Hsin-I Huang

Parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters

This paper proposes a procedure to construct the membership functions of the system characteristics of a repairable system with two primary units, one standby unit, and one repair facility when switching to standby may fail. Failure times of primary and standby units are assumed to follow fuzzified exponential distributions, and repair times of the failed units are also assumed to have a fuzzified exponential distribution. The @a-cut approach is used to extract from the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.

Fuzzy analysis for steady-state availability: a mathematical programming approach

Steady-state availability has been widely applied as a measure to evaluate the reliability characteristics of a repairable system. However, it is generally not realistic to make assumptions concerning failure time and repair time distributions. Thus, this article has developed a procedure to construct the membership function for fuzzy steady-state availability. Based on Zadeh’s extension principle, a pair of mathematical programs is formulated to find α-cuts of fuzzy steady-state availability. An explicit closed-form expression for the membership function is derived by taking the inverse function of the

Two-unit repairable systems with common-cause shock failures and fuzzy parameters: parametric programming approach

\alpha

Parametric Programming Approach for a Two-Unit Repairable System With Imperfect Coverage, Reboot and Fuzzy Parameters

-cut. To illustrate the interpretation and practical value of fuzzy availability in real-world applications, several numerical examples are provided and discussed.

Reliability-based measures for a system with an uncertain parameter environment

This article, proposes a procedure to construct the membership functions of the system characteristics of a two-unit repairable system in series and parallel, which is subject to individual failures and common-cause shock failures. Time to individual failure and common-cause shock failure of the operating units are assumed to follow fuzzified exponential distributions. In addition, time to repair of the failed units also follow fuzzified exponential distributions. The α-cut approach is used to extract from the fuzzy repairable system a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Since the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.

An algorithmic analysis of multi-server vacation model with service interruptions

This paper proposes a procedure for constructing the membership functions of the system characteristics of a two-unit repairable system in which the coverage factor for an operating unit failure is possibly considered. Times to failure, and times to repair of the operating units are assumed to follow fuzzified exponential distributions. In addition, the recovery times, and reboot times of the failed units also follow fuzzified exponential distributions. The alpha-cut approach is used to extract the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. Two numerical examples illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.

Parametric programming approach for batch arrival queues with vacation policies and fuzzy parameters

This article proposes a procedure to construct membership functions of the system characteristics of a repairable system with one primary machine, one standby machine and an unreliable service station. Failure and repair times of both the operating and standby machines are assumed to follow fuzzified exponential distributions. In addition, the failure and repair times of the service station also follow fuzzified exponential distributions. The α-cut approach is used to extract a family of conventional crisp intervals for the desired system characteristics from the fuzzy repairable system, determined with a set of parametric nonlinear programs using their membership functions. A numerical example successfully illustrates the practicality of the proposed approach. Because system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.

The approximation analysis of the discrete-time Geo/Geo/1 system with additional optional service

Motivated by the trade-off between reliability and utilization level of a stochastic service system, we considers a Markovian multi-server vacation queueing system with c unreliable servers. In such a system, some servers may not be available due to either planned stoppage (vacations) or unplanned service interruptions (server failures). The vacations are controlled by a threshold policy. With this policy, at a service completion instant, if d (=

Entropy maximization and NT vacation M/G/1 model with a startup and unreliable server: comparative analysis on the first two moments of system size

This work constructs the membership functions of the system characteristics of a batch arrival queuing model with vacation policies and fuzzy batch arrival, customer service and server vacation rates. The α-cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp queues with a vacationing server. Two numerical examples are solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, more information is provided for use by management. By extending this model to the fuzzy environment, fuzzy queues with a vacationing server are represented more accurately and the analytic results are more useful for system designers and practitioners.

A Nonpreemptive Priority System with Fuzzy Parameters

This paper analyses a discrete-time Geo/Geo/1 queueing system, where all arriving customers demand the first essential service and some of them may further demand an additional optional service. The interarrival times, the service times of the essential service and the second optional service for arrivals are assumed to be random variables with Geometric distributions. Such a model has potential applications in computer or digital communication network systems. We model this system by the level-dependent and independent quasi-birth-death processes and develop efficient computation algorithms of the stationary distribution of the number of customers in the system using matrix analytic method. A cost model is derived to determine the optimal values of the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach.