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We demonstrate that the recently introduced triple generally weighted moving average (GWMA) chart and its counterpart, the double GWMA chart, incorporate sub‐optimal weighting patterns that may assign more weight to certain historical data points at the expense of more recent ones. Moreover, these control charts, when compared to the exponentially weighted moving average (EWMA) chart, exhibit a substantial computational burden. Our findings underscore that a well‐designed EWMA chart offers superior overall performance in comparison to these control charts. [ABSTRACT FROM AUTHOR]

This study advances the application of the first‐to‐signal (FTS) concept to evaluate the effectiveness of multivariate charts when detecting shifts in the mean vector of a multivariate normally distributed process. Using Monte Carlo simulations, we estimate steady‐state average run‐length profiles and the probabilities of multivariate charts being the FTS an out‐of‐control state. Notably, our findings indicate that while the multivariate cumulative sum (MCUSUM) chart serves as a viable alternative to the multivariate exponentially weighted moving average (MEWMA) chart when detecting small shifts in the process mean vector, the latter surpasses the former in detecting moderate‐to‐large shifts. In addition, the Hotelling's T2$T^2$ chart outperforms the MEWMA and MCUSUM charts when detecting large shifts. [ABSTRACT FROM AUTHOR]

In this article, we propose a new adaptive exponentially weighted moving average (AEWMA) chart for monitoring the joint shifts in the location and scale parameters of the two‐parameter exponential distribution, namely the AEWMA‐II chart. A key feature of the proposed chart is its straightforward post‐signal diagnostics. The Monte Carlo simulation method is used to compute the steady‐state run‐length profiles of the proposed chart. The run‐length properties include the average run‐length and standard deviation of the run‐length. Through a comprehensive run‐length comparison, it is found that the AEWMA‐II chart performs better than the existing AEWMA chart. Moreover, with post‐signal diagnostics, the proposed chart also surpasses the existing chart. Finally, a real dataset is applied to illustrate the excellent performance and practical application of the proposed chart. [ABSTRACT FROM AUTHOR]

Recently, several control charts have been proposed in the statistical process monitoring literature based on a belief statistic. In this article we compare the zero‐state average run‐lengths and conditional expected delay profiles of the exponentially weighted moving average (EWMA) and belief statistic‐based (BSB) charts. We show that an ordinary EWMA chart is far better than the BSB chart when detecting delayed shifts in the mean of a normally distributed process. [ABSTRACT FROM AUTHOR]

The cumulative sum (CUSUM) charts are well‐structured and widely used for detecting small‐to‐moderate changes in the process parameters. However, their performance can be limited when the shift size is unknown or varies over time. Various methods have been developed to address this issue, including dual CUSUM (DCUSUM), adaptive CUSUM, adaptive EWMA, and weighted CUSUM charts, all of which offer better sensitivity compared to traditional CUSUM charts. In this study, we propose a new weighted DCUSUM chart designed to effectively detect the mean shifts in a normally distributed process. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the control charts. The ARL performances of the control charts are evaluated in terms of expected relative ARL (ERARL) and expected weighted run‐length (EWRL). Our results show that the proposed chart may outperform existing counterparts in terms of the ARL, ERARL, and EWRL measures, indicating superior performance in detecting a range of the mean shift sizes. Finally, we apply the existing and proposed charts to a real dataset, showcasing their practical utility in process monitoring. [ABSTRACT FROM AUTHOR]

The two‐parameter exponential distribution (TPED) is often used to model time‐between‐events data. In this paper, we propose CUmulative SUM and exponentially weighted moving average charts for simultaneously monitoring the parameters (location and scale) of the TPED. A key feature of the proposed charts is their straightforward post‐signal diagnostics. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the proposed charts. The ARL performances of existing and proposed charts are assessed in terms of expected weighted run‐length and relative mean index. It is found that the proposed charts outperform the existing charts. A real dataset is used to illustrate the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

A primary objective in detecting disease outbreaks is to precisely identify substantial increases in process means to control the spread of outbreaks. In this paper, we introduce a novel directionally sensitive adaptive multivariate exponentially weighted moving average chart for efficiently detecting either increases or decreases in the mean vector of a multivariate normally distributed process. In addition, the chart's sensitivity is enhanced through features such as variable sample size, variable sampling interval, and a combination of both. Monte Carlo simulation is employed to estimate zero‐state and steady‐state average time‐to‐signal (ATS) profiles. Performance measures, including expected weighted and relative ATS, are used for evaluating the performances of multivariate charts. Our results indicate that the proposed charts outperform existing charts in detecting various mean shift sizes. The application of these multivariate charts is demonstrated through illustrative examples. [ABSTRACT FROM AUTHOR]

Control charts are widely used in the manufacturing and service sectors to track, regulate, and enhance process output. A manufacturing industry desires to utilize a control chart that has an effective structure and is sensitive to detect infrequent variations in the process. Generally, control charts are developed with the presumption that the understudy quality variable is normally distributed. In actual application, many processes have skewed distributions. The purpose of this study is to use the moving average (MA) charts to track the dispersion of a log‐normal distribution. The design of the proposals is developed and the performance is assessed by run‐length properties. The cumulative distributions of run‐length under in‐control and out‐of‐control are provided to have a broad view of the performance. The simulation findings show that when the value of the log‐normal dispersion parameter is large, the proposed chart is more sensitive to the changes in the dispersion. Additionally, an industrial application is given to illustrate the suggested charts in this research. [ABSTRACT FROM AUTHOR]

Bayesian reliability assessment plays an integral role in determining the success of product development and deployment into the market, especially when limited information is available to estimate the reliability of products. Nevertheless, the Bayesian reliability approach has untapped research potential when it is used to evaluate systems consisting of dependent components, that is, a situation that reflects real‐world conditions. This study addresses the research gap by applying a copula to encode the dependency structure between the failure rates of the components, particularly for the simple series systems. Unfortunately, this study found that Bayesian aggregation error still occurs when information is used at different levels. By employing Monte Carlo simulation and classification tree learning, this study also investigates the key factors affecting such error over a wide range of possible scenarios and derives useful guidelines for reliability practitioners so that they can choose a more suitable analysis under certain circumstances. [ABSTRACT FROM AUTHOR]

A robust tool for monitoring the process mean in the presence of abrupt changes or estimation errors in the process standard deviation is the cumulative sum (CUSUM)‐t$t$ chart. However, optimizing the existing CUSUM‐t$t$ chart to minimize the out‐of‐control average run‐length value often involves intricate Markov chain techniques. This complexity prompted the development of a near‐optimal CUSUM‐t$t$ chart, presented in this paper, which simplifies the determination of the chart's reference parameter. The reference parameter calculation is based on a predefined shift size in the mean, allowing for swift detection. Meanwhile, the chart's decision interval can be derived through Monte Carlo simulations. Interestingly, both the newly devised near‐optimal CUSUM‐t$t$ chart and the established CUSUM‐t$t$ chart yield similar out‐of‐control average run‐length values for identical shift sizes and sample sizes. Consequently, the former can serve as a practical alternative to the latter, considering its ease of optimization and implementation. [ABSTRACT FROM AUTHOR]

Effective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in‐control average run‐length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time‐varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run‐length performance for an in‐control process compared to that of the geometric distribution. [ABSTRACT FROM AUTHOR]

In this article, we study the effect of estimation error on the conditional false alarm rate (CFAR) of the exponentially weighted moving average (EWMA) chart based on the estimated dynamic probability control limits (EDPCLs). It is found that the effect is large, but with an increase in the Phase‐I sample size, the effect of estimation error may be reduced. In addition, an alternative approach is suggested for determining the EDPCLs for the EWMA chart that may help reduce the effect of estimation error on the CFAR profiles. [ABSTRACT FROM AUTHOR]

In the paper, we conduct an assessment of the conditional expected delay (CED) profiles of the EWMA, CUSUM, and dual CUSUM charts based on a statistic linked to Brownian motion. The study reveals a noteworthy observation: the CED curves for these control charts may exhibit an increasing trend over time. Moreover, in a steady‐state scenario, it becomes evident that these control charts could be outperformed by their established counterparts. [ABSTRACT FROM AUTHOR]

To identify small‐to‐moderate shifts (also known as outliers and anomalies) in the process parameters (location and/or dispersion), the classical cumulative sum (CUSUM) and exponential weighted moving average (EWMA) control charts are famous. The traditional CUSUM control chart is less capable to detect out‐of‐control signals of ±$ \pm $1.0 standard deviation shifts. The advanced versions of the traditional CUSUM and EWMA control charts are ACUSUM (adaptive CUSUM) and AEWMA (adaptive EWMA) control charts, respectively. The aforementioned issue of the traditional CUSUM control chart can be addressed through the ACSUUM control chart. It also identifies various sizes of shifts in the process parameters. In order to efficiently identify and remove outliers and anomalies (i.e., shifts) from datasets, the score functions are typically used to establish ACUSUM control charts. The goal of the study is to propose a new ACUSUM control chart based on the Hampel (score) function and it is symbolized as ACUSUMHampel${\mathrm{ACUSU}}{{\mathrm{M}}_{{\mathrm{Hampel}}}}$ control chart. Different sizes of shift in the process location parameter can be distinguished using the ACUSUMHampel${\mathrm{ACUSU}}{{\mathrm{M}}_{{\mathrm{Hampel}}}}$ control chart. The primary novelty is the substitution of a proposed time‐varying parameter for the typical CUSUM control chart's prioritization of the process characteristic by appropriate weights. The proposed ACUSUMHampel${\mathrm{ACUSU}}{{\mathrm{M}}_{{\mathrm{Hampel}}}}$ control chart's run length feature is obtained through the Monte Carlo simulation technique for zero‐state and steady‐states. For evaluating a single shift, performance measures like average run length (ARL), standard deviation of run length (RL), and different percentiles of run length are preferred. However, for evaluating a range of shifts, extra quadratic loss, relative average run length, and performance comparison index are used. Comparison based on performance measures shows the superiority of the proposed ACUSUMHampel${\mathrm{ACUSU}}{{\mathrm{M}}_{{\mathrm{Hampel}}}}$ control chart against the classical CUSUM and EWMA, ACUSUM, AEWMA, mixed EWMA‐CUSUM, and mixed CUSUM‐EWMA control charts. Furthermore, the proposed ACUSUMHampel${\mathrm{ACUSU}}{{\mathrm{M}}_{{\mathrm{Hampel}}}}$ control chart is also implemented with real‐life data which is taken from cost of medical insurance to demonstrate its competency in statistical process control field for quality engineers, practitioners, experts, and researchers. [ABSTRACT FROM AUTHOR]

Zaman et al.1 proposed an adaptive exponential weighted moving average (AEWMA) control chart (CC) by integrating Hampel function features into the traditional EWMA CC structure. The purpose of this study is to find and fix the inaccuracies in the AEWMA CC by Zaman et al.1. We reproduce the results after rectifying the errors of the AEWMA control chart by applying Monte Carlo simulation. The results of corrected version of the AEWMA CC indicates better performance as compared to Zaman et al.1 The average run length is chosen as a performance measure for comparison reason. [ABSTRACT FROM AUTHOR]

Mission Success Probability is a top‐level indicator that integrates reliability, maintainability, and spare parts security during the system's mission. Numerical simulation is used for mission success evaluation of complex system because it can consider any form of system structure and component failure distribution model. In actual engineering, system components usually deteriorate or fail with the extension of service time and need to be repaired or replaced, so there are dynamic changes in component status during the life cycle. To evaluate the mission success in such dynamic scenarios, it is necessary to repeat the simulation based on the whole system once the local parameters are adjusted. Despite the continuous improvement in computational performance, traditional numerical simulations are not well matched for rapid evaluation and timely decision making in dynamic scenarios. Therefore, an evaluation method that mixes proxy model and simulation sampling is proposed in this paper. The method uses the simulation to complete the data acquisition, and then analyzes the data by inverse function sampling and Copula function to obtain the model training samples, and finally realizes the approximate description of the local unit simulation process by proxy model. The experimental results show that the method can reduce the repetitive simulation scale from the whole system to local unit while ensuring high accuracy, avoiding many repeated calculations in variable scenarios. [ABSTRACT FROM AUTHOR]

Monitoring of the process coefficient of variation (CV) with one‐sided CUSUM charts has been considered in the literature. In this short note, we develop a near‐optimal one‐sided CUSUM chart (with an explicit mathematical expression of the reference parameter) for detecting either increases or decreases in the CV of a normally distributed process. It is shown that the run‐length profiles of the existing and proposed one‐sided CUSUM‐CV charts (despite the fact that both charts possess different control‐charting structures) approximately remain the same. However, the proposed one‐sided CUSUM‐CV charts can be easily optimized when detecting a specific upward or downward shift in the in‐control process CV. [ABSTRACT FROM AUTHOR]

The classical memory Exponential Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts (CCs) are important to detect small‐to‐moderate sizes of shift in the process location and/or dispersion parameters. To make the memory control chart (CC) more efficient for broad range of shift, the score functions in particular Huber and Bi‐square functions are incorporated in the classical memory CCs. These score functions help to formulate the parameters of memory CCs and are called Adaptive EWMA (AEWMA) and Adaptive CUSUM (ACUSUM). The AEWMA and ACUSUM are capable to handle various sizes (i.e., small, moderate, and large) of shift. The aim of this study is to utilize Hampel function as the alternative of the mentioned score functions, and propose a new AEWMA CC, symbolized as AEWMAHample. To develop the proposed AEWMAHample CC, the standard EWMA statistic and Hampel function are incorporated in the classical EWMA CC structure. The proposed AEWMAHample CC is also efficient to handle certain sizes of shift in the process location parameter. Performance evaluation procedures, like average run length is considered for a particular shift. Similarly, the performance comparison index, relative average run length, and extra quadratic loss function are estimated over a range of shift. All these performance measures are calculated from run length (RL) characteristic of the proposed control chart. An algorithm in MATLAB is developed based on Monte Carlo simulation procedure to generate the RLs. Some existing control charts including EWMA, CUSUM, MEC, MCE, ACUSUMc(1)${\rm{ACUSUM}}_{\rm{c}}^{(1)}$, ACUSUMc(2)${\rm{ACUSUM}}_{\rm{c}}^{(2)}$, IACCUSUM, AEWMA∅hu${\rm{AEWMA}}_{{\emptyset }_{{\rm{hu}}}}$, and AEWMA∅bs${\rm{AEWMA}}_{{\emptyset }_{{\rm{bs}}}}$ are taken for comparison reason. For specific sizes of shift, the proposed AEWMAHample CC reveals the superiority. Besides, to address the practical significance for practitioners and quality engineers, the real‐life and simulated data examples are considered. [ABSTRACT FROM AUTHOR]

We show that the so‐called modified exponentially weighted moving average (EWMA) control chart is very closely related to a moving average‐based EWMA chart. These charts have ill‐advised weighting functions that assign more weight to some past data values than to the most recent data values. We show that these weighting functions adversely affect their run length properties and that one can obtain better overall performance with an ordinary EWMA chart. [ABSTRACT FROM AUTHOR]

The accelerated life testing (ALT) is frequently used in examining the component reliability and acceptance testing. The ALT is carried out by exposing the unit to higher stress levels in order to observe data faster than those are producing under the normal conditions. The simple step‐stress model based on type‐II censoring Weibull lifetimes is studied here. In addition, the lifetimes satisfy Khamis‐Higgins model assumption. In this paper, Bayesian approaches are developed for estimating the model parameters and predicting times to failure of future censored of the simple step‐stress model from Weibull distribution using Khamis‐Higgins model. The main goal of this work consists of two parts. First, the Bayesian estimation of the unknown parameters involved in the model is considered by adopting Devroye method to generate log‐concave densities within sampling‐based algorithm under different loss functions. The Bayes and highest posterior density credible intervals are then established. Second, the estimation of the posterior predictive density of the future lifetimes are discussed to obtain the point and prediction intervals with a given coverage probability. Monte Carlo simulation is performed to check the efficiency of the developed procedures and analyze a real data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

The EWMA chart is effective in detecting small shifts in the process mean or process variance. Numerous EWMA charts for the process variance have been suggested in the literature. In this article, new one‐sided and two‐sided EWMA charts are developed for monitoring the variance of a normal process. In developing these new EWMA charts, first, new unbiased estimators of the process variance are developed, followed by incorporating the developed estimators into the new EWMA charts' statistics. The Monte Carlo simulation method is adopted to evaluate the zero‐state and steady‐state run‐length performances of the proposed EWMA variance charts, in comparison with that of three existing EWMA variance charts and the weighted adaptive CUSUM variance chart. The findings reveal that the proposed charts generally perform better than the existing charts. An example of application is given to show the implementation of the proposed and existing charts in detecting increases or decreases in the process variance. [ABSTRACT FROM AUTHOR]

The estimations of parameters and percentiles for a three‐parameter Marshall Olkin extended inverse Weibull distribution based on progressively type‐II censored sample are concerned. The Bayesian, least‐squares, maximum likelihood and percentiles estimate methods for the model parameters have been developed. Comparing all estimate methods, the least‐squares, maximum likelihood and percentiles estimate methods are shown not stable due to the identification problem in the extended parametric space. Therefore, the Bayes estimate methods are focused. Three Bayesian estimations of the distribution parameters and p percentiles for p=$p =$ 2.5, 50 and 97.5 under the squared error loss, absolute error loss and LINEX loss functions are respectively calculated by using the Markov chain Monte Carlo sampling procedure. Moreover, two real data sets are presented for the application illustration. Finally, concluding remarks are addressed. [ABSTRACT FROM AUTHOR]

Inspired by the process of self‐healing of biological damage, high technology materials with self‐healing and self‐repairing mechanisms have been developed for high reliability and long lifetime. Therefore, the reliability modeling on intelligent systems with healing performance has become a research hotspot. Based on the diversity of healing mechanisms, this paper proposes a two‐phase reliability model method on self‐healing and self‐repairing systems. Impacts of environments, shock loads, self‐healing, and self‐repairing mechanisms are taken into account in this novel model. Besides, system lifetime and some reliability indexes under two shock models are derived, respectively. Moreover, Monte Carlo simulations are conducted to verify the accuracy of reliability under two models. Finally, an engineering case of metallized film capacitor is provided to illustrate the effectiveness and applicability of the proposed models by comparing numerical results and simulation results. [ABSTRACT FROM AUTHOR]

In this work, a methodology to monitor a shift in the quantile of a distribution that is a member of the log‐symmetric family is proposed. Because the sampling distribution of a quantile estimator is often not available, the parametric bootstrap method is used to determine this sampling distribution and to establish the control limits when the process measurements follow a log‐symmetric distribution. The mentioned family is helpful for describing the behavior of data following a distribution with positive support and that is skewed to the right. Monte Carlo simulations are carried out to investigate the performance of the proposed bootstrap control charts for quantiles. An application regarding failure data due to stress on carbon fibers is presented for illustration when monitoring reliability data. This illustration shows that non‐conventional models, other than the Birnbaum‐Saunders, log‐normal and Weibull distributions, have potential to be used in practice. Two model selection procedures are considered to assess adequacy to the data. To facilitate the public use of the proposed methodology, we have created an R package named chartslogsym whose main functions are detailed in this paper. [ABSTRACT FROM AUTHOR]

Monitoring the multivariate coefficient of variation (MCV) is conducted when the multivariate process variation changes proportionally with the mean vector because under this situation the traditional multivariate charts for the mean and variance cannot work correctly. All existing MCV charts in the literature are implemented based on sample MCVs computed from samples of size larger than unity (n>1)$(n>1)$ each. However, there are situations when forming samples (of n>1$n>1$) is not feasible. To address the aforementioned limitation of existing MCV charts, in this paper, an EWMA chart based on individual observations for monitoring the MCV is developed. Numerical studies based on Monte Carlo simulations are conducted to investigate the run length properties of the proposed chart in detecting either increases or decreases in the MCV, for two and three quality characteristics and various parameter values. A real bivariate dataset on the diameter and length of dowel pins is adopted to illustrate the implementation of the proposed chart. [ABSTRACT FROM AUTHOR]

In practice, the process standard deviation is usually unknown or is estimated inaccurately. The X¯$\bar{X}$‐type charts, such as the exponentially weighted moving average (EWMA) X¯$\bar{X}$ chart, which works under the assumption that the process standard deviation is either known or it is estimated accurately, may not perform well when the process standard deviation is actually unknown or estimated inaccurately. To address the aforesaid setback of the EWMA‐X¯$\bar{X}$ chart, the EWMA‐t chart was developed for monitoring the process mean when errors in estimating the process standard deviation occur or when the standard deviation is unknown. In this paper, new EWMA‐t charts, which are also robust against estimation errors in the process standard deviation and are applicable when the standard deviation is unknown, are developed for detecting mean shifts of a normal process. The new EWMA‐t charts are developed using the newly derived t‐statistics, based on the fixed sampling interval (FSI) and variable sampling interval (VSI) features. The new FSI/VSI EWMA‐t charts are found to outperform the existing FSI/VSI EWMA‐t chart, in terms of the zero‐state (ZS) and steady‐state (SS) average, median and standard deviation of the run‐length (SDRL)/time‐to‐signal criteria, for various shift sizes in the process mean, values of smoothing parameter and shift sizes in the process standard deviation. The application of the existing and new FSI/VSI‐EWMA‐t charts for detecting increases and decreases in the process mean is demonstrated with the automobile piston rings dataset. [ABSTRACT FROM AUTHOR]

New adaptive multivariate EWMA (AME) charts based on the variable sample size (VSS), variable sampling interval (VSI) and variable sample size and sampling interval (VSSI) techniques are proposed to reduce the time of the existing AME chart in detecting a mean shift in the multivariate normal process. A Monte Carlo simulation is conducted to compare the time to signal characteristics of the new VSS/VSI/VSSI AME and existing fixed sampling rate (FSR) AME and VSSI multivariate EWMA (ME) charts. It is found that the VSS/VSI/VSSI AME charts generally surpass the existing FSR AME and the non‐adaptive VSSI ME charts in detecting small and moderate shifts in the mean of a multivariate normal process, in terms of the expected weighted time‐to‐signal and expected relative average time‐to‐signal performance measures. An example is given to show the implementation of the existing and proposed charts. [ABSTRACT FROM AUTHOR]

An adaptive cumulative sum (ACUSUM) control chart is an advance form of the classical CUSUM control chart to identify different sizes of shift in the process parameters (location and/or dispersion). In the continuation of the ACUSUM control chart, this study also proposed ACUSUM control charts to enhance the performance of the process dispersion for a broad range of shift. The proposed ACUSUM control charts methodologies are based on the dispersion CUSUM statistic, score (Huber and Bi‐square) functions, generalized likelihood ratio test, and nonlinear optimization technique. The use of dispersion CUSUM statistic helps to distinguish a specific shift as the classical CUSUM statistic does, the score functions, the nonlinear optimization technique and generalized likelihood ratio test enhance the ability of the proposed ACUSUM control charts to distinguish a shift of different size. For the assessment of control charts, run length (RL) measure is used, and it is generated by developing an algorithm in MATLAB through Monte Carlo simulation method. Further, average of RL is utilized to carry out comparative analysis of control charts for a single shift, while for a certain range of shift (comprehensive analysis), extra quadratic loss (EQL), relative average run length (ARL), and performance comparison index (PCI) measures are used. Findings based on numerical results and visual presentations reveal the superiority of the proposed control charts against some existing control charts. Moreover, for real‐world point of assessment, the proposed control chart is implemented with numerical data to show the worth over other control charts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new process capability index, Cpmk′$\mathcal {C}^{\prime }_{pmk}$ based on an asymmetric loss function (linear exponential) for normal process. To estimate Cpmk′$\mathcal {C}^{\prime }_{pmk}$, we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponential loss function. Extensive simulations are carried out to investigate the performance of these estimation methods in terms of the mean squared errors. In addition, we compare the performance of four bootstrap confidence intervals and the highest posterior density interval of Cpmk′$\mathcal {C}^{\prime }_{pmk}$ in terms of average width and coverage probability. Finally, three real‐data applications from electronic industries are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

Decision making processes often rely on subjective evaluations provided by human raters. In the absence of a gold standard against which check evaluation trueness, rater's evaluative performance is generally measured through rater agreement coefficients. In this study some parametric and non‐parametric inferential benchmarking procedures for characterizing the extent of rater agreement—assessed via kappa‐type agreement coefficients—are illustrated. A Monte Carlo simulation study has been conducted to compare the performance of each procedure in terms of weighted misclassification rate computed for all agreement categories. Moreover, in order to investigate whether the procedures overestimate or underestimate the level of agreement, misclassifications have been computed also for each specific category alone. The practical application of coefficients and inferential benchmarking procedures has been illustrated via two real data sets exemplifying different experimental conditions so as to highlight performance differences due to sample size. [ABSTRACT FROM AUTHOR]

The EWMA chart is an advanced process monitoring tool because of its sensitive nature against small and moderate shifts that occur in the process parameter(s). In this paper, with a transformation related to the Brownian motion, we propose novel EWMA, double EWMA, triple EWMA, and quadruple EWMA charts for monitoring the mean of a process that follows a normal distribution. The Monte Carlo simulations are used to compute the run length properties of the proposed charts. Based on a comparative study, it is found that the newly proposed charts are uniformly and substantially better than their existing counterparts when detecting different kinds of shifts in the process mean. Real datasets are also considered to demonstrate the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

The regular exponential‐dispersion (ED) process with a nonlinear path can be used to model degradation processes of many products, while it has the shortage that the degradation increment is only age‐dependent, which limits its application in some circumstances. To overcome this shortage, two extensions of the ED process are suggested. For many degradation phenomena with self‐modulating mechanisms, the degradation increment during the next time interval may depend on the current degradation state. To describe this degradation phenomenon, an improved ED process model with state‐dependent degradation increment and a nonlinear path is proposed. Further, as an extension of the regular ED process and the improved ED process models, the generalized improved ED process is introduced, in which the degradation increment during an interval is both age‐ and state‐dependent. For the three discussed models, the MLE method is applied to estimate the model parameters. The numerical integration and Monte Carlo (MC) simulation methods are used to evaluate the reliability. Finally, two sets of fatigue crack size data are used to illustrate the proposed models and methods. [ABSTRACT FROM AUTHOR]

Monitoring time between events (TBE${\rm{TBE}}$) is an essential aspect of the high‐yield processes where the events of interest rarely occur. This study proposes a one‐sided scheme of a hybrid exponentially weighted moving average (HEWMA) chart for monitoring TBE${\rm{TBE}}$, where it is assumed that the TBE${\rm{TBE}}$ observations follow a gamma distribution. This chart is symbolized as the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart. The HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart detects the downward shift, that is, a decrease in the interarrival times that can lead to a deterioration of the process. A simulation study is carried out for the numerical results, and one‐sided HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart is evaluated along with one‐sided triple EWMA${\rm{EWMA}}$ (TEWMATBE)${\rm{TEWM}}{{\rm{A}}_{{\rm{TBE}}}})$, double EWMA${\rm{EWMA}}$(DEWMATBE)${\rm{(DEWM}}{{\rm{A}}_{{\rm{TBE}}}})$, EWMA${\rm{EWMA}}$(EWMATBE)${\rm{(EWM}}{{\rm{A}}_{{\rm{TBE}}}})$, double GWMA${\rm{GWMA}}$(DGWMATBE)${\rm{(DGWM}}{{\rm{A}}_{{\rm{TBE}}}})$, and GWMA${\rm{GWMA}}$(GWMATBE)${\rm{(GWM}}{{\rm{A}}_{{\rm{TBE}}}})$ charts. The results show that the one‐sided HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart outperforms its rivals, particularly in the case of small‐to‐moderate downward shifts. Moreover, this study also investigated the robustness of the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart, where the true distribution of the TBE${\rm{TBE}}$ observations is assumed to be Weibull or lognormal, and it is found that the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart is reasonably robust. Finally, two examples are given to demonstrate how to use the HEWMATBE${\rm{HEWM}}{{\rm{A}}_{{\rm{TBE}}}}$ chart in real‐world situations. [ABSTRACT FROM AUTHOR]

The run length performances of adaptive/nonadaptive multivariate exponentially weighted moving average (MEWMA) charts depend on the smoothing parameter. In this research, a new partially parameter‐free adaptive MEWMA (AMEWMA) chart, called the AMEWMA‐III chart, which does not contain any control chart parameter (except the control limit) is developed to monitor the mean vector of a process that follows a multivariate normal distribution. A Monte Carlo simulation is used to compute the run length characteristics of the MEWMA, AMEWMA‐I, AMEWMA‐II, and AMEWMA‐III charts. The AMEWMA‐III chart surpasses the MEWMA chart for small and moderate shifts whilst the latter with a larger smoothing parameter prevails over the former for large shifts. Additionally, the AMEWMA‐III chart outperforms the AMEWMA‐I and AMEWMA‐II charts for moderate‐to‐large shifts but for small‐to‐moderate shifts, all the AMEWMA charts have similar performances. Applications on two real datasets are given to illustrate the implementation of the AMEWMA‐III chart in comparison to the AMEWMA‐I and AMEWMA‐II charts. [ABSTRACT FROM AUTHOR]

The conventional CUSUM chart is usually designed for a known shift size against which the protection is required. In practice, the shift sizes are rarely known, but they may vary within a given interval. Given a range of the shift size, the weighted adaptive CUSUM (WAC) chart provides better protection than the CUSUM chart. In this paper, we propose two types of the WAC chart for monitoring different kinds of shifts in the variance of a normal process, named WAC‐I and WAC‐II charts, based on the CUSUM and Crosier CUSUM charts, respectively. Monte Carlo simulations are used to compute the run length characteristics of the proposed one‐sided and two‐sided charts. The proposed charts are compared with existing adaptive and non‐adaptive charts in terms of the average run length. It is found that the proposed charts perform uniformly and substantially better than the existing charts. A real dataset is considered to support the theory. [ABSTRACT FROM AUTHOR]

Memory‐type charts are well‐recognized as an advanced process monitoring tool because of their sensitive nature against small‐to‐moderate shifts that occur in the process parameters. One of those memory‐type charts is a CUmulative SUM (CUSUM) chart. In order to increase the sensitivity of the CUSUM mean chart, the CUSUM statistic is updated with the CUmulative EWMA‐SUM (CUESUM), which results into the CUESUM chart. The CUESUM chart encompasses the Crosier CUSUM (CCUSUM) chart. Using the Monte Carlo simulations, the run‐length properties of the CUESUM chart are computed. Based on detailed run‐length comparisons, it turns out that the CUESUM chart is more sensitive than the CCUSUM, EWMA, and double EWMA charts when detecting small shifts in the process mean. In addition, the CUESUM chart is uniformly more sensitive than the EWMA‐CUSUM chart. Real and simulated datasets are considered to demonstrate the implementation of the proposed chart. [ABSTRACT FROM AUTHOR]

In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out-of-control signal against these control charts. Moreover, real-life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts. [ABSTRACT FROM AUTHOR]

In this paper, we propose an auxiliary‐information‐based (AIB) double EWMA‐t (AIB‐DEWMA‐t) chart for monitoring the process mean. The DEWMA‐t chart encompasses the EWMA‐t and AIB‐EWMA‐t charts. The Monte Carlo simulations are used to compute the run length characteristics of the AIB‐DEWMA‐t chart. Based on detailed run length comparisons, it is found that the AIB‐DEWMA‐t chart may uniformly and substantially outperform the AIB‐EWMA‐t chart when detecting different shifts in the process mean. In addition, the AIB‐DEWMA‐t chart is uniformly more sensitive than the DEWMA‐t chart. Similar trends are observed when comparing these control charts with the variable sampling interval feature. A real dataset is also considered to demonstrate the implementation of the proposed chart. [ABSTRACT FROM AUTHOR]

Multiple auxiliary information-based (MAIB)memory-type t charts are proposed with fixed and variable sampling intervals for an improved monitoring of the process mean, which include adaptive/non adaptive cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) t charts. These control charts are constructed based on a unique uniformly minimum variance unbiased estimator of the process mean that requires information on a study variable as well as on several correlated auxiliary variables. The Monte Carlo simulation technique is used to compute the run length characteristics of the proposed charts when sampling from a multivariate normal distribution. The run length comparisons show that the proposed MAIB-t charts outperform their existing auxiliary information based (AIB) and non-AIB t charts, where the normalizing transformation is used for all considered t charts in order to have uniformity in the comparisons. A real data application is also given to support the proposed theory. [ABSTRACT FROM AUTHOR]

In many service and manufacturing industries, process monitoring involves multivariate data, instead of univariate data. In these situations, multivariate charts are employed for process monitoring. Very often when the mean vector shifts to an out‐of‐control situation, the exact shift size is unknown; hence, multivariate charts for monitoring a range of the mean shift sizes in the mean vector are adopted. In this paper, directionally sensitive weighted adaptive multivariate CUSUM charts are developed for monitoring a range of the mean shift sizes. Directionally sensitive charts are useful in situations where the aim lies in monitoring either an increasing or a decreasing shift in the mean vector of the quality characteristics of interest. The Monte Carlo simulation is used to compute the run length characteristics in comparing the sensitivities of the proposed and existing multivariate CUSUM charts. In general, the directionally sensitive and weighted adaptive features enhance the sensitivities of the proposed multivariate CUSUM charts in comparison with the existing multivariate CUSUM charts without the adaptive feature or those that are directionally invariant. It is also found that the variable sampling interval feature enhances the sensitivities of the proposed and existing charts as compared to their fixed sampling interval counterparts. The implementation of the proposed charts in detecting upward and downward shifts in the in‐control process mean vector is demonstrated using two different datasets. [ABSTRACT FROM AUTHOR]

Existing multivariate cumulative sum (MCUSUM) control charts involve entire associated variables of a process to monitor variations in the mean vector. In this study, we have offered MCUSUM control charts with principal component method (PCM). The proposed MCUSUM control charts with PCM capture the whole process variations using fewer latent variables (principal components) while preserving as much data variability as possible. To show the significance of proposed MCUSUM control charts with PCM, various performance measures are considered including average run length, extra quadratic loss, relative average run length, and performance comparison index. Furthermore, performance measures are calculated through advanced Monte Carlo simulation method to explore the behavior of proposed MCUSUM control charts and to conduct comparative analysis with existing models. Results revealed that proposed MCUSUM control charts with PCM are efficient to detect variations timely by involving smaller number of principal components instead of considering entire associated variables. Also, proposed MCUSUM control charts have the ability to accommodate the features of existing control charts, which are illustrated as the special cases. Besides, to highlight the implementation mechanism and advantages of proposed MCUSUM control charts with PCM, a real‐life example from wind turbine process is included. [ABSTRACT FROM AUTHOR]

Memory‐type auxiliary‐information‐based (AIB) control charts are very effective in detecting small‐to‐moderate shifts in the process mean. In this study, we first develop a unique uniformly minimum variance unbiased estimator of the process mean that requires information on the study variable as well as on several correlated auxiliary variables. Then, based on this estimator, adaptive and nonadaptive CUSUM and EWMA charts are developed with either fixed or variable sampling interval for monitoring the process mean, namely, the multiple AIB (MAIB) charts. The proposed charts encompass existing charts with or without the auxiliary information. The run length characteristics of the proposed charts are computed with the Monte Carlo simulations when sampling from a multivariate normal distribution. Based on the run length comparisons, it is found that the MAIB charts are uniformly and substantially more sensitive than the AIB charts when monitoring the process mean. Real datasets are also considered to explain the implementation of the MAIB charts. [ABSTRACT FROM AUTHOR]

In the context of a disease outbreak detection, a prime interest is to only detect increases in the process mean. It is thus desirable to have a directionally sensitive multivariate chart that can effectively detect either increases or decreases in the process mean vector. In this paper, with a suitable transformation that truncates multivariate observations either above or below the process mean vector, we propose one‐sided and two one‐sided MCUSUM charts for monitoring the mean of a multivariate normal process. Among the proposed charts, the one‐sided MCUSUM charts are directionally sensitive, while the two one‐sided MCUSUM charts are directionally insensitive. In addition, the fast initial response feature is also incorporated into the proposed charts to enhance their sensitivities against initial process shifts. The run length characteristics of these control charts are computed with the Monte Carlo simulation. Based on the run length comparisons, it is found that the proposed charts are more sensitive than the existing charts when detecting moderate‐to‐large shifts in the process mean. The proposed charts are also applied on real datasets to support the theory. [ABSTRACT FROM AUTHOR]

The CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion–based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory. [ABSTRACT FROM AUTHOR]

An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided. [ABSTRACT FROM AUTHOR]

The coefficient of variation (CV) is an important quality characteristic when the process variance is a function of the process mean for a production process. In this paper, we develop an auxiliary information–based (AIB) estimator for estimating the squared CV, along with its approximated mean and variance. This estimator is then used to devise new one‐sided EWMA charts for monitoring the increases or decreases in the squared CV of a normal process, named the AIB‐EWMA CV charts. In addition, the sensitivities of these control charts are also enhanced with the fast initial response feature. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed CV charts. Based on detailed run length comparisons, it is found that the proposed AIB‐EWMA CV charts are uniformly and substantially better than the existing EWMA CV charts when detecting different kinds of upward/downward shifts in the squared CV. The proposed charts are also applied to a real dataset to support the proposed theory. [ABSTRACT FROM AUTHOR]

Control charts are popular monitoring tools in statistical process control toolkit. These are used to identify assignable causes in the process parameters (location and/or dispersion). These assignable causes result in a shift in the process parameter(s). The shift can be categorized into three sizes (small, moderate, and large). Memory control charts such as the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are effective for identifying small‐to‐moderate shift(s) in the process. Likewise, mixed memory control charts are useful for efficient process monitoring. In this study, we have proposed two new mixed memory control charts based on auxiliary information named MxMEC and MxMCE control charts to improve the efficiency of these mixed charts. The MxMEC chart is a merger of the auxiliary information based MxEWMA chart and the classical CUSUM chart. Likewise, the MxMCE chart integrates the auxiliary information based MxCUSUM with the classical EWMA chart. The proposed MxMEC and MxMCE charts are evaluated through famous performance measures including average run length, extra quadratic loss, relative average run length, and performance comparison index. The performance of the study proposals is compared with the existing counterparts such as the classical CUSUM and EWMA, MxCUSUM, MxEWMA, MEC, MCE, and runs rules‐based CUSUM charts. The comparisons revealed the superiority of the proposed charts against other competing charts particularly for small‐to‐moderate shifts in the process location. Finally, a real‐life data is used to show the implementation procedure of the proposed charts in practical situations. [ABSTRACT FROM AUTHOR]

This paper proposes two optimal control charts by using the generalized multiple dependent state (GMDS) plan to monitor the process mean. These charts make advantageous use of the ranked set sampling schemes and integrate them with the GMDS plan to improve the shift detection ability of the Shewhart‐type control charts. The proposed control charts have two pairs of control limits, inner and outer, which enables them to consider the current and previous sample information while making a decision about the process state. The run‐length profiles of the proposed charts are obtained through extensive Monte Carlo simulations. The individual and overall mean shift detection abilities of the proposed charts are compared with various competing control charts by using out‐of‐control average run length (ARL1) and the average extra quadratic loss (AEQL) as performance metrics. The comparison establishes the complete dominance of the proposed charting strategy. In the end, the practical implementation of the proposed charts is demonstrated by using a real data set related to the cement manufacturing industry. [ABSTRACT FROM AUTHOR]

Control charts are developed to make the specific quality measures for a successful production process and follow normal distribution behaviors. But some real‐life practices do not match such practices and exhibit some positively skewed behavior like lognormal distribution. The present study has considered this situation and proposed a monitoring control chart based on lognormal process variation using a repetitive sampling scheme. This concept proved better for detecting shifts as quickly as possible, and compared with the existing concept, results are elaborated through extensive tables. The average run lengths and standard deviations of the run lengths are being used as a performance evaluation measures and computed by using Monte Carlo simulations performed in R language. A real‐life situation has been discussed in the example section to strengthen the proposed control chart concept in a real‐life situation. [ABSTRACT FROM AUTHOR]

It is customary to increase the sensitivity of a control chart using an efficient estimator of the underlying process parameter which is being monitored. In this paper, using an auxiliary information‐based (AIB) mean estimator, we propose dual multivariate CUSUM (DMCUSUM) and mixed DMCUSUM (MDMCUSUM) charts, called the AIB‐DMCUSUM and AIB‐MDMCUSUM charts, with and without fast initial response features for monitoring the mean vector of a multivariate normally distributed process. The DMCUSUM chart combines two similar‐type multivariate CUSUM (MCUSUM) charts while the MDMCUSUM chart combines two different‐type MCUSUM charts, into a single chart. The objective of two multivariate subcharts in the DMCUSUM/MDMCUSUM chart is to simultaneously detect small‐to‐moderate and moderate‐to‐large shifts in the process mean vector. Monte Carlo simulations are used to compute the run length characteristics, including the average run length (ARL), extra quadratic loss, and integral of the relative ARL. Based on detailed run length comparisons, it turns out that the AIB‐DMCUSUM and AIB‐MDMCUSUM charts uniformly and substantially outperform the DMCUSUM and MDMCUSUM charts when detecting different sizes of shift in the process mean vector. A real dataset is used to explain the implementation of proposed AIB multivariate charts. [ABSTRACT FROM AUTHOR]