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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 coefficient of variation (CV) is one of the most important quality characteristics in industrial applications. There have been some control charts for monitoring this dimensionless and normalized characteristic. This paper presents three double exponentially weighted moving average (DEWMA) charts for monitoring the CV. Many numerical simulations are performed and the results are given in several tables to show the properties of the proposed DEWMA CV charts. Through comparisons with other existing exponentially weighted moving average (EWMA) CV charts using the average run length (ARL) metric, it is shown that the proposed DEWMA CV charts perform better than the existing EWMA CV charts for small shifts, especially when the smoothing parameter increases. In addition, a detailed comparison among the proposed three DEWMA CV charts is also presented. A real date example from industry is used to show the implementation of the proposed charts. [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]

The coefficient of variation (CV) chart is widely used in the process where the standard deviation is proportional to the mean. In this work, two separate one-sided triple exponentially weighted moving average control charts are proposed to monitor the CV squared (denoted as TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 chart). By adding the variable sampling interval (VSI) feature to the proposed - $ {\mathrm{\gamma }^2} $ γ 2 charts, the VSI TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts are further proposed to improve the performance of the TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts. Through extensive Monte Carlo simulations, the zero-state and steady-state run length (RL) performances are presented. The comparisons with the existing CV charts, based on several run length metrics show the superiority of the proposed charts, especially for small shifts. Moreover, the overall measure, expected ARL (EARL), also shows the outperformance of the $ {\mathrm{\gamma }^2} $ γ 2 charts. In addition, based on the average time to signal (ATS) and adjusted ATS (AATS), it is shown that the VSI strategy makes the TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts detect the shifts more quickly. An illustrative example from the sintering process is finally provided to display the application of the proposed charts. [ABSTRACT FROM AUTHOR]

This paper examines how the Durkheimian approach to the 'ideal' delineates a possible way of straddling the dilemma between the normative orientation of 'powerful knowledge' accounts and the critical orientation of 'knowledge of the powerful' accounts. It argues that the normative aims are embedded in the fabrics of the sociological description with which the Durkheimian notion of 'elementary form' is concerned. To see where this enterprise can lead, this paper turns to the sociology of education of Bourdieu and Bernstein. Both draw on Durkheim's writings on primitive classifications in education and society, working towards uncovering the regularities of the world of knowledge classifications. Keeping in line with Bourdieu and Bernstein, this paper argues that one has to make the same refusal to the advocates of an abstract ideal of educational knowledge that is dissociated from its social conditions of historical realization in pedagogic contexts, and to the advocates of a cynical relativism of ideal that rejects any necessities socially established. [ABSTRACT FROM AUTHOR]