Optimal one-sided shewhart control charts with variable sampling intervals

Reynolds, Marion R.; Arnold, Jesse C.

doi:10.1080/07474948908836167

Cited by 126 publications

(61 citation statements)

References 9 publications

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“…It is also known that X for the given Y = y is normally distributed with a mean of 100.41 + 0.86y and a variance of (12.57 µm) 2 and that the correlation coefficient between X and Y is ρ = 0.799. Table 3 shows the TRISO fuel sizes measured using the PSA and X-ray methods.…”

Section: Application To a Nuclear Fuel Measurement Systemmentioning

confidence: 99%

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Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

Lee

Hong

Kwon

et al. 2016

Management and Production Engineering Review

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Accepted: 28 July 2016 In many cases, a X control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. However, if the performance variable is too costly or impossible to measure, and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we present a model for the economic statistical design of a VSI (Variable Sampling Interval) X control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) X control chart, EWMA, CUSUM charts and so on.

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Section: Application To a Nuclear Fuel Measurement Systemmentioning

confidence: 99%

“…VSI control charts have received much attention, for example, Reynolds and Arnold, Runger and Montgomery, Reynolds, Costa and Rahim, Lin et al, Chew et al and Zhang Min et al [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

Lee

Hong

Kwon

et al. 2016

Management and Production Engineering Review

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“…According to Reynolds and Arnold (1989) and , the VSI chart is better than FSI chart in terms of ATS and ANSS. They also showed that the two sampling intervals VSI chart is optimal for larger gap between two sampling intervals for one-and two-sided Shewhart chart.…”

Section: Variable Sampling Intervals Schemementioning

confidence: 99%

Switching performances of multivarite VSI chart for simultaneous monitoring correlation coefficients of related quality variables

Chang¹

2017

Journal of the Korean Data and Information Science Society

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There are many researches showing that when a process change has occurred, variable sampling intervals (VSI) control chart is better than the fixed sampling interval (FSI) control chart in terms of reducing the required time to signal. When the process engineers use VSI control procedure, frequent switching between different sampling intervals can be a complicating factor. However, average number of samples to signal (ANSS), which is the amount of required samples to signal, and average time to signal (ATS) do not provide any control statistics about switching performances of VSI charts. In this study, we evaluate numerical switching performances of multivariate VSI EWMA chart including average number of switches to signal (ANSW) and average switching rate (ASWR). In addition, numerical study has been carried out to examine how to improve the performance of considered chart with accumulate-combine approach under several different smoothing constant and sample size. In conclusion, process engineers, who want to manage the correlation coefficients of related quality variables, are recommended to make sample size as large and smoothing constant as small as possible under permission of process conditions.

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“…investigated the theoretical aspects of a VSI two-sided control charts. Reynolds and Arnold (1989) investigated the theoretical aspects of a VSI one-sided Shewhart control charts. Reynolds (1995) evaluated properties of variable sampling interval control charts.…”

Section: Properties Of Vsi Proceduresmentioning

confidence: 99%

“…Also Reynolds and Arnold (1989) developed general expressions such as ARL and ATS for VSI control charts. But VSI procedures have a disadvantage that is frequent switching between different sampling intervals which requires more cost and effort to administer the process than corresponding FSI procedures.…”

Section: Introductionmentioning

confidence: 99%

Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix

Gwon¹,

Cho²

2015

Journal of the Korean Data and Information Science Society

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A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. We construct bivariate Shewhart control charts based on the trace of the product of the estimated variance-covariance matrix and the inverse of the in-control matrix and investigate the properties of bivariate Shewart control charts with VSI procedure for monitoring covariance matrix in term of ATS (Average time to signal) and ANSW (Average number of switch) and probability of switch, ASI (Average sampling interval). Numerical results show that ATS is smaller than ARL. From examining the properties of switching in changing covariances and variances in Σ, ANSW values show that it does not switch frequently and does not matter to use VSI procedure.

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Optimal one-sided shewhart control charts with variable sampling intervals

Cited by 126 publications

References 9 publications

Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

Switching performances of multivarite VSI chart for simultaneous monitoring correlation coefficients of related quality variables

Switching properties of bivariate Shewhart control charts for monitoring the covariance matrix

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