**7. Conclusions**

This paper has proposed a second-order Markov model for estimating the frame-level transmission errors in an industrial WSN based on the experimental traces obtained in a real-world factory environment over a ~24 h period. A statistical analysis has shown that the proposed model provides a better description of the transmission quality in industrial WSNs than conventional methods. In addition, the simulation results have shown that the proposed error model improves the accuracy of the estimated transmission reliability in the OpenWSN simulator by up to 12% compared to that achieved using the original independent error model. The performance advantage of the proposed model is particularly apparent when the transmission failure events are non-uniformly dispersed in a certain time interval.

**Author Contributions:** Conceptualization, Y.-S.Y. and Y.-S.C.; methodology, Y.-S.Y.; software, Y.-S.Y.; validation, Y.-S.Y. and Y.-S.C.; formal analysis, Y.-S.Y.; investigation, Y.-S.Y.; resources, Y.-S.Y.; data curation, Y.-S.Y. and Y.-S.C.; writing—original draft preparation, Y.-S.Y. and Y.-S.C.; writing—review and editing, Y.-S.Y. and Y.-S.C.; visualization, Y.-S.Y.; supervision, Y.-S.Y. and Y.-S.C.; project administration, Y.-S.Y.; funding acquisition, Y.-S.Y. and Y.-S.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially supported by the Ministry of Science and Technology, Taiwan, under grant No. MOST 108-2221-E-150-008. Also, the APC was funded by the Ministry of Science and Technology, Taiwan, under the same grant No.

**Conflicts of Interest:** The authors declare no conflict of interest.
