Majid Khan

The most difficult aspect in statistical process monitoring is an extensive evaluation of memory‐type charts in zero‐state and steady‐state scenarios. In actual practice, a chart does well at the zero state but poorly at the steady state. Nevertheless, some researchers argued for the superiority of their charts merely based on performance under zero‐state conditions, which may not hold true with respect to long‐term monitoring stability. However, recent literature underlines that a chart can be regarded as superior only if it performs well both in zero‐state and in steady‐state scenarios. The novel Cumulative Sum (CUSUM) chart is accordingly constructed based on variable transformations under an exponential distribution, hence termed . The chart has been developed particularly for maximizing effectiveness in both zero‐state and steady‐state conditions. The Monte Carlo simulations have been carried out to assess the performance and demonstrate the utility of the approach. To thoroughly assess its performance, various traditionally accepted metrics, average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), extra quadratic loss (EQL), performance comparison index (PCI), and relative ARL (RARL), are applied. The proposed chart is compared with existing alternatives based on the metrics included. The analysis establishes that the is superior to its rivals in terms of shift detection under both zero‐state and steady‐state scenarios. The efficacy of the proposed chart has been illustrated through its application to two real healthcare datasets, which have verified its practicality for process monitoring.

Conventional control chart schemes often assume normality when monitoring processes, a condition that is not consistently applicable. The aforementioned constraint is notably apparent in a variety of engineering dealings, especially when characterized by the prevalence of the inverse Maxwell process. An important development in the field of process monitoring is the growing importance of an adaptive exponentially weighted moving average () control chart. This study proposed an control chart for inverse Maxwell processes, abbreviated as . The chart is evaluated using several criteria, including average run length, median run length, and standard deviation run length. The comprehensive analysis includes extra quadratic loss, relative average run length, and performance comparison index. A two‐step optimization procedure was utilized to identify the optimal design parameters, ensuring that the monitoring scheme is capable of effectively detecting both large and small shifts. To evaluate the effectiveness of the chart, it is compared to other charts in the same family, for inverse Maxwell distribution, such as control chart, and exponentially weighted moving average ( control chart. The results indicate that the proposed chart exhibits higher efficiency compared to its competitors. To demonstrate the practical application of the proposed control chart, two real‐life examples are provided, using brake pad failure data and the COVID‐19 estimated reproduction number to demonstrate its utilization in an actual data set. The findings of our study reveal the significant role of the proposed chart in improving process monitoring. Its effectiveness in detecting shifts in different scenarios has been established, as evidenced by its successful use in practical settings.

Adverse events are frequently encountered in manufacturing and service processes. Control charts are commonly used to monitor adverse events. In high‐quality processes, the adverse events count rate can be very low, with zero counts for multiple time intervals. As a result, control chart limits become narrower, which may increase the number of false alarms. Thus, in high‐quality processes, control charts for monitoring the time between events (TBE) are more effective than control charts for monitoring adverse events. This article presents one‐sided exponentially weighted moving average (EWMA) control charts, based on power transformation and model reset modification, that monitor the downward and upward shifts in the exponentially distributed TBE data. These control charts are called lower‐ and upper‐sided TBE control charts. The designs of lower‐ and upper‐sided TBE control charts are based on a two‐level optimal model that optimizes the parameters of the control charts by minimizing the expected average run length (EARL) and expected weighted run length (EWRL). In addition, comparisons based on average run length (ARL) of the TBE control charts against the existing TBE control charts reveal the superiority of the TBE control charts over the existing TBE control charts. Finally, two real‐life data applications are also provided to highlight the implementation and sensitivity of the TBE control charts, revealing the superiority of the TBE control charts over the existing TBE control charts.

Nonconforming events rarely occur in high‐quality processes, and the time between events () is likely to be followed by a skewed distribution, such as an exponential distribution. This paper proposes the upper and lower‐sided improved adaptive exponentially weighted moving control charts for monitoring data modeled by the exponential distribution. The proposed control charts are labeled as control charts, that is, the and control chart, respectively. The control chart detects the upward shifts, while the control chart identifies the downward shifts in the process. The Monte Carlo simulations are used to approximate the run length distribution of the proposed control charts. Numerical results associated with various performance measures, such as average run length (), standard run length (), median run length (), extra quadratic loss (), relative average run length (), and performance comparison index () are computed. The proposed control charts compared to the respective existing control charts, such as , , , and control charts, at a single shift, as well as over a specified range of shifts. The comparison reveals that the proposed control charts outperform the existing control charts for both single specified shifts and over a certain range of shifts. Finally, real‐life data of hospital stay time for male patients with traumatic brain injury are analyzed for the applicability of the control chart in the health sector.

The quality characteristic(s) are assumed to follow the normal distribution in many control chart constructions, although this assumption may not hold in some instances. This study proposes the Bayesian-I and Bayesian-II Shewhart-type control charts for monitoring the Maxwell scale parameter in the phase II study. The posterior and predictive distributions are used to construct the control limits for the proposed Bayesian-I and Bayesian-II Shewhart-type control charts, respectively. Various performance indicators, including average run length, quadratic loss, relative average run length, and performance comparison index, are utilized to evaluate the performance of the proposed control charts. The Bayesian-I and Bayesian-II Shewhart-type control charts are compared to their competitive CUSUM_V, EWMA_V and V control charts. Sensitivity analysis is also performed to study the effect of hyperparameter values on the performance behavior of the proposed control charts. Finally, real-life data is analyzed for the implementation of the proposed control charts.

Nonconforming events are rare in high-quality processes, and the time between events (TBE) may follow a skewed distribution, such as the gamma distribution. This study proposes one- and two-sided triple homogeneously weighted moving average charts for monitoring TBE data modeled by the gamma distribution. These charts are labeled as the THWMA TBE charts. Monte Carlo simulations are performed to approximate the run length distribution of the one- and two-sided THWMA TBE charts. The THWMA TBE charts are compared to competing charts like the DHWMA TBE, HWMA TBE, THWMA TBE, DEWMA TBE, and EWMA TBE charts at a single shift and over a range of shifts. For the single shift comparison, the average run length (ARL) and standard deviation run length (SDRL) measures are used, whereas the extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are employed for a range of shifts comparison. The comparison reveals that the THWMA TBE charts outperform the competing charts at a single shift as well as at a certain range of shifts. Finally, two real-life data applications are presented to evaluate the applicability of the THWMA TBE charts in practical situations, one with boring machine failure data and the other with hospital stay time for traumatic brain injury patients.

Homogeneously weighted moving average (HWMA) charts have recently achieved popularity for monitoring small changes in process parameters (location and/or dispersion). Furthermore, the DHWMA (double HWMA) and THWMA (triple HWMA) are the advanced versions of the HWMA charts. The HWMA chart for the process dispersion is designed to detect only the upward (one‐sided) shift (i.e., process deterioration). Employing a two‐sided chart for concurrently detecting both process improvement and process deterioration is an important aspect of statistical process monitoring. By taking this point as motivation, one and two‐sided THWMA charts (symbolized as the THWMAV) are proposed for monitoring the process dispersion. The Monte Carlo simulations are performed to investigate the performance behavior of the THWMAV charts in terms of certain performance indicators, including ARL, SDRL, EQL, RARL, and PCI. The comparison among the THWMAV versus existing charts (DHWMAV, HWMAV, TEWMAV, DEWMAV, and EWMAV) indicates that the THWMAV charts outperform the existing charts. Finally, a dataset is also analyzed to illustrate the implementation of the THWMAV charts.

The recently introduced triple exponentially weighted moving average (TEWMA) chart is the extended form of the classical EWMA and double EWMA (DEWMA) charts. On the other hand, the auxiliary information-based (AIB) homogeneously weighted moving average () chart is used for the monitoring of process location shifts efficiently as compared to the HWMA chart. Combining TEWMA with HWMA features is a new idea and is not seen in the literature until now. So, the objective of this study is to combine the idea of and TEWMA charts and propose an AIB triple HWMA, symbolized as chart to further improve the process location shift monitoring. The proposed chart is developed by combining the AIB double HWMA plotting statistic into the other HWMA chart. The numerical results are computed using the Monte Carlo simulation method. Average run length (), relative , performance comparison index, and extra quadratic loss are used as comparison tools for the proposed chart with the classical EWMA, TEWMA, mixed HWMA-CUSUM (MHC), AIB EWMA (), HWMA, double HWMA (DHWMA), , AIB mixed EWMA-CUSUM (), and AIB mixed CUSUM-EWMA () charts. Finally, a practical application is also provided for users to demonstrate the proposed study’s vitality.