Moments of accumulated reward and completion time in Markovian models with application to unreliable manufacturing systems

Abstract

Performance evaluation models are used by companies to design, adapt, manage and control their production systems. In the literature, most of the effort has been dedicated to the development of efficient methodologies to estimate the first moment performance measures of production systems, such as the expected production rate, the buffer levels and the mean completion time. However, there is industrial evidence that the higher moments of the production output may drastically impact on the capability of managing the system operations, causing the observed system performance to be highly different from what expected. This paper presents a methodology to analyze the cumulated output and the lot completion time moments of Markovian reward models. Both the discrete and the continuous time cases are considered. The technique is applied to unreliable manufacturing systems characterized by general Markovian structures. Numerical results show how the theory developed in this paper can be applied to analyse the dependency of the output variability and the service level on the system parameters. Moreover, they highlight previously uninvestigated features of the system behavior that are useful while operating the system in practical settings.

A Comprehensive Fuzzy Decision-Making Method for Minimizing Completion Time in Manufacturing Process in Supply Chains

“…Angius et al proposed a method to analyze the cumulated output and the lot completion time moments in unreliable manufacturing systems characterized by general Markovian structures. Their outcomes showed that the proposed method could help analyze the dependency of the output variability and the service level of a system [23]. Mokhtari and Salmasnia addressed a neighborhood search algorithm for reducing the processing time of a multiple-machine manufacturing system.…”

Formal analysis of production line systems by probabilistic model checking tools

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“…a path σ. A next formula Xϕ is satisfied by σ if ϕ is satisfied in the state which is next to the initial state of σ, i.e., σ [1]…”

“…In this paper we consider production line models composed of buffers and unreliable machines with Markov behavior. Building on previous works dealing with the same or similar models (see, e.g., [1], [2], [7]- [9]), in this paper we introduce an integrated framework for formal modeling and performance analysis of such systems. Our proposal is to describe the system with a well-known and widely applied model checking tool called PRISM [13] which allows for specifying the system in terms of a DTMC, expressing and calculating performance indices, and verifying complex temporal properties of the model [11].…”

Design and management of reconfigurable assembly lines in the automotive industry

“…According to these data, the stochastic distribution of the duration of each event reported in the event set is gathered, and the dynamic behaviour of the system is approximated by a continuous time Markov Chain. The evaluation of the main performance measures of the system, such as the average throughput, the average lead time and the distribution of the lot completion time for the given lots are calculated by using the method developed in [13]. The main innovation proposed by this module is the automatic generation of feasible material flow dynamics in the assembly system, starting from a static selection of resources in FAGs.…”