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Moment-based approximations for first- and second-order transient performance measures of an unreliable workstation

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Abstract

Performance measures of manufacturing systems have been intensively researched. However, little attention has been paid to the transient performance analysis of non-Markovian production systems. Therefore, this paper proposes a method to approximate the properties of a two-state non-Markovian system. In particular, an unreliable workstation with two states, operating and failed states, is considered. This system is a simplified version of an industrial manufacturing system. Moment-based approximations for the expected output quantity of the workstation at any arbitrary time is derived and discussed. In addition, an upper bound approximation for the variation of the produced amount is proposed. Failure and repair times are assumed to be arbitrarily distributed. The proposed approximations are compared with a simulated model using the ARENA 10 free version software to demonstrate the accuracy of the method. These approximations are nonparametric, easy to implement and depend only on the first three moments of the underlying distributions without recourse to the functional form of the distributions.

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Acknowledgments

We are indebted to the editor and anonymous referees of the journal for their constructive comments that helped us to improve the quality of this paper. In addition, the first author would like to thank Professor Alagar Rangan for sharing his insights regarding this study and for his suggestions. This work was partially supported by National Research Foundation of Korea (NRF). Grant funded by the Korean government (MSIP) under Grant No. NRF-2014R1A2A2A03003874.

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  1. Department of Information and Industrial Engineering, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul, 120-749, South Korea

    Farhood Rismanchian & Young Hoon Lee

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  1. Farhood Rismanchian
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  2. Young Hoon Lee
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Correspondence to Farhood Rismanchian.

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Rismanchian, F., Lee, Y.H. Moment-based approximations for first- and second-order transient performance measures of an unreliable workstation. Oper Res Int J 18, 75–95 (2018). https://doi.org/10.1007/s12351-016-0254-9

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