The performance of the one-sided truncated exponentially weighted moving average X¯ control chart in the presence of measurement errors

Abstract

When the direction of a potential mean shift can be anticipated, the one-sided exponentially weighted moving average (EWMA) $\overline{X}$ control chart using the truncation method (namely, the one-sided TEWMA $\overline{X}$ chart) is more efficient than those conventional one- and two-sided EWMA $\overline{X}$ schemes for process monitoring. Although attractive, there are no studies on designing the one-sided TEWMA $\overline{X}$ chart by taking measurement errors into account. In this context, we investigate the effect of measurement errors on the performance of the one-sided TEWMA $\overline{X}$ chart based on the linear covariate error model. Additionally, a Markov chain model is established to evaluate the run length properties of the scheme in the presence of measurement errors. Then, an optimal design procedure is developed for searching the optimal design parameters of the scheme. Based on these mentioned studies, several tables and figures are presented to evaluate the detecting performance of the scheme under different parameters of the linear covariate error model, and then a conventional one-sided EWMA $\overline{X}$ chart with reflecting boundary is introduced to further study the effect of the presence and absence of measurement errors on control chart comparison studies. Simulation results show that although the detecting performance of the proposed scheme is significantly affected by measurement errors, its performance is still superior to the classic competing chart under the same comparison conditions. Finally, an illustrative example is given to show the implementation of the recommended scheme.

Keywords:

• One-sided EWMA $\overline{X}$ control chart
• measurement errors
• Markov chain model
• truncation method
• average run length

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 72301130 and 72101123]; Scientific Research Foundation of Nanjing Institute of Technology [grant number YKJ202308]; Humanity and Social Science Foundation of Ministry of Education of China [grant number 19YJA630061]; Natural Science Foundation of Jiangsu Province [grant number BK20200750]; Nanjing Science and Technology Innovation Project for Overseas Educators [grant number NJKCZYZZ2022-08].