A periodic testing model for a preparedness system with a defective state

This paper considers the periodic testing of a preparednesssystem where in addition to working and failed state recognition,a working but defective state also exists. Based upon the delaytime model, an expected availability model is derived and evaluatedas a function of the constant inspection period. The model enablesthe range of inspection periods which satisfy a pre-set availabilitycriterion to be established, and the optimal availability inspectionperiod to be identified. Variants of the basic model are considered including: wherea delay time period exists, but the technology to detect a defectis not available; where the delay time is zero, so that onlyfailures are detected; and where the system is replaced on aregular basis without any state testing. These variants enablethe value and effectiveness of the ability to detect defectsand to detect failures to be identified and quantified. The models are demonstrated in the context of a missile buffersystem, where the numerical example clarifies the value of modellingand the insight into the potential effectiveness of defect andfailure detection.     

Fleet-sizing and service availability for a vehicle rental system via closed queueing networks

In this paper, we address the problem of determining the optimal fleet size for a vehicle rental company and derive analytical results for its relationship to vehicle availability at each rental station in the company’s network of locations. This work is motivated by the recent surge in interest for bicycle and electric car sharing systems, one example being the French program Vélib (2010). We first formulate a closed queueing network model of the system, obtained by viewing the system from the vehicle’s perspective. Using this framework, we are able to derive the asymptotic behavior of vehicle availability at an arbitrary rental station with respect to fleet size. These results allow us to analyze imbalances in the system and propose some basic principles for the design of system balancing methods. We then develop a profit-maximizing optimization problem for determining optimal fleet size. The large-scale nature of real-world systems results in computational difficulties in obtaining this exact solution, and so we provide an approximate formulation that is easier to solve and which becomes exact as the fleet size becomes large. To illustrate our findings and validate our solution methods, we provide numerical results on some sample networks.     

Minimizing the total completion time on a single machine with the learning effect and multiple availability constraints

This paper considers a single machine scheduling problem with the learning effect and multiple availability constraints that minimizes the total completion time. To solve this problem, a new binary integer programming model is presented, and a branch-and-bound algorithm is also developed for solving the given problem optimally. Since the problem is strongly NP-hard, to find the near-optimal solution for large-sized problems within a reasonable time, two meta-heuristics; namely, genetic algorithm and simulated annealing are developed. Finally, the computational results are provided to compare the result of the binary integer programming, branch-and-bound algorithm, genetic algorithm and simulated annealing. Then, the efficiency of the proposed algorithms is discussed.     

Maintenance scheduling of a protection system subject to imperfect inspection and replacement

An inspection and replacement policy for a protection system is described in which the inspection process is subject to error, and false positives (false alarms) and false negatives are possible. We develop two models: one in which a false positive implies renewal of the protection system; the other not. These models are motivated by inspection of a protection system on the production line of a beverage manufacturer. False negatives reduce the efficiency of inspection. Another notion of imperfect maintenance is also modelled: that of poor installation of a component at replacement. These different aspects of maintenance quality interact: false alarms can, in a worst case scenario, lead to the systematic and unnecessary replacement of good components by poor components, thus reducing the availability of the system. The models also allow situations in which maintenance quality differs between alternative maintainers to be investigated.     

Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times

In this paper, we study the identical parallel machine scheduling problem with a planned maintenance period on each machine to minimize the sum of completion times. This paper is a first approach for this problem. We propose three exact methods to solve the problem at hand: mixed integer linear programming methods, a dynamic programming based method and a branch-and-bound method. Several constructive heuristics are proposed. A lower bound, dominance properties and two branching schemes for the branch-and-bound method are presented. Experimental results show that the methods can give satisfactory solutions.     

Effects of soil pH and organic matter on distribution of thorium fractions in soil contaminated by rare-earth industries

The labilities of thorium fractions including mobility and bioavailability vary significantly with soil properties. The effects of soil pH and soil organic matter on the distribution and transfer of thorium fractions defined by a sequential extraction procedure were investigated. Decrease of soil pH could enhance the phytoavailability and the potential availability of thorium in soil. Increase of organic matter reduced the phytoavailability of thorium, but enhanced the potential availability of it. The reasons why soil pH and soil organic matter affect thorium fractions were discussed, and the behavior of the effects of soil properties on thorium fractions was elucidated. Fourier-transform infrared (FTIR) spectra were employed to reveal the positive relationship between the amounts adsorbed in humic material and/or amorphous oxides and the content of soil organic matter.     

Ergodic and light traffic properties of a complex repairable system

A repairable system is composed of components ofI types. A component can be loaded, put on standby, queued or repaired. The repair facility is here assumed to be a queueing system of a rather general structure though interruption of repairs is not allowed. Typei components possess a lifetime distributionA _i (t) and repair time distributionB _t (t). The lifetime of componentj is exhausted with a state-dependent rate _j (t). A Markov process Z(t) with supplementary variables is built to investigate the system behaviour. An ergodic result, Theorem 1, is established under a set of conditions convenient for light traffic analysis. In Theorems 2 to 6, a light traffic limit is derived for the joint steady state distribution of supplementary variables. Applying these results, Theorems 7 to 10 derive light traffic properties of a busy period-measured random variable. Essentially, the concepts of light traffic equivalence due to Daley and Rolski (1992) and Asmussen (1992) are used. The asymptotic (light traffic) insensitivity of busy period and steady state parameters to the form ofA _i(t) [given their means and (in some cases) values of density functions for smallt], is observed under some analytic conditions.Some abbreviations & notations LHS, RHS lefthand side, righthand side - w.r.t. with respect to - (i.i.d.) r.v. (independent identically distributed) random variables - A ^c complement event - d.f., p.d.f. distribution function, probability density function - m.g.f. moment generating function - I _A indicator function of eventA - (t) =1–A(t)     

A polynomial time algorithm for makespan minimization on one machine with forbidden start and completion times

We consider the problem of scheduling independent jobs on a single resource under a special unavailability constraint: a set of forbidden instants is given, where no job is allowed to start or complete. We show that a schedule without idle time always exists if the number of forbidden instants is less than the number of distinct processing times appearing in the instance. We derive quite a fast algorithm to find such a schedule, based on an hybridization between a list algorithm and local exchange. As a corollary minimizing the makespan for a fixed number of forbidden instants is polynomial.     

Modelling of a deteriorating system with repair satisfying general distribution

In this paper, we model a deteriorating system that cannot be repaired “as good as new” after failures, the model comes from [19, Applied Mathematics and Computation, 217(2011), 4980-4989]. Suppose that the system has one repairman who can have multiple vacations, and if the system fails when the repairman is on vacation, it will wait for repair until the repairman is available. Herein the repair time is taken into account and supposes that the repair satisfies the general distribution. Under these assumptions, by means of the geometric process and the supplementary variable techniques, we derive a complete model of the partial differential equations, which will correct an error of mathematical model in [19]. Moreover, we deduce some important reliability indices of the system such as the availability of system, the probability of the repairman working and the rate of occurrence of failures. In particular, we prove that the rate of occurrence of failures m_f is not equal to zero.     

Stability analysis of a new kind n-unit series repairable system

In this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution. C₀-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.