Jau-Chuan Ke

Optimal randomized control policy of an unreliable server system with second optional service and startup

Purpose – To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers.Design/methodology/approach – Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter‐breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two‐...

Simulation inferences for an availability system with general repair distribution and imperfect fault coverage

Abstract We study the statistical inferences of an availability system with imperfect coverage. The system consists of two active components and one warm standby. The time-to-failure and time-to-repair of the components are assumed to follow an exponential and a general distribution respectively. The coverage factors for an active-component failure and for a standby-component failure are assumed to be the same. We construct a consistent and asymptotically normal estimator of availability for such repairable system. Based on this estimator, interval estimation and testing hypothesis are performed. To implement the simulation inference for the system availability, we adopt two repair-time distributions, namely, lognormal and Weibull and three types of Weibull distributions characterized by their shape parameters are considered. Finally, all simulation results are displayed in appropriate tables and curves for highlighting the performance of the statistical inference procedures.

Sensitivity analysis of the optimal management policy for a queuing system with a removable and non-reliable server

The management policy of an M/G/1 queue with a single removable and non-reliable server is considered. The decision-maker can turn the single server on at any arrival epoch or off at any service completion. It is assumed that the server breaks down according to a Poisson process and the repair time has a general distribution. Arrivals form a Poisson process and service times are generally distributed. In this paper, we consider a practical problem applying such a model. We use the analytic results of the queueing model and apply an efficient Matlab program to calculate the optimal threshold of management policy and some system characteristics, Analytical results for sensitivity analysis are obtained. We carry out extensive numerical computations for illustration purposes. An application example is presented to display how the Matlab program could be used. The research is useful to the analyst for making reliable decisions to manage the referred queueing system.

Computational analysis of machine repair problem with unreliable multi-repairmen

This paper considers a multi-repairmen problem comprising of M operating machines with W warm standbys (spares). Both operating and warm standby machines are subject to failures. With a coverage probability c, a failed unit is immediately detected and attended by one of R repairmen if available. If the failed unit is not detected with probability 1-c, the system enters an unsafe state and must be cleared by a reboot action. The repairmen are also subject to failures which result in service (repair) interruptions. The failed repairman resumes service after a random period of time. In addition, the repair rate depends on number of failed machines. The entire system is modeled as a finite-state Markov chain and its steady state distribution is obtained by a recursive matrix approach. The major performance measures are evaluated based on this distribution. Under a cost structure, we propose to use the Quasi-Newton method and probabilistic global search Lausanne method to search for the global optimal system parameters. Numerical examples are presented to demonstrate the effectiveness of our approach in solving a highly complex manufacturing system subject to multiple uncertainties.

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.

Original article: Standby system with general repair, reboot delay, switching failure and unreliable repair facility-A statistical standpoint

This study statistically examines an availability system with reboot delay, standby switching failures and an unreliable repair facility, which consists of two active components and one warm standby. The time-to-failure and the reboot time are assumed to be exponentially distributed. The repair time of the service station and the time-to-repair of component are assumed to be generally distributed. A consistent and asymptotically normal estimator of availability of such a repairable system is developed. Based on this estimator, interval estimation and testing hypothesis are performed by using logit transformation. To implement the simulation inference for the system availability, two repair-time distributions, lognormal and Weibull distributions, are used. Three Weibull distributions characterized by distinct shape parameters are considered. Finally, all simulation results are displayed as appropriate tables and curves to reveal the performance of the statistical inference procedures.

On a repairable system with detection, imperfect coverage and reboot: Bayesian approach

Abstract System characteristics of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of one active component and one standby component. The detection of standby, the coverage factor and reboot delay of failed components are possibly considered. Time to failure of the components is assumed to follow exponential distribution. Time to repair and time to reboot of the failed components also follow exponential distributions. When time to failure, time to repair and time to reboot have uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.

A repairable system with imperfect coverage and reboot: Bayesian and asymptotic estimation

System characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor for an operating unit failure is possibly considered. Time to failure and time to repair of the operating units are assumed to follow exponential distributions. In addition, the recovery time and reboot time of the failed units also follow exponential distributions. When time to failure, time to repair, recovery time and reboot time are with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.

Modeling of multi-server repair problem with switching failure and reboot delay and related profit analysis

This study examines a warm-standby machine repair problem which involves a switching failure probability, reboot delay and a repair pressure coefficient. The machine repair problem has M operating machines with W warm standbys and R repairpersons. When all repairpersons are busy and waiting line is very long (heavy loading), the repairpersons increase their repair rate to reduce the queue length because of the pressure. This phenomenon is very common in many realistic service systems. A matrix-analytic method is adopted to develop a function of the steady-state expected profit per unit time. The probabilistic global search Lausanne (PGSL) method is employed to determine the joint optimal parameter values that maximize the profit and satisfy the availability constraint. Some numerical results of various system performance measures under optimal operating conditions are presented. Finally, several managerial insights are provided by demonstrating an example of the application to assist system analysts for decision making.

A batch arrival queue under randomised multi-vacation policy with unreliable server and repair

This article examines an M[x]/G/1 queueing system with an unreliable server and a repair, in which the server operates a randomised vacation policy with multiple available vacations. Upon the system being found to be empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 − p. When one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. It is possible that an unpredictable breakdown may occur in the server, in which case a repair time is requested. For such a system, we derive the distributions of several important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle and busy periods. We perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximisation model is constructed to show the benefits of such a queueing system.