VSSI median control chart with estimated parameters and measurement errors

Cheng, Xiao‐Bin; Wang, Fu‐Kwun

doi:10.1002/qre.2297

Cited by 20 publications

(12 citation statements)

References 28 publications

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“…where e q T ¼ 1; 0; 0 ð Þis a vector representing the initial probabilities of the modified Markov chain. From Equations (18) and (20), ASS 1 (δ) can be computed as 25…”

Section: Tarl Tsdrl Ass and P(i)mentioning

confidence: 99%

“…Additionally, Yeong et al presented the VSS chart that monitors the CV directly instead of the transformed statistics employed by Castagliola et al Amiri et al extended the VSS approach to the exponentially weighted moving average (EWMA) control chart. More research works on the VSS control charts can be found in Mahadik, Wu and Luo, Noorossana and Maryam, Mahadik, Cheng and Wang, Aslam et al, Zhou and Lian, Nyau et al, and Lee . In VSS charts, the sample sizes change as a function of the prior sample position, ie, small or large sample size.…”

Section: Introductionmentioning

confidence: 99%

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Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Chong

Khoo

Haq

et al. 2018

Quality & Reliability Eng

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Short production runs are common in enterprises that require a high degree of flexibility and variety in manufacturing processes. To date, past research on short production runs has little focus on the multivariate control charts. In view of this, fixed sample size (FSS) and variable sample size (VSS) Hotelling's T2 charts are designed to monitor the process mean when the production horizon is finite. Optimal parameters to minimize the out‐of‐control (1) truncated average run length (TARL) and (2) expected TARL (ETARL) are provided such that the in‐control TARL is equal to the number of inspections (say I). The numerical study considers the run length performances of the FSS and VSS T2 short‐run charts for both known and unknown shift sizes. The VSS T2 short‐run chart performs well in swiftly detecting various mean shifts in comparison with the FSS T2 short‐run chart. Additionally, the VSS T2 short‐run chart is superior to the FSS T2 short‐run chart, in terms of the truncated standard deviation of the run length, expected truncated standard deviation of the run length, probability that the chart signals an alarm within the I inspections, ie, P(I) and expected P(I). A case study on the impurity profile of a crystalline drug substance illustrates the implementation of the VSS T2 short‐run chart.

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“…where e q T ¼ 1; 0; 0 ð Þis a vector representing the initial probabilities of the modified Markov chain. From Equations (18) and (20), ASS 1 (δ) can be computed as 25…”

Section: Tarl Tsdrl Ass and P(i)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Chong

Khoo

Haq

et al. 2018

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…Their results indicated that the presence of measurement errors significantly affect the performance of the monitoring procedure. Cheng and Wang [20] presented a VSSI median control chart with estimated parameters in the presence of measurement errors. Their results showed that the VSSI median chart performs better than the Shewhart median, VSS median and VSI median control charts in terms of the average time to signal.…”

Section: Introductionmentioning

confidence: 99%

Effect of Measurement Errors on the Performance of Coefficient of Variation Chart With Short Production Runs

et al. 2020

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This paper investigates the performance of the coefficient of variation chart in the presence of measurement errors for finite production horizon. We study a two-sided Shewhart coefficient of variation chart with measurement errors for detecting both increase and decrease in the coefficient of variation for short run processes using an error model with linear covariate. The performance of the coefficient of variation chart is evaluated by the truncated average run length and the expected value of the truncated average run length. The numerical results indicate that the precision error and the accuracy error have negative effect of the measurement errors on the performance of the coefficient of variation chart. In addition, the constant coefficient B in the linear covariate error model reduces the negative effect of the measurement errors on the performance of the coefficient of variation chart. However, taking multiple measurements per item in each sample is not an effective method to enhance the performance of the coefficient of variation chart. An example is provided to illustrate the implementation of the coefficient of variation chart. In addition, the economic criterion is also added to study the effect of measurement errors on the expected inspection cost. The result shows that an increase in the precision error reduces the expected inspection cost.

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“…The optimal VSSI X chart was also proposed by using the estimated parameters [21] and adjusted loss function [22]. Reference [23] introduced the VSSI median control chart with estimated parameters and measurement errors while reference [24] studied the effect of measurement errors on the performance of the VSSI X chart. References [25] and [26] considered the VSSI chart for the process mean using auxiliary information and the coefficient of variation, respectively.…”

Section: Introductionmentioning

confidence: 99%

Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal

Khaw¹,

Chew²,

Teh³

et al. 2019

IJMLC

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A control chart is one of the effective tools in statistical process control (SPC) for improving productivity, reducing defective products and providing diagnostic information. Control charting techniques have gained increasing importance recently due to the rapid advancement in technology. Many industries tend to use control charts to monitor the quality of their products or services. The adoption of variable sample size and sampling interval (VSSI) strategy significantly improved the sensitivity of Shewhart X chart in detecting small and moderate process mean shifts, in terms of average time to signal (ATS) criterion when the process shifts are specified. However, for some scenarios in real industries, the process shift size is not set to a specific value. In this case, the expected average time to signal (EATS) can be used as a measure of performance when the process shift is unknown. The EATS of the optimal VSSI X chart is numerically evaluated based on a Markov chain approach. The findings show that the VSSI X chart prevails over the Shewhart X chart under comparison. Being able to vary the sample size and sampling interval, a practitioner will have more flexibility and better control of the process and at the same time is able to detect an out-of-control signal quicker. Index Terms-Expected average time to signal, Markov chain, process mean, variable sample size and sampling interval.

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VSSI median control chart with estimated parameters and measurement errors

Cited by 20 publications

References 28 publications

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Effect of Measurement Errors on the Performance of Coefficient of Variation Chart With Short Production Runs

Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal

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VSSI median control chart with estimated parameters and measurement errors

Cited by 20 publications

References 28 publications

Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

Effect of Measurement Errors on the Performance of Coefficient of Variation Chart With Short Production Runs

Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal

Contact Info

Product

Resources

About

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs