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When the direction of a potential mean shift can be anticipated, the one-sided exponentially weighted moving average (EWMA) $ \bar {X} $ X ¯ control chart using the truncation method (namely, the one-sided TEWMA $ \bar {X} $ X ¯ chart) is more efficient than those conventional one- and two-sided EWMA $ \bar {X} $ X ¯ schemes for process monitoring. Although attractive, there are no studies on designing the one-sided TEWMA $ \bar {X} $ X ¯ chart by taking measurement errors into account. In this context, we investigate the effect of measurement errors on the performance of the one-sided TEWMA $ \bar {X} $ X ¯ chart based on the linear covariate error model. Additionally, a Markov chain model is established to evaluate the run length properties of the scheme in the presence of measurement errors. Then, an optimal design procedure is developed for searching the optimal design parameters of the scheme. Based on these mentioned studies, several tables and figures are presented to evaluate the detecting performance of the scheme under different parameters of the linear covariate error model, and then a conventional one-sided EWMA $ \bar {X} $ X ¯ chart with reflecting boundary is introduced to further study the effect of the presence and absence of measurement errors on control chart comparison studies. Simulation results show that although the detecting performance of the proposed scheme is significantly affected by measurement errors, its performance is still superior to the classic competing chart under the same comparison conditions. Finally, an illustrative example is given to show the implementation of the recommended scheme. [ABSTRACT FROM AUTHOR]

Traditional process monitoring control charts (CCs) focused on sampling methods using fixed sampling intervals ( $ \mathrm {FSI} $ FSI s). The variable sampling intervals ( $ \mathrm {VSI} $ VSI s) scheme is receiving increasing attention, in which the sampling interval ( $ \mathrm {SI} $ SI ) length varies according to the process monitoring statistics. A shorter $ \mathrm {SI} $ SI is considered when the process quality indicates the possibility of an out-of-control (OOC) situation; otherwise, a longer $ \mathrm {SI} $ SI is preferred. The $ \mathrm {VSI} $ VSI multivariate exponentially moving average for compositional data ( $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa ) CC based on a coordinate representation using isometric log-ratio ( $ \operatorname {ilr} $ ilr) transformation is proposed in this study. A methodology is proposed to obtain the optimal parameters by considering the zero-state ( $ \mathrm {ZS} $ ZS ) average time to signal ( $ \mathrm {ZATS} $ ZATS ) and the steady-state (SS) average time to signal ( $ \mathrm {SATS} $ SATS ). The statistical performance of the proposed CC is evaluated based on a continuous-time Markov chain ( $ \mathrm {CTMC} $ CTMC ) method for both cases, the $ \mathrm {ZS} $ ZS and the SS using a fixed value of in-control (IC) $ \mathrm {ATS}_0 $ ATS 0 . Simulation results demonstrate that the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC has significantly decreased the OOC average time to signal ( $ \mathrm {ATS} $ ATS ) than the $ \mathrm {FSI}\,\mathrm {MEWMA}\,\mathrm {CoDa} $ FSI MEWMA CoDa CC. Moreover, it is found that the number of variables (d) has a negative impact on the $ \mathrm {ATS} $ ATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC, and the subgroup size (n) has a mildly positive impact on the $ \mathrm {ATS} $ ATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC. At the same time, the $ \mathrm {SATS} $ SATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC is less than the $ \mathrm {ZATS} $ ZATS of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC for all the values of n and d. The proposed $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC under steady-State performs effectively compared to its competitors, such as the $ \mathrm {FSI} $ FSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC, the $ \mathrm {VSI} $ VSI - $ T^2\,\mathrm {CoDa} $ T 2 CoDa CC and the $ \mathrm {FSI} $ FSI - $ T^2\,\mathrm {CoDa} $ T 2 CoDa CC. An example of an industrial problem from a plant in Europe is also given to study the statistical significance of the $ \mathrm {VSI} $ VSI - $ \mathrm {MEWMA}\,\mathrm {CoDa} $ MEWMA CoDa CC. [ABSTRACT FROM AUTHOR]

Exponentially weighted moving average (EWMA) control charts for time-between-events (TBE) are commonly suggested to monitor high-quality processes for the early detection of process deteriorations. In this study, an enhanced one-sided EWMA TBE scheme is developed for rapid detection of increases or decreases in the process mean. The use of the truncation method helps to improve the sensitivity of the proposed scheme in the process mean detection. Moreover, by taking the effects of parameter estimation into account, the proposed scheme with estimated parameters is also investigated. Both the average run length (ARL) and standard deviation of run length (SDRL) performances of the proposed scheme with known and estimated parameters are studied using the Markov chain method, respectively. Furthermore, an optimal design procedure is developed for the recommended one-sided EWMA TBE chart based on ARL. Numerical results show that the proposed optimal one-sided EWMA TBE chart is more sensitive than the existing optimal one-sided exponential EWMA chart in monitoring both upward and downward mean shifts. Meanwhile, it also performs better than the existing comparative scheme in resisting the effect of parameter estimation. Finally, two illustrative examples are considered to show the implementation of the proposed scheme for simulated and real datasets. [ABSTRACT FROM AUTHOR]

One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) X ˉ scheme recommended in this paper is a control chart that combines a Shewhart X ˉ scheme and a new one-sided EWMA X ˉ scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The truncation method used in this paper helps to improve the sensitivity of the recommended scheme for detecting both small and large mean shifts simultaneously. To further improve the detection efficiency of the recommended scheme, we also suggest integrating a variable sampling interval (VSI) feature into the recommended scheme. Markov chain models are established to analyze the run length (RL) properties of the recommended scheme in both the zero-state and the steady-state cases. Comparison results show that the recommended one-sided ATEWMA X ˉ scheme works better than the conventional adaptive EWMA (AEWMA) X ˉ chart and the improved one-sided EWMA X ˉ chart in detecting a wide range of mean shifts. Finally, a numerical example is presented to illustrate the usage of the proposed one-sided ATEWMA X ˉ scheme for detecting process mean shifts. [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]

Exponential type charts are useful tools to monitor the time between events in high-quality processes with a low defect rate. Most studies on exponential charts are designed with the average run length (ARL) metric. The only use of ARL in the design of control charts is sometimes criticized because the shape of the run length (RL) distribution of control charts changes with the shift size. In fact, the RL distribution of the exponential exponentially weighted moving average (EWMA) chart is skewed, especially when the process is in-control. Hence, the median run length (MRL) serves as a more meaningful indicator. Moreover, in some situations, the shift size in the process is unknown in advance. Under this case, the expected median run length (EMRL) can be used as the metric. In this paper, the RL properties of both the upper- and lower-sided exponential EWMA charts are studied through a Markov chain approach. Two optimal design procedures are developed for one-sided exponential EWMA charts based on the MRL and EMRL, respectively. The choices of reflecting boundaries for one-sided exponential EWMA charts are discussed through many numerical studies. The MRL and EMRL performances of the one-sided exponential EWMA charts are investigated. [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]

The Adaptive Exponentially Weighted Moving Average (AEWMA) chart is known to combine the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been investigated under the assumptions that the data are free from outliers and the chart's parameters are known or can be accurately estimated from in-control historical samples. However, there are many situations where the process parameters (a) are estimated from a very limited number of samples (b) they can potentially contain unexpected outliers. Therefore, in this article, we develop an AEWMA median chart with known and estimated parameters to monitor the mean value of a normal process. Taking the 'Phase I between-practitioners variability' into account, both the Average of () and the Standard Deviation of the () are used to evaluate the conditional effect of the number of Phase I samples on the Phase II performance. Using a Markov Chain approach, it is shown that (a) the performance of the proposed AEWMA median chart is seriously affected when parameters are estimated compared with the known-parameter case, and (b) it requires a large amount of Phase I data to reduce the variation in the in-control distribution up to a reasonable level. Therefore, a bootstrap-based design approach is applied here and, the performance of the AEWMA median chart is compared with that of the existing Shewhart and EWMA median charts. The comparative results show that the AEWMA median chart represents a good alternative to achieve a reasonable balance for various shift sizes. [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]