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

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.