An adaptive variable-parameters scheme for the simultaneous monitoring of the mean and variability of an autocorrelated multivariate normal process

Self Cite

Process monitoring is regarded as a continuous phenomenon requiring careful consideration to acquire an enhanced output quality. Dispersion and location are significant parameters in the entire process, and timely detection of the changes that occur in a stable process is needed. Today, quality practitioners recommend using a single charting setup offering better capability of detecting joint changes in the parameters of a process. As provided in the literature, a detailed review paper for simultaneous monitoring is conducted in 2013 which many reaserchers were attracted to publish papers in this field. In this paper, a meticulous content analysis (on the basis of 59 reviewed papers in the field of joint monitoring from 2013 to 2021) is exploited to classify the papers that includes joint control charts for statistical process monitoring (SPM), to identify the potential topics and present some suggestions for further studies in simultaneous monitoring.

Section: Adaptive Control Chartmentioning

confidence: 99%

“…Moreover, examining how measurement errors affect joint monitoring schemes by discussing auto-correlated data for various time series models can be conducted in the future. To date, there is only one paper 83 that deals with an adaptive scheme for joint monitoring of auto-correlated processes. 9.…”

Section: Conclusion and Research Directionsmentioning

confidence: 99%

A literature review on joint control schemes in statistical process monitoring

Jalilibal

Amiri

Khoo

2022

Self Cite

“…Data collection in production systems can be done easily and quickly thanks to industrial automation, which in turns facilitates the statistical analysis of processes. In addition, production systems are partly dynamically driven so, if the data are collected at a higher rate, the observations are expected to be autocorrelated 27 . Some examples include steel foundries, blast furnace operations, wastewater treatment plants, chemical processes, tin/copper layer diode composition, semiconductors, injection moulding, temperature readout for ceramic furnaces, rolling mill operations, water toxicity, cavities in the same casting, integrated circuits, adding potassium to yogurt production and mechanical pieces, pharmaceutical industry, paint production, among others 28,29 .…”

Section: Introductionmentioning

confidence: 99%

Statistical design of an adaptive synthetic X¯$\bar{X}$ control chart for autocorrelated processes

Quintero‐Arteaga

Peñabaena‐Niebles

Vélez

et al. 2022

This paper aims to design a variable parameters synthetic X¯$\bar{X}$ control chart for first‐order AR(1) autocorrelated data following a Gaussian process. To improve the statistical performance in detecting small changes and maintaining a low false alarm rate, the variable parameters X¯$\bar{X}$ control chart was combined with the Conforming Run Length (CRL) sub‐chart to determine when to implement tight or relaxed control and intervene to identify an assignable cause. The statistical design of the proposed chart was performed under a discrete‐time Markov chain approach and a non‐linear programming mathematical model to obtain, using a genetic algorithm (GA), the values of the design parameters that minimise the average time to signal the out‐of‐control state (ATS1$\text{ATS}_{1}$). A sensitivity analysis was performed to examine the behaviour of the ATS1$\text{ATS}_{1}$ in the face on changes in the parameters. Also, a performance evaluation was conducted to compare the proposed chart with other adaptive synthetic charts, the synthetic X¯$\bar{X}$ control chart and the chart developed by Costa and Machado. Our results indicate that this proposal is faster to detect small changes in the process mean considering the autocorrelation of the data.

“…The second method is to revise the upper and lower control limits of control charts to achieve an expected performance. [9][10][11][12][13][14][15][16][17][18] The third approach is to use residual control charts. [19][20][21][22][23][24][25][26] In this case, the residuals are obtained by subtracting predicted values from observed values.…”

Section: Introductionmentioning

confidence: 99%

“…Also, because only every 10th data is used, the discovery of process shifts may be delayed. The second method is to revise the upper and lower control limits of control charts to achieve an expected performance 9–18 . The third approach is to use residual control charts 19–26 .…”

Section: Introductionmentioning

confidence: 99%

On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

Pan

Yan

2020

With the development of automation technologies, data can be collected in a high frequency, easily causing autocorrelation phenomena. Control charts of residuals have been used as a good way to monitor autocorrelated processes. The residuals have been often computed based on autoregressive (AR) models whose building needs much experience. Data have been assumed to be firstorder autocorrelated, and first-order autoregressive (AR(1)) models have been employed to obtain residuals. But for a pth-order autocorrelated process, how the AR(1) model affects the performance of the control chart of residuals remains unknown. In this paper, the control chart of exponentially weighted moving average of residuals (EWMA-R) is used to monitor the pth-order autocorrelated process. Taking the mean and standard deviation of run length as performance indicators, two types of EWMA-R control charts, with their residuals obtained from the pth-order autoregressive AR(p) and AR(1) models, respectively, are compared. The results of the numerical experiment show that for detecting small mean shifts, EWMA-R control charts based on AR(1) models outperform ones based on AR(p) models, whereas for detecting large shifts, they are sometimes slightly worse. A practical application is used to give a recommendation that a large number of samples are necessary for determining an EWMA-R control chart before using it.