The Hotelling's T2 CONTROL chart, is the most widely used multivariate procedure for two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. Recently, the VARIABLE SAMPLING INTERVALS AND CONTROL LIMITS (VSICL) CONTROL scheme has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the fixed ratio SAMPLING (FRS) T2 CONTROL chart. Moreover, it is shown that the VSICL scheme is more economical than the classical one. This article studies the economic consequences of a new CONTROL scheme named VARIABLE SAMPLE SIZES, SAMPLING INTERVALS AND CONTROL LIMITS ((VSSICL)) in that the SAMPLE size n, SAMPLING interval h AND CONTROL limit k vary between minimum AND maximum values. We apply the cost model proposed by Costa AND Rahim (2001). This model considers the cost of false alarms, the cost of finding AND repairing an assignable cause, the cost of producing out of CONTROL items AND the cost of SAMPLING AND testing. Furthermore, we assume that the length of time that the process remains in CONTROL is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. Finally, the both VSICL AND (VSSICL) T2 CONTROL charts are compared with respect to the expected cost per unit time.

The CCC-r chart is developed based on cumulative count of a conforming (CCC) CONTROL chart that considers the cumulative number of items inspected until observing r nonconforming ones. Typically, the SAMPLEs obtained from the process are analyzed through 100% inspection to exploit the CCC-r chart. However, considering the inspection cost AND time would limit its implementation. In this paper, we investigate the performance of CCC-r chart with VARIABLE SAMPLING interval (CCC-rVSI chart). The efficiency of CCC-rVSI chart is compared with fixed SAMPLING interval (FSI) scheme of CCC-r chart (CCC-rFSI chart) AND CCCVSI chart. The comparison results show that CCC-rVSI chart is more efficient than the CCCVSI chart in reducing the average time to signal (ATS) AND also CCC-rVSI chart performs better than CCC-rFSI chart. In addition, some sensitivity analyses are performed to illustrate the effect of the input parameters on the performance of CCC-rVSI chart.

The familiar multivariate process monitoring AND CONTROL procedure is the Hotelling’s T2 CONTROL chart, a direct analog of the univariate shewhart  chart. But, its efficiency for detecting small to moderate shifts in the process mean is poor. To improve the power of chart, this paper presents the VARIABLE SAMPLING INTERVALS (VSI) scheme. It is assumed that the length of time the process remains in CONTROL has exponential distribution. The chart is modeled using Markov chains AND is optimized using genetic algorithm optimization method. The results show that the T2 chart with VARIABLE ratio SAMPLING scheme is quicker than the classical one in detecting almost all shifts in the process mean.

The CONTROL charts are graphical tools AND proven techniques to improve the performance of a process. Usually, the processes are not naturally CONTROLled, so the use of CONTROL charts will help to reduce the variability AND increase the stability of the process. In the traditional approach, CONTROL charts with fix SAMPLE size AND constant SAMPLING INTERVALS were used to identify the changes in the process. While, CONTROL charts can be examined from different statistical AND economical directions using different SAMPLING schemes for achieving a better result. In past studies, it has been shown that np CONTROL charts show better results in detecting shifts by using VARIABLE SAMPLING schemes but it is also important to consider how the cost of using VARIABLE SAMPLING schemes will be, since the cost of a process depends on the parameters of the CONTROL chart. In this paper, the economic-statistical design of np CONTROL chart with VARIABLE SAMPLE size AND SAMPLING interval (VSSI) is formulated AND then we compare AND analyze the resulted obtained with other schemes. Results show significant improvement in terms of economic AND statistical performance.

Today, quality improvement AND cost reduction are key factors for achieving business success, growth AND position. One of the primary tools for quality improvement AND cost reduction in online activities of statistical process CONTROL is CONTROL charts. As the need for monitoring several correlated quality characteristics is extensively growing, the use of multivariate CONTROL charts becomes more popular. Among these, the T2 CONTROL chart is the most popular due to many advantages. In this paper, the VARIABLE SAMPLING scheme is studied to increase the power of the fixed SAMPLING rate (FRS) T2 CONTROL chart to show small shifts. In this study, one of the parameters of T2CONTROL chart, e.g., the SAMPLE size, vary between three values, depending on the most recent T2 value.The design of T2 CONTROL chart with three VARIABLE SAMPLE SIZES (3VSS) from the statistical AND economic perspective has been investigated, when the shift in the process mean does not occur at the beginning but at some rANDom time in the future. Therefore, the Markov Chain approach used to develop the cost function. Then, the genetic algorithm (GA) is applied to search for the optimal values of the parameters of the3VSS CONTROL chart. Finally, numerical comparisons among FRS AND 3VSS schemes are made AND discussed.

The effect of measurement errors on adaptive AND non-adaptive CONTROL charts has been occasionally considered by researchers throughout the years. However, that effect on the VARIABLE SAMPLE size AND SAMPLING interval (VSSI) X CONTROL charts has not so far been investigated. In this paper, we evaluate the effect of measurement errors on the VSSI X CONTROL charts. After a model development, the effect of measurement errors AND multiple measurements on the performance of VSSI scheme are evaluated in terms of the out-of-CONTROL average time to signal (ATS) criterion, which is obtained using a Markov Chain approach. At last, a real case is presented to show the application of the proposed scheme.

In this paper, a VSS scheme with three adaptive SAMPLE SIZES is proposed. The model is constructed based on the Markov chain approach AND optimized using genetic algorithm optimization method. Finally, a comparison between the proposed VSS scheme AND the one that is proposed by Faraz AND Moghadam (2008) is made to investigate whether more improvements can be achieved by applying three adaptive SAMPLE SIZES or two ones are adequate.

Postmodernism represents skepticism toward metanarratives AND universal ideologies that dominated the modernist era. The study focuses on three key postmodernist concepts - alternative assessment, process syllabi, AND self-directed learning. Alternative assessment emphaSIZES evaluating the learning process over summative testing. Process syllabi focus on the learning experience rather than rigid outcomes. Self-directed learning enables student responsibility in setting learning goals AND processes. This paper examined the effects of postmodernist educational concepts on improving Iranian EFL learners’ autonomy. A quasi-experimental pre-test/post-test design was utilized with 60 intermediate level Iranian EFL students divided into an experimental AND CONTROL group (n=30 each). The experimental group received instruction utilizing the three postmodernist concepts over 14 weeks, while the CONTROL group received traditional modernist instruction. Autonomy was measured using a validated questionnaire before AND after the intervention. The results showed the experimental group demonstrated significant increases in autonomy compared to the CONTROL group. Paired SAMPLE t-tests revealed significant differences between pre-test AND post-test autonomy for the experimental group across all three postmodern concepts - alternative assessment, process syllabi, AND self-directed learning. This suggests postmodernist concepts that decentralize instruction AND emphasize student process over outcomes can enhance Iranian EFL learners’ self-direction AND responsibility for language acquisition. The study implies EFL syllabus designers AND instruction should transition to postmodern models centered on individualized assessment, flexible syllabi, AND student-guided learning to boost autonomy. Further research can expAND SAMPLE SIZES AND explore additional postmodernist concepts across diverse demographics.

Nonparametric CONTROL chart based on signed-rank statistic is used for detecting changes in mean (median). Although the Sign-Rank (SR) chart is more efficient under heavy-tailed distributions (double exponential AND Cauchy) but the performance of this chart is very inappropriate in light-tailed distributions (uniform AND normal). In this paper, signed-rank chart is developed with VARIABLE SAMPLING interval. The performance of signed-rank chart with VARIABLE SAMPLING interval (VSI-SR) is compared to signed-rank chart with fixed SAMPLING interval (FSI-SR) AND `X chart. The numerical results demonstrated the VSI-SR chart is better from the FSI-SR chart. Also the VSI-SR chart is more efficient from `X chart in heavy-tailed distributions AND some of changes under normal light-tailed distribution.

The performance of an X-bar chart is usually studied under the assumption that the process stANDard deviation is well estimated AND does not change. This is, of course, not always the case in practice AND X-bar charts are not robust against errors in estimating the process stANDard deviation or changing stANDard deviation. In this paper, the use of an exponentially weighted moving average (EWMA) t chart with VARIABLE SAMPLING INTERVALS to monitor the process mean is discussed. We have determined the optimal CONTROL LIMITS for the VSI EWMA t chart so that the chart has the desired robustness property against errors in estimating the process stANDard deviation or changing stANDard deviation. Performance of the proposed chart is compared with similar charts using the Markov chain approach AND simulation studies.