma quality level of just 3.4 defects per million opportunities. Hence, as a practice of continuous quality improvement, it is suggested to use the proposed control chart every time with improvement till the goal of Six Sigma with 3.4 defects per million opportunities is achieved. An innovative cyclic approach for performing the continuous quality improvement activity is also presented. The construction of the proposed Six Sigma-based X-bar control chart is demonstrated using an illustrative example.

Study design Retrospective cohort study. Objectives To evaluate surgical consistency and clinical outcomes in intramedullary ependymoma (WHO grade II) cases by using X-bar charts as a tool to assess procedural stability. Setting The single institution in Japan. Methods This study included patients who underwent resection of intramedullary ependymomas between 2001 and 2023. All surgeries were performed by one of five board-certified spine surgeons. Operative time was analyzed for stability using X-bar charts. Neurological outcomes were assessed using the modified McCormick Scale (mMS), and regression analysis was performed to evaluate the relationship between operative time and mMS. Results The study included 144 patients (82 men, 62 women; average age 50.3 ± 14.6 years). Tumors were located at cervical (67.4%) or thoracic (32.6%) levels, averaging 3.0 ± 1.2 vertebrae. The surgeon who performed 71 cases was defined as the experienced surgeon, and the other surgeons performed 10–24 cases, respectively. The mean operative time was 380.6 ± 140.7 min, and 135 cases achieved gross total resection. The average follow-up duration was 6.9 ± 3.9 years. X-bar charts showed surgical stability once the average number of cases exceeded 17. No significant correlation was found between operative time and mMS for any surgeon. Perioperative complications were minimal. Conclusions X-bar charts are a valuable tool for objectively evaluating surgical stability. In intramedullary ependymoma surgeries, consistency in operative time was achieved after 17 cases, and longer procedures did not adversely affect neurological outcomes. This method could be extended to monitor procedural reliability in other complex surgical interventions.

Process monitoring plays a vital role in ensuring quality stability, and, operational efficiency across fields such as manufacturing, finance, biomedical science, and environmental monitoring. Among statistical tools, control charts are widely adopted for detecting variability and abnormal patterns. Since the introduction of the basic X-bar control chart by Shewhart in the 1920s, various improved methods have emerged to address the challenge of identifying small and latent process shifts, including CUSUM, MA, EWMA, and Exp-EWMA control charts. This study introduces a novel control chart—the Moving Average–Exponentiated Exponentially Weighted Moving Average (MA-Exp-EWMA) control chart—combining the smoothing effect of MA and the adaptive weighting of Exp-EWMA. Its goal is to improve the detection of small shifts and gradual changes. Performance is evaluated using average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL). Monte Carlo simulations under different distributions (normal, exponential, gamma, and Student’s t) and parameter settings assess the control chart’s sensitivity under various shift scenarios. Comparisons with existing control charts and an application to real data demonstrate the practical effectiveness of the proposed method in detecting small shifts.

This study investigates the detection of crack faults in bevel gears with a new method based on univariate statistical control charts (USCCs). The focus was on determining four types of operating states for the gears: healthy operation, faulty operation with a crack length of 0.25 mm, a crack length of 0.5 mm, and a crack length of 0.75 mm. Laboratory vibration signals of the single-stage bevel gearbox system are obtained as a first step to implement the proposed approach. Next, the time-domain features each of the standard deviation (STD), root mean square (RMS), and kurtosis extracted from the vibration signal segments measured in a number of gear revolutions are used. Then, based on the normal distribution of the STD feature, it is selected among the other features as the most fault-sensitive univariate indicator to construct the USCC. Subsequently, the X-bar control chart and the exponentially weighted moving average (EWMA) chart are designed and tested. Finally, a comparison was made between the performance of the control schemes, and EWMA obtained the best performance, as it detected all crack lengths quickly and at an early stage, as a result of the specificity of EWMA in giving a weighted average of the observed samples by combining the previous and current data of the samples throughout the control process.

PurposeThe traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices.Design/methodology/approachThe authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of Cpk, to compare and analyze the efficiency of the proposed design.FindingsThis study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed.Originality/valueA framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (Cp and Cpk) in addition to m and n were introduced in the expected ARL equation. The Cpk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.

The non-uniform sampling scheme and economic statistical design approaches have been successfully applied to determine three parameters of x-bar control charts to monitor a manufacturing process with increasing hazard functions for the last three decades. Nevertheless, a primary assumption for these cost models is that measurements within a sample are independent. However, the conventional supposition may significantly underestimate the type I error probability for the x-bar control chart. Hence, we develop a cost model that combines different researches with the multivariate normal distribution model that given the maximum probability of type I error and the minimum value of power. The optimal parameters of non-uniform sampling interval x-bar control charts are used for the measurements within a sample being correlated. In addition, an industrial example is applied to indicate the solution procedure. Sensitivity analysis is accompanied with input parameters including correlated coefficients as well as process and cost parameters of the model are performed. The genetic algorithm is adopted to reveal the optimal solution of the economic design. The method proposed can be used on related industries to achieve the ability of production monitoring and cost reducing. The human resource consuming and the amount of scraps will be avoided toward the conclusive goals of economic benefit, environmental benefit and social benefit.

Various types of abnormal control chart patterns can be linked to certain assignable causes in industrial processes. Hence, control chart patterns recognition methods are crucial in identifying process malfunctioning and source of variations. Recently, the hybrid soft computing methods have been implemented to achieve high recognition accuracy. These hybrid methods are complicated, because they require optimizing algorithms. This paper investigates the design of efficient hybrid recognition method for widely investigated eight types of X -bar control chart patterns. The proposed method includes two main parts: the features selection and extraction part and the recognizer design part. In the features selection and extraction part, eight statistical features are proposed as an effective representation of the patterns. In the recognizer design part, an adaptive neuro-fuzzy inference system (ANFIS) along with fuzzy c-mean (FCM) is proposed. Results indicate that the proposed hybrid method (FCM-ANFIS) has a smaller set of features and compact recognizer design without the need of optimizing algorithm. Furthermore, computational results have achieved 99.82% recognition accuracy which is comparable to published results in the literature.