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IJEETC 2022 Vol.11(4): 269-276
doi: 10.18178/ijeetc.11.4.269-276

Another Look at the VSI EWMA x̄ Chart when Estimating Process Parameters

W. L. Teoh1, Michael B. C. Khoo2, S. Y. Teh3, Z. L. Chong4, W. H. Moy5, and H. W. You6
1. School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya, Malaysia
2. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia
3. School of Management, Universiti Sains Malaysia, Penang, Malaysia
4. Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kajang, Selangor, Malaysia
5. School of Materials & Mineral Resources Engineering, Universiti Sains Malaysia, Penang, Malaysia
6. Pusat GENIUS@Pintar Negara, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia

Abstract—The performance of the variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart is generally investigated under the assumption of known process parameters. Nevertheless, the process parameters need to be estimated from a historical Phase-I dataset because they are usually unknown in practice. When the process parameters are estimated, the chart’s performance differs among practitioners as different number of Phase-I samples is used. This leads to different parameter estimates in constructing the chart’s limits and variation in the average time to signal (ATS). This type of variation is crucial to be considered when evaluating the performance of the control chart with estimated process parameters. To consider practitioner-to-practitioner variation, this paper investigates the performance of the VSI EWMA  chart with estimated process parameters by using standard deviation of the ATS. Monte Carlo simulation results show that the VSI EWMA x̄ chart requires many Phase-I samples to achieve the desired performance. The results also show that a greater number of Phase-I samples is needed for the VSI EWMA  chart when the smoothing constants are large. This is because larger values of smoothing constants lead to higher variation in the run-length distribution.

Index Terms—EWMA control chart, expected value of the average time to signal, parameter estimation, standard deviation of the average time to signal, statistical process control, variable sampling interval

Cite: W. L. Teoh, Michael B. C. Khoo, S. Y. Teh, Z. L. Chong, W. H. Moy, and H. W. You, "Another Look at the VSI EWMA x̄ Chart when Estimating Process Parameters," International Journal of Electrical and Electronic Engineering & Telecommunications, Vol. 11, No. 4, pp. 269-276, July 2022. Doi: 10.18178/ijeetc.11.4.269-276

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