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

Abstract

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.

Run sum ratio chart when measurement errors are present

“…The cdf, pdf and icdf of 𝑍 * can be defined using Equations ( 3), ( 6) and ( 7) by substituting ρ, 𝛾 𝑋 , 𝛾 𝑌 and ω with 𝜌 * , 𝛾 𝑋 * , 𝛾 𝑌 * and 𝜔 * , respectively, in Equations ( 21)- (24).…”

“…More recently, Tran et al 23 developed CUSUM schemes for the coefficient of variation (CV) when measurement errors are present. Lee et al 24 investigated the impact of measurement errors on the efficacy of short runs based CV chart. In the same vein, Ayyoub et al 25 explored the capabilities of the Shewhart and EWMA charts for the multivariate CV when measurement errors are present, while Umar et al 26 investigated the consequence of measurement errors on the triple sampling X chart.…”

A new EWMA median chart with measurement errors in short production runs–An application in yogurt cup filling process

“…Noor‐ul‐Amin and Noor 33 studied the Bayesian EWMA chart under the squared error and linex loss functions in the presence of measurement errors. Other literatures that deal with the impact of measurement errors on control charts include those by Yeong et al, 34 Cheng and Wang, 35 Tang et al., 11 Sabahno et al., 36 Tran et al., 37 Lee et al 38 . and Riaz et al 39 …”

“…The effect of measurement errors on the performance of the variable sampling interval EWMA median chart was investigated by Tran et al 32 Noor-ul-Amin and Noor 33 studied the Bayesian EWMA chart under the squared error and linex loss functions in the presence of measurement errors. Other literatures that deal with the impact of measurement errors on control charts include those by Yeong et al, 34 Cheng and Wang, 35 Tang et al, 11 Sabahno et al, 36 Tran et al, 37 Lee et al 38 and Riaz et al 39 Recently, Khoo et al 15 proposed the Shewhart median chart for SPR. Motivated to improve the effectiveness of this chart, the authors of this article develop the EWMA SPR median chart.…”

Monitoring multivariate coefficient of variation with upward Shewhart and EWMA charts in the presence of measurement errors using the linear covariate error model

“…Tran et al 24 adopted the one‐sided run rules in monitoring the CV when measurement errors are present. Additionally, Lee et al 25 discussed the effects of measurement errors on the performance of the CV chart for short production runs.…”