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To improve the detecting abilities of upward and downward parameter changes in high‐quality process, two combined schemes by integrating memory‐type, that is, exponentially weighted moving average (EWMA) or cumulative sum (CUSUM), and memoryless, that is, Shewhart, are proposed for monitoring the time between events (TBE), which is modeled as an exponential distributed variable. A Monte Carlo simulation method is employed to obtain the Run Length (RL$RL$) properties, that is average run length (ARL$ARL$), of the proposed schemes for different parameter settings. The nearly optimal monitoring parameter combinations under different change size are obtained by minimizing the out‐of‐control ARL$ARL$ with the satisfied in‐control ARL$ARL$. Using the designed parameters, the ARL$ARL$ performance of the proposed monitoring schemes is compared with the existing EWMA and CUSUM TBE. The results show that the proposed combined Shewhart–EWMA or Shewhart–CUSUM TBE generally perform better than the corresponding EWMA or CUSUM TBE for large changes and they also show better performance than the Shewhart TBE for small changes. Finally, a real dataset of organic light‐emitting diode (OLED) failure time from Sumsung company is employed to indicate the usage and implementation of combined TBE schemes. [ABSTRACT FROM AUTHOR]

Monitoring the ratio of two normal random variables, which is usually denoted as RZ, is one of the most important directions in statistical process control (SPC). In production scenarios, when the product specification is related to the relative ratio of two components in a mixture, or when the ratio represents a property of the product, or the difference between a product's quality measurement before and after an operation (such as a chemical reaction), the product quality can be improved by applying monitoring schemes for RZ. To further enhance the sensitivity of traditional RZ schemes in detecting process changes, especially small and moderate ones, this paper proposes an improved exponentially weighted moving average (IEWMA) monitoring scheme. The run length (RL) distribution of the proposed IEWMA‐RZ scheme is obtained by using the Monte‐Carlo (MC) simulation. The superiority of the proposed monitoring scheme is shown by comparing with the existing EWMA‐RZ scheme. [ABSTRACT FROM AUTHOR]

The adaptive exponential weighted moving average (AEWMA) monitoring technique has recently received increasing attention as a robust alternative requiring no knowledge of the actual shift magnitudes. In this paper, we develop a discrete state nonparametric AEWMA chart based on the Wilcoxon signed‐rank statistics. The major characteristic of this monitoring scheme is that it takes into account the discrete nature in terms of the statistics being used as well as the chart structure design. Moreover, an accurate evaluation of the chart's statistical properties is provided using an appropriate Markov chain approach. Simulation results show that this AEWMA signed‐rank scheme performs robustly across a diverse variety of distributions, and it can also provide an effective performance for detecting both small and large shifts. Finally, a real data example is cited for showing practical implications of our monitoring scheme. [ABSTRACT FROM AUTHOR]

Many control charts have been developed for monitoring the time between adverse events (TBE) to improve the quality of processes. In practice, the decrease in the TBE mean usually implies a deterioration of the process, while the increase indicates an improvement of the process. In this paper, an improved lower‐sided EWMA control chart is developed based on the power of the TBE observations to detect the decreasing TBE mean. Furthermore, an optimization model is developed to design the proposed EWMA chart, including the determination of the power and smoothing parameters to ensure the best overall performance. Simulation studies show the proposed EWMA chart is best among several charts for monitoring small shifts, and performs better than most alternative methods in detecting moderate shifts. Moreover, the in‐control performance of the proposed method with parameter estimation is studied via many numerical simulations. Finally, a real data example is given to further illustrate the application and sensitiveness of the improved EWMA chart. [ABSTRACT FROM AUTHOR]

The usual practice in Statistical Process Monitoring (SPM) techniques assumes that the data distribution is known and the related parameters are accurately estimated. In practice, the underlying distribution and its parameters are rarely known, and control charts need to be constructed with parameters being estimated. Such issues have recently received an increasing attention in evaluating the properties of both parametric and nonparametric charts. However, the same study is seldom conducted for the control charts based on the data‐driven tools. In this paper, we investigated the in‐control performance of a nonparametric control chart based on the Support Vector Data Description (SVDD) theory. More specifically, we discuss the conditional effect of the training Phase‐I samples on the Phase‐II efficiency when different distributions are considered. Simulation results show that the conditional performance of the SVDD‐based chart can be strongly affected by the Phase‐I samples. It this situation, adjusted control limits with a specific number of available training sample is suggested. [ABSTRACT FROM AUTHOR]

Traditional robust parameter design (RPD) is a useful tool for offline quality improvement, which is mainly applied to physical experiment. If the optimal setting for controllable factors is not desirable, the offline PRD cannot utilize the new‐obtained sample to update the optimal setting. In this paper, the offline RPD is extended to online PRD; and the background for RPD is enlarged from physical experiment to computer experiment, where the Kriging model is typically utilized to create a single response surface. In the process of building the incremental Kriging (IKriging), if the optimal setting is not desirable, it can be regarded as a new‐arrival sample with the online measurements of the noise factors to update the Kriging model. While constructing the response surface with the IKriging, it is updated according to the new‐arrival sample rather than the all (n+1) samples, substantially enhancing the efficiency of constructing the response surface. In the proposed IKriging based online RPD strategy, an appropriate algorithm is designed to numerically get the next optimal setting for the controllable factors, and a criterion is established to determine the next site for the noise factors to observe the response. By employing the IKriging model, the response surface can be online constructed efficiently, and furthermore the optimal setting for the controllable factor can be obtained immediately, meeting the requirement of online quality adjustment. The proposed methodology is confirmed using five examples, which illustrate that the underlying optimal settings can be found by utilizing the proposed IKriging based online RPD strategy for the computer experiment, and the IKriging based RPD method is preferable to existing online robust design methods. [ABSTRACT FROM AUTHOR]

Several scholarly works intrinsically assume that the frequency and magnitude of events are two independent variables. However, in many practical situations, it is necessary to consider the dependence between these two characteristics of events. In this paper, two Smith–Adelfang–Tubbs (SAT) models, namely, the four‐ and the five‐parameter bivariate Gamma distributions (BGD) with a particular dependency parameter, are first reviewed. Then, a synthetic multivariate exponentially weighted moving average (synthetic MEWMA, or SMEWMA) type scheme is proposed to monitor the individual BGD observations (subgroups of size one) generated from those two specific SAT models. The Monte‐Carlo simulation method is developed to evaluate the run length (RL$\mathrm{RL}$) properties of the recommended SMEWMA BGD scheme in both the zero‐state and the steady‐state cases. Furthermore, we discuss the average run length (ARL) of the proposed SMEWMA BGD scheme with different design parameters, and then compare both the zero‐state and the steady‐state out‐of‐control ARL performances of the recommended SMEWMA BGD scheme with those of the classic MEWMA chart, the paired individual Gamma chart, and the MCUSUM chart. Simulation results suggest that the overall performance of the recommended SMEWMA BGD scheme is superior to the other comparative schemes. Finally, the implementation of the proposed SMEWMA BGD scheme is illustrated with a natural flood event dataset. [ABSTRACT FROM AUTHOR]

The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one‐ and two‐sided performance of a new adaptive EWMA (exponentially weighted moving average)‐type chart for monitoring Poisson count data. An appropriate discrete‐state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed. [ABSTRACT FROM AUTHOR]

As a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high‐quality processes. Considering both known and estimated parameter cases, the one‐sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run length (RL) distribution of the one‐sided exponential CUSUM charts is skewed and it also changes with the mean shift size and the number of Phase I samples used to estimate the process parameter, the median run length (MRL) is employed as a good alternative performance measure for the charts. The optimal design procedures based on MRL of the one‐sided exponential CUSUM charts with known and estimated parameters are discussed. By comparing the MRL performance of the chart with known parameters with the one of the chart with estimated parameters, we investigate the effect of estimated process parameters on the properties of the chart. Finally, an application is illustrated to show the implementation of the chart. [ABSTRACT FROM AUTHOR]

Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice. [ABSTRACT FROM AUTHOR]

Synthetic‐type charts are efficient tools for process monitoring. They are easy to design and implement in practice. The properties of these charts are usually evaluated under the assumption of known process parameters. This assumption is sometimes violated in practice, and process parameters have to be estimated from different phase I data sets collected by different practitioners. This fact causes the between‐practitioners variability among the properties of the synthetic‐type charts designed for each practitioner. In fact, the shape of the run length distribution of the synthetic‐type charts changes with the mean shift size. As a good alternative, the median run length (MRL) metric is argued to evaluate the properties of different control charts. In this paper, the MRL is used as a measure of the synthetic X¯ chart's performance, and the conditional MRL properties of the synthetic X¯ chart with unknown process parameters are investigated. Both the average MRL (AMRL) and the standard deviation of MRL (SDMRL) are used together to investigate the chart's properties when the process parameters are unknown. If the available number of phase I samples is not large enough to reduce the variability of the in‐control MRL values to an acceptable level, a bootstrap‐type approach is suggested to adjust the control limits of the synthetic X¯ chart and to further prevent many unwanted lower in‐control MRL values. [ABSTRACT FROM AUTHOR]

Space‐filling and projective properties are probably the two most important features in computer experiment. The existing research works have tried to develop different kinds of sequential Latin hypercube design (LHD) to meet these two properties. However, most if not all of them cannot simultaneously ensure these two properties in their versions of sequential LHD. In this paper, we propose a novel sequential LHD that can simultaneously meet the space‐filling and the projective properties at each stage. A search algorithm is employed to find how many design points should be added in each stage to ensure the projective property; and the "Maximin" criterion is used to meet the space‐filling property. Two kinds of examples for low dimension and higher dimension are presented to illustrate how these sequential sampling processes are realized. The proposed method can be applied to the areas where computationally expensive simulations are involved. [ABSTRACT FROM AUTHOR]

In quality control applications, the control chart is a powerful tool but its performance is adversely affected by the contamination from either the inspector or the measuring device leading to measurement errors. In this paper, we investigate the performance of the AEWMA median chart with measurement errors, and a methodology is proposed to obtain the optimal parameters by considering a linearly covariate error model. Several figures and tables show that, with the existence of measurement errors, the efficiency of the AEWMA median chart can be strongly affected, but this negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the Shewhart and the classical EWMA schemes confirm the superiority of the AEWMA scheme for detecting a wide range of shifts in the case of precise and imprecise data. An example is provided to illustrate the use of the AEWMA median chart with measurement errors. [ABSTRACT FROM AUTHOR]

Abstract: Control charts are usually investigated under the assumption of known process parameters. In practice, however, the process parameters are rarely known and they have to be estimated from different Phase I data sets. The properties of control charts with estimated parameters are usually investigated with the unconditional average of the average run length. Control chart's performance is known to vary among practitioners because of the use of different Phase I data sets. Considering the between‐practitioners variability in control chart's performance, the standard deviation of the average run length is developed to reevaluate the properties of the synthetic X ¯ chart with estimated parameters. Because of the limited amount of Phase I data in practice, the bootstrap method is used as a good adjustment technique for the synthetic X ¯ chart's parameters. [ABSTRACT FROM AUTHOR]

Abstract: The AEWMA chart is an Adaptive EWMA (Exponentially Weighted Moving Average)–type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been studied under the assumption that there is no measurement error in the quality characteristic. In this paper, we investigate the performance of the AEWMA chart when measurement errors exist using a linearly covariate error model. The presence of measurement errors with a linearly increasing measurement error standard deviation is also investigated. It turns out that, with the existence of measurement errors, the efficiency of the AEWMA chart can be strongly affected, and the negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the classical EWMA scheme confirm the superiority of the AEWMA scheme in detecting a wide range of shifts even in the presence of measurement errors. An example is provided to illustrate the use of the AEWMA chart with measurement errors. [ABSTRACT FROM AUTHOR]

A common assumption for most control charts is the fact that the process parameters are supposed to be known or accurately estimated from Phase I samples. But, in practice, this is not a realistic assumption and the process parameters are usually estimated from a very limited number of samples that, in addition, may contain some outliers. Recently, a median chart with estimated parameters has been proposed to overcome these issues and it has been investigated in terms of the unconditional Average Run Length (ARL). As this median chart with estimated parameters does not take the 'Phase I between-practitioners' variability into account, in this paper, we suggest to revisit it using the Standard Deviation of the ARL as a measure of performance. The results show that this Standard Deviation of the ARL-based median chart actually requires a much larger amount of Phase I data than previously recommended to sufficiently reduce the variation in the chart performance. Due to the practical limitation of the number of the Phase I data, the bootstrap method is recommended as a good alternative approach to define new dedicated control chart parameters. [ABSTRACT FROM AUTHOR]

The AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart in terms of the A T S(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the A T S values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts. [ABSTRACT FROM AUTHOR]

The variable sample size (VSS) [ABSTRACT FROM AUTHOR]

Measurement errors often exist in quality control applications. In this paper, the performance of the synthetic ... chart is investigated when measurement errors exist using a linearly covariate error model. It is shown that the performance of the synthetic ... chart is significantly affected in the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of synthetic N X chart is also investigated in this paper. An example is provided in order to illustrate the application of the synthetic ... chart with measurement errors. [ABSTRACT FROM AUTHOR]