Evaluation of Variable Parameter MCV Control Chart in Downward Process Shifts

Previous studies revealed that the coefficient of variation (CV) is important in ensuring process quality, especially for monitoring a process where its process mean and variance are highly correlated. The fact that almost all industrial process monitoring involves a minimum of two or more related quality characteristics being monitored simultaneously. The existing adaptive charts for monitoring the multivariate CV are focused on detecting upward process shifts. The downward process monitoring is crucial since it shows process improvement. Very little research works are available on the downward adaptive multivariate CV chart. This makes it difficult for the quality engineer who wishes to implement the adaptive multivariate CV chart on the downward process monitoring. Therefore, this paper filled the research gap by proposing a downward variable parameter chart for the multivariate coefficient of variation. The performance measures of the proposed charts are derived based on the Markov-chain approach. Numerical comparisons between the proposed and existing charts have been made, in terms of the average time to signal criterion. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate downward process shifts

The Design of GLR Control Chart for Monitoring the Geometric Observations Using Sequential Sampling Scheme

The control charts’ design is focused on system forecasting which is important in mathematics and statistics; these techniques are commonly employed in manufacturing industries. The need for a control chart that can conceptualize and identify the symmetric or asymmetric structure of the monitoring phase with more than one aspect of the standard attribute is a necessity of industries. The generalized likelihood ratio (GLR) chart is a well-known method to track both the decrease and increase in the mechanism effectively. A control chart, termed as a GLR control chart, is established in this article, focusing on a sequential sampling scheme (the SS GLR chart) to evaluate the geometrically distributed process parameter. The SS GLR chart statistic is examined on a window of past samples. In contexts of the steady-state average time to signal, the output of the SS GLR control chart is analyzed and compared with the non-sequential geometric GLR chart and the cumulative sum (CUSUM) charts. In this article, the optimum parameter options are presented, and regression equations are established to calculate the SS GLR chart limits.

A combined variable sampling interval and double sampling control chart with auxiliary information for the process mean

In recent years, the suitable use of auxiliary information technique in control charts has shown an improved run length performance compared to control charts that do not have this feature. This article proposes a combined variable sampling interval (VSI) and double sampling (DS) chart using the auxiliary information (AI) technique (called VSIDS-AI chart, hereafter). The plotting-statistic of the VSIDS-AI chart requires information from both the study and auxiliary variables to efficiently detect process mean shifts. The charting statistics, optimal design and performance assessment of the VSIDS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) are considered as the performance measures. The ssATS and ssEATS results of the VSIDS-AI chart are compared with those of the DS AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The results of comparison show that the VSIDS-AI chart outperforms the charts under comparison for all shift sizes, except the EWMA-AI and RS-AI charts for small shift sizes. An illustrative example is provided to demonstrate the implementation of the VSIDS-AI chart.

Variable sampling interval run sum X‾ chart with estimated process parameters

The X‾ type control chart is often evaluated by assuming the process parameters are known. However, the exact values of process parameters are hardly known and thus Phase-I dataset is needed to estimate them. In this paper, the performance of the variable sampling interval run sum X‾ chart with estimated process parameters is evaluated by using the performance measure of the average of the average time to signal (AATS) and the optimal design of the proposed chart in minimizing the out-of-control AATS is developed. The performance measure of the standard deviation of the average time to signal (SDATS) is then used to identify the number of Phase-I samples (w) needed to have an in-control AATS performance close to its known process parameter case. Results show that large w is needed to minimize the performance gap between known and unknown process parameters cases of the VSI RS X‾ chart.

Performance of adaptive np-chart with estimated parameter

Purpose – The purpose of this paper is to compare the performances of np-VP control chart with estimated parameter to the np-VP control chart with known parameter using average time-to-signal (ATS), standard deviation of the time-to-signal (SDTS), and average number of observations to signal (ANOS) as performance measures. Design/methodology/approach – The approach used in this study is probabilistic in which the expected values of performance measures are calculated using probabilities of different estimators used to estimate process parameter. Findings – Numerical results indicate different performances for the np-VP control chart in known and estimated parameter cases. It is obvious that when process parameter is not known and is estimated using Phase I data, the chart does not perform as user expects. To tackle this issue, optimal Phase I estimation scenarios are recommended to obtain the best performance from the chart in the parameter estimation case in terms of performance measures. Practical implications – This research adds to the body of knowledge in quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where products are monitored to reduce the number of defectives and np chart parameter needs to be estimated. Originality/value – The originality of this paper lies within the context in which an adaptive np control chart is studied and the process parameter unlike previous studies is assumed unknown. Although other types of control charts have been studied when process parameter is unknown but this is the first time that adaptive np chart performance with estimated process parameter is studied.

ON THE HOTELLING’S T, MCUSUM AND MEWMA CONTROL CHARTS' PERFORMANCE WITH DIFFERENT VARISBILITY SOURCES: A SIMULATION STUDY

This work is a simulation study to investigate the sensitivity of multivariate control charts for monitoring mean vectors in a bivariate Gaussian process with individual observations. The multivariate cumulative sum (MCUSUM), the multivariate exponentially weighted moving average (MEWMA) and Hotelling’s T charts are selected for analysis due to their common dependency on the noncentrality parameter. The chart performance is evaluated through the average run length (ARL) or the average time to signal. The impact of utilising in-control limits computed from known parameters or Phase I sample estimates is considered for mean vector shifts. Although designed to monitor mean vectors, the sensibility of the control charts is additionally analysed through different variability sources, including the mixing effect of mean vector shifts with increasing variances or positive autocorrelation in the out-of-control process.