Economic design of variable sampling intervals &lt;span style="text-decoration: overline"&gt;X&lt;/span&gt; charts with B&amp;L switching rule

Chou, Chao Yu; Lin, Yu Chang; Wang, Shu Ling; Chen, Chung Ho

doi:10.1504/ijise.2013.057493

Cited by 3 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, as these problems are NP‐hard, metaheuristics are an efficient way to solve them in a reasonable computational time. Thus, here we implement a genetic algorithm (GA), since it has a widely used in most studies for this purpose 10,34–39 . The overall procedure is described in Figure 4.…”

Section: Genetic Algorithm For Model Optimisationmentioning

confidence: 99%

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

Quintero‐Arteaga

Peñabaena‐Niebles

Vélez

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

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.

show abstract

Section: Genetic Algorithm For Model Optimisationmentioning

confidence: 99%

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

Quintero‐Arteaga

Peñabaena‐Niebles

Vélez

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…The control chart technique may be considered as the graphical expression and operation of statistical hypothesis test. Researches on the designs of various control charts may be traced back to 1960's and a lot of theoretical developments and applications on control charts can be still found in recent literatures, such as Haridy et al (2012), Chou et al (2013), Requeijo and Cordeiro (2013), Karaoglan and Bayhan (2014), Liu et al (2014). The control charts with exponentially weighted moving average (EWMA) scheme was first introduced by Roberts (1966) and had been shown to be effective for detecting small shifts in the mean of the process characteristic (e.g., see Saccucci and Lucas, 1990).…”

Section: Introductionmentioning

confidence: 99%

“…One of popular adaptive control schemes is called 'variable sampling interval (VSI)'. The control charts with VSI scheme, in which the sampling interval is not fixed but instead switches between short and long intervals depending on what is observed from the process, had been developed and shown to give substantially faster detection of most process shifts than conventional control charts (see Lin and Chou, 2011;Chou et al, 2013). Therefore, extension to robustness of the EWMA median chart with VSI control scheme to non-normality may be left for further study.…”

mentioning

confidence: 99%

Robustness of the EWMA median control chart to non-normality

Lin

Chou

Chen

2017

IJISE

Self Cite

View full text Add to dashboard Cite

Abstract:The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.

show abstract

Adaptive Shewhart Control Charts Under Fuzzy Parameters with Tuned Particle Swarm Optimization Algorithm

Amiri

Salmasnia

Zarifi

et al. 2021

J. Ind. Intg. Mgmt.

View full text Add to dashboard Cite

In recent years, adaptive control charts in which the design parameters depend on the observed samples have been successfully used as efficient alternatives for traditional control charts with constant parameters. In crisp run control rules, the process state may change very sharply from in-control to out-of-control conditions which increase the rate of false alarms. To overcome this drawback, this paper presents an adaptive Shewhart-type control chart, where the design parameters (sample size ([Formula: see text]), sampling interval ([Formula: see text]), and control limit coefficients ([Formula: see text] and [Formula: see text])) are defined with linguistic variables. To accomplish that, the chart parameters are determined based on the location of eight previous chart statistics using a set of fuzzy rules in a continuous environment. In order to improve the sensitivity of the proposed control chart in detecting small shifts in both location and scale parameters, the adaptive procedure is designed by integration of fuzzy Western Electric rules and fuzzy adaptive sampling rules. After designing the control charts using a fuzzy inference system (FIS), in order to provide an economic design of the proposed control chart, a tuned Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal values corresponding to membership functions of the control chart parameters. Finally, using simulation studies, the capability of the proposed control chart is analyzed and compared with common charts in the literature. The results confirm that under different shifts in location and scale parameters, the proposed control chart outperforms other charts in terms of both economic and statistical criteria.

show abstract

Economic design of variable sampling intervals <span style="text-decoration: overline">X</span> charts with B&L switching rule

Cited by 3 publications

References 27 publications

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

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

Robustness of the EWMA median control chart to non-normality

Adaptive Shewhart Control Charts Under Fuzzy Parameters with Tuned Particle Swarm Optimization Algorithm

Contact Info

Product

Resources

About