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In many industrial manufacturing processes, the quality of products can depend on the relative amount between two quality characteristics X and Y. Often, this calls for the on-line monitoring of the ratio Z = X / Y as a quality characteristic itself by means of a control chart. A large number of control charts monitoring the ratio have been investigated in the literature under the assumption of independent normal observations of the two quality characteristics. In practice, due to the high frequency in sensor data collection, both autocorrelation and cross-correlation between consecutive observations can exist for X and Y and should be modelled to protect against the false alarm rate inflation when implementing a control chart for monitoring the ratio Z = X / Y. In this paper, we tackle this problem by investigating the performance of the Phase II Shewhart-type RZ control chart monitoring the ratio of two normal variables whose relationship is captured by a bivariate time series autoregressive model VAR(1), which can also account for the cross-correlation between the two quality characteristics. With the numerical study, we discuss how the design and the statistical performance of the Shewhart-type RZ control chart change with the VAR(1) model's parameters. We also provide an example to illustrate the use of the Shewhart-type RZ control chart with bivariate time series of observations in a furnace process. [ABSTRACT FROM AUTHOR]

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]

Statistical process monitoring (SPM) offers an important toolkit used to monitor the stability of a process to improve the quality of outputs and/or services. More often, the design of control charts requires the estimation of the probability density function that involves selecting a common distribution that facilitates the estimation of the process parameters. The Bayesian approach is one of the most efficient techniques used in such instances. It incorporates informative and non-informative priors, i.e., uses information on past data and charting structures, to estimate parameters more efficiently than classical approaches. Bayesian approaches reduce the total expected cost over a finite horizon or the long-run expected average cost. This paper introduces a new Bayesian exponentially weighted moving average (EWMA) monitoring scheme for long runs based on an ARMA-GARCH model. The properties of the new monitoring scheme are investigated in terms of the run-length distribution. A case study on monitoring the USD to ZAR exchange rate is provided using the proposed Bayesian ARMA-GARCH EWMA monitoring scheme. [ABSTRACT FROM AUTHOR]

The primary aim of this research is to propose a revised triple sampling (TS) X ¯ chart, where the derivations of new formulae for computing the average run length of the triple sampling (TS) X ¯ chart correctly are provided. The secondary aim is to develop the revised TS X ¯ chart with estimated process parameters. The revised TS X ¯ charts are compared with the double sampling (DS) X ¯ , two stage adaptive sample size (AS2) X ¯ and three stage adaptive sample size (AS3) X ¯ charts when process parameters are known and estimated using the average run length (ARL), average number of observations to signal (ANOS), average of the average run lengths (AARL), standard deviation of the average run lengths (SDARL), average of the average number of observations to signal (AANOS) and standard deviation of the average number of observations to signal (SDANOS) criteria, where the revised TS X ¯ charts are found to be superior. Additionally, a table giving the minimum number of Phase-I samples for estimating the process mean so that the revised TS X ¯ chart with estimated process parameters has the desired in-control AARL and AANOS performances is provided. [ABSTRACT FROM AUTHOR]

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the X ¯ chart) and, for this reason, practitioners often compensate it by supplementing them with an EWMA (Exponentially Weighted Moving Average) scheme. However, because of the discrete nature of count data, it is unfortunately impossible to compute exactly and accurately (by means of Markov chain of integral equation methods) the run length (RL) properties, such as its mean (ARL) and its standard deviation (SDRL) of these EWMA attribute control charts and, consequently, it is impossible to efficiently design them in order to minimize some out-of-control characteristics. For this reason, we propose in this paper a dedicated approach called "continuousify" method which, coupled with a classical Markov chain technique, allows to compute the RL properties of any EWMA attribute control chart in a reliable way. A numerical comparison shows that the RL properties obtained by using the proposed "continuousify" approach are very much alike to the ones calculated via simulation and without the "continuousify" approach. Illustrative examples are also provided to show how the proposed method can be implemented in practice. [ABSTRACT FROM AUTHOR]

Adapted from the acceptance sampling field, the double sampling monitoring schemes implement a two-stage strategy to decide whether the process being monitored is in-control or out-of-control. That is, a master sample is split into two separate subgroup samples, with the first subgroup sample used in the first stage and, depending on which type of double sampling method is used, either only the second or the combined first and second, subgroup sample(s) are used in the second stage. This strategy has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations. For these reasons, it has received some attention in the statistical process monitoring (SPM) literature and, in this review paper, all 92 existing publications on the basic double sampling monitoring schemes and other different schemes that are integrated with the basic double sampling schemes are reviewed. The double sampling schemes are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Finally, concluding remarks and some directions for future research ideas are given. [ABSTRACT FROM AUTHOR]

The EWMA Sign control chart is a distribution-free scheme used for monitoring shifts in the location parameter during process monitoring. In this work, we propose a modified Phase II EWMA chart based on a general Sign statistic, capable of monitoring shifts in the process variability. Regarding the determination of the proposed chart's in- and out-of-control Run Length properties, Markov chain methods are used in combination with a continuous transformation of the suggested general Sign statistic. Our results show the power of the proposed method regarding the proposed chart's exact Run Length properties and its efficiency in detecting shifts in the process variability. [ABSTRACT FROM AUTHOR]

Distribution-free control charts are an efficient quality monitoring tool to inspect lots of parts manufactured within a finite production horizon. In this work, the performance of the Exponentially Weighted Moving Average chart based on the Wilcoxon signed rank statistic is investigated for on-line monitoring of finite production runs. The chart's on-target performance is evaluated through a specific non-homogeneous Markov chain model under different process scenarios. A numerical analysis is conducted for determining its optimal design and a performance comparison with other available schemes is presented for different symmetric distributions of observations. Finally, an illustrative example is presented to show a practical implementation of the investigated chart. [ABSTRACT FROM AUTHOR]