Random Duration Research Articles

Effects of extension of subcontracting on a production system in a joint maintenance and production context

This paper considers the problem of subcontracting constraints under a joint maintenance management and production control approach. Our objective is to study the effect of an unforeseen extension of subcontracting duration on a production system provider of subcontracting services. We will study a system with a production unit M subject to corrective maintenance actions, a result of random breakdowns. We perform a preventive maintenance action (PM) for each time T. Corrective and preventive maintenance have random durations. A buffer stock S with a capacity h, is built up with a production rate U in order to satisfy the constant demand d of the principal costumer, such as U max > d . We note α = U max - d , the maximum stock accumulation rate. In addition, the machine M is allocated to perform subcontracting tasks (ST) to a contractor production system, at each moment A 1, for a useful duration A 2 , during which it is unavailable for our system. Thus, the machine must satisfy at the same time the constant demand (under a costumer–supplier relationship) and subcontracting tasks (under a contractor–subcontractor relationship). In this context, a mathematical model is developed to determine the impact of an unforeseen extension of subcontracting duration on the generated costs. We will determine the optimal values of T and h and we will discuss the impact of the extension of a ST with θ time units.

Highly efficient SHG of a sequence of laser pulses with a random peak intensity and duration

One of the methods of obtaining a highly efficient second-harmonic generation (SHG) for laser pulses with random amplitudes and durations is mathematically modeled. The essence of the method proposed consists of the use of quadratic nonlinearity of the medium under conditions of a large mismatch between the wave numbers of the fundamental wave and the second harmonic. In the literature, the SHG under these conditions is referred to as the cascade SHG. Under certain conditions, this process is equivalent to the action similar to that of the cubic nonlinearity. This allows one to implement the both compression and decompression of laser pulses due to the cascade generation at a fairly low intensity of the pulses such that the Kerr nonlinearity does not manifest itself. The cascade generation is shown to enable one to implement tenfold or higher suppression of fluctuations of the input peak intensity of the laser radiation in the regime of free generation, which potentially makes it possible to implement the SHG under optimum conditions for all pulses in the sequence.

Contribution of simulation to the optimization of maintenance strategies for a randomly failing production system

This paper compares two strategies for operating a production system composed of two machines working in parallel and a downstream inventory supplying an assembly line. The two machines, which are prone to random failures, undergo preventive and corrective maintenance operations. These operations with a random duration make the machines unavailable. Moreover, during regular subcontracting operations, one of these machines becomes unavailable to supply the downstream inventory. In the first strategy it is assumed that the periodicity of preventive maintenance operations and the production rate of each machine are independent. The second strategy suggests an interaction between the periods of unavailability and the production rates of the two machines in order to minimize production losses during these periods. A simulation model for each strategy is developed so as to be able to compare them and to simultaneously determine the timing of preventive maintenance on each machine considering the total average cost per time unit as the performance criterion. The second strategy is then considered, and a multi-criteria analysis is adopted to reach the best cost-availability compromise.

Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange

Abstract This paper investigates the use of tick-by-tick data for intraday market risk measurement. We propose a method to compute an Intraday Value at Risk based on irregularly spaced high-frequency data and an intraday Monte Carlo simulation. A log-ACD–ARMA–EGARCH model is used to specify the joint density of the marked point process of durations and high-frequency returns. We apply our methodology to transaction data for three stocks actively traded on the Toronto Stock Exchange. Compared to traditional techniques applied to intraday data, our methodology has two main advantages. First, our risk measure has a higher informational content as it takes into account all observations. On the total risk measure, our method allows for distinguishing the effect of random trade durations from the effect of random returns, and for analyzing the interaction between these factors. Thus, we find that the information contained in the time between transactions is relevant to risk analysis, which is consistent with predictions from asymmetric-information models in the market microstructure literature. Second, once the model has been estimated, the IVaR can be computed by any trader for any time horizon based on the same information and with no need of sampling the data and estimating the model again when the horizon changes. Backtesting results show that our approach constitutes reliable means of measuring intraday risk for traders who are very active in the market.

The value of reliability

We derive the value of reliability in the scheduling of an activity of random duration, such as travel under congested conditions. Using a simple formulation of scheduling utility, we show that the maximal expected utility is linear in the mean and standard deviation of trip duration, regardless of the form of the standardised distribution of trip durations. This insight provides a unification of the scheduling model and models that include the standard deviation of trip duration directly as an argument in the cost or utility function. The results generalise approximately to the case where the mean and standard deviation of trip duration depend on the starting time. An empirical illustration is provided.

Clinical evaluation of a non-immersive virtual environment in stroke rehabilitation

Background and purpose: We describe our attempts to evaluate the effectiveness of a virtual environment developed to rehabilitate stroke patients in the task of making a hot drink. Methods: Single case studies were performed in 13/138 (9%) stroke patients undergoing rehabilitation in a UK stroke unit. Participants in AB/BA (n = 5) and ABA (n = 2) design studies received 5 one-hour sessions of attention control training (A phase) and 5 one-hour sessions of virtual environment training (B phase). An AB design with random duration of A and B phases (minimum duration of A and B phases 3 and 5 days respectively, with total duration of 3 weeks) was used in 6 participants. Results: Visual inspection of scores across all cases showed a trend towards improvement over time in both real and virtual hot drink making ability in both control and intervention phases. There was no significant difference (Wilcoxon, p > 0.05) in the improvements in real and virtual hot drink making ability during all control and intervention phases in the 13 cases. Ceiling effects limited the evaluation of effectiveness in 5 of the 8 cases in which daily performance measures were used. Conclusions: Few people in this setting were suitable for this intervention. The case studies showed no evidence of a strong effect of this intervention, but we had great difficulty in performing single case studies. We conclude that more testing and development of this system is required before it is subjected to rigorous testing of clinical effectiveness.

Evaluating project completion time in project networks with discrete random activity durations

Deterministic models for project scheduling suffer from the fact that they assume complete information and neglect random influences, that occur during project execution. A typical consequence is the underestimation of the project duration as frequently observed in practice. This phenomenon occurs even in the absence of resource constraints and has been the subject of extensive research in the scientific community. This paper presents a method for obtaining relevant information about the project makespan for scheduling models, with dependent random processing time available in the form of scenarios.

Joint quality control and preventive maintenance strategy for imperfect production processes

In this paper, we develop a joint quality control and preventive maintenance policy for a production system producing conforming and nonconforming units. The considered system consists of one machine which must supply another production line operating on a just-in-time basis. Each lot produced by the machine is subject to a quality control. According to the proportion l of nonconforming units observed and compared to a threshold value lm, one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine for preventive and corrective maintenance actions of random durations, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. The proposed strategy is modelled using simulation and experimental design. This approach allows to generate a second order response surface allowing to easily determine the optimal rate, \({l_{m}^*}\), of nonconforming units on the basis of which preventive maintenance actions should be performed, and the optimal size, h*, of the buffer stock to be built. These values minimize the total cost per time unit which includes the costs related to maintenance, quality and inventory.

Analysis of joint maintenance and production policies under a subcontracting constraint

In this paper, we deal with the problem of joint maintenance and production management under a subcontracting constraint. We will study a system with a machine M which undergoes corrective maintenance actions together with preventive maintenance actions, both of which have random durations. A stock S with a capacity h is developed at a rate α = U max – d, where U max = production rate, d = constant demand, and U max > d. In addition, machine M is allocated to carry out subcontracting tasks (ST) at a frequency A 1, for an effective duration A 2, during which time it cannot be used to fulfil our system's demand d. We initially study the system analytically when the machine M is forced to carry out a single subcontracting task during each cycle T. We thereafter present a generalization of the subcontracting constraint which entails assigning the machine M to subcontracting several times during each cycle.

An integrated production and maintenance model for one failure prone machine-finite capacity buffer system for perishable products with constant demand

This paper proposes an optimal design and operation model for a production system producing a perishable product. This production system consists of one failure prone machine and a finite capacity buffer. The machine is replaced or submitted to an overhaul at failure and at predetermined instants T, 2T, 3T, … During these inactivity periods of random durations due to preventive and corrective maintenance, the demand is fulfilled from the buffer stock whose capacity S is to be determined. A mathematical model and a numerical procedure are developed to determine a couple (S*, T*) which minimizes the expected total cost per unit of time over an infinite horizon. Included are the maintenance costs, holding and shortage costs and waste cost due to the fact that the product is perishable. Calculations are carried out through a numerical example to validate the coherence of the model.

INFINITE-SERVER QUEUES WITH SYSTEM'S ADDITIONAL TASKS AND IMPATIENT CUSTOMERS

A system is operating as an M/M/∞ queue. However, when it becomes empty, it is assigned to perform another task, the duration U of which is random. Customers arriving while the system is unavailable for service (i.e., occupied with a U-task) become impatient: Each individual activates an “impatience timer” having random duration T such that if the system does not become available by the time the timer expires, the customer leaves the system never to return. When the system completes a U-task and there are waiting customers, each one is taken immediately into service. We analyze both multiple and single U-task scenarios and consider both exponentially and generally distributed task and impatience times. We derive the (partial) probability generating functions of the number of customers present when the system is occupied with a U-task as well as when it acts as an M/M/∞ queue and we obtain explicit expressions for the corresponding mean queue sizes. We further calculate the mean length of a busy period, the mean cycle time, and the quality of service measure: proportion of customers being served.

Project management for arbitrary random durations and cost attributes by applying network approaches

This paper concentrates on the quality management of a project by applying network approaches and statistics methods. A large-scale project can be modeled as a project network. This paper tries to schedule the duration of the project by applying the approaches in network analysis in case the activity duration and the corresponding cost are both arbitrary random variables with a probability distribution. Subject to the project time (the deadline to complete the project) constraint and the budget constraint, this paper studies how to schedule all activity durations of the project. Two algorithms are proposed to generate all upper and lower duration vectors for the project. All feasible activity durations are among such upper and lower duration vectors. Whenever any constraint is changed during the project period, we can re-schedule the activity durations efficiently by applying the proposed algorithm. Furthermore, we can evaluate the probability that the project will be executed successfully, subject to the time and budget constraints. Such a probability is an index for measuring the quality and feasibility of the project.

Quantitative tests for stratigraphic cyclicity

AbstractPeriodic Milankovitch (M‐) orbital forcing provides an explanation for subjectively recognized short‐term repetition of lithofacies‐‘cycles’‐in the stratigraphic record. Tests of this explanation often find no order in the lithofacies and/or no regularity in the recurrence of lithofacies. This does notdisprovethe influence of M‐forcing, but a sedimentary response in terms ofirregularM‐forced ‘cycles’ is indistinguishable from one in which repetition of facies is not M‐forced. Use of such cycles in time calibration is correspondingly suspect. Stricter,dimensionalcyclicity invokes Sander's Rule, which suggests periodicity in sedimentation, for which M‐forcing provides an obvious explanation. Time calibration on the basis of strict cyclicity thus appears more dependable. Objective tests for regular M‐forced stratigraphic cyclicity commonly depend upon spectral analyses. Such tests are not unambiguous. Bilogarithmic thickness/frequency plots derived from objective layer thickness inventories (LTI) provide an alternative. Commonly, such plots show power‐law relationships that preclude dimensional M‐cyclicities. By contrast, a model data series that perfectly encodes the M‐cyclic fluctuations in terrestrial insolation generates a strongly inflected, non‐power‐law LTI plot. Power‐law plots result where the model data series is decimated by random hiatuses, with numbers and durations tuned to M‐cycle frequencies. It seems improbable that natural data series record such tuning. The general absence of strict cyclicity in the M‐frequency range is more likely to reflect the nonlinear response of sedimentary systems to cyclic M‐forcing of insolation. Interestingly, when applied to the classically cyclic lacustrine Triassic sediments of the Newark Basin, USA, the LTI test suggests a decimated record, preserving some evidence of M‐cyclicity. Copyright © 2008 John Wiley & Sons, Ltd.

Inventory system with renewal demands at service facilities

Inventory systems where customers join waiting line to receive their demanded items are recently considered by many researchers, as these models allow the study of both queue length and size of the inventory. This article considers a continuous review inventory system at a service facility, wherein an item demanded by a customer is issued to him/her only after performing service of random duration on the item. The service facility is assumed to have waiting hall of infinite size. The arrival time points of customers form a renewal process. The service times are assumed to be distributed as negative exponential. The operating policy is ( s , S ) policy with instantaneous supply of ordered items. We consider two models which differ in the way that ordered items, when received, is brought into the stock. In the first model, the ordered items are brought into the stock immediately. In the second model, the supplied items are brought into the stock only at the next demand epoch. The stationary distribution of the underlying Markov chain is obtained in matrix-geometric form. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady-state case.

On an (s, S) Inventory Policy with Service Time, Vacation to Server and Correlated Lead Time

We consider an inventory with random positive service time. The control policy is of (s, S) type. Customer demands constitute a Markovian arrival process (MAP). Service times have phase type distribution. Lead time for replenishment of inventory follows a correlated process similar to the customer arrival process. At a service completion epoch if no customer is waiting or the inventory level is zero then the server goes on a vacation of random duration. The vacation time is also phase type distributed. On return from vacation if the server finds no customer waiting or inventory level is zero, the server goes on another vacation of random duration having the same phase type distribution as the earlier one; we assume that the successive vacation times are independent of each other. This goes on until on return he finds at least one customer and at least one item in the inventory at which he starts serving. The customer arrival process is subject to balking. While waiting for service, customers may become impatient and leave the system (renege). Under these assumptions the underlying level dependent quasi birth-death process (LDQBD) is analysed. Several particular cases are considered in which the system is exhaustively studied. Numerical illustrations are provided. A cost function is introduced to numerically evaluate the optimal values of s and S.

Behavioral and physiological responses of the congeneric largemouth ( Micropterus salmoides) and smallmouth bass ( M. dolomieu) to various exercise and air exposure durations

Two of the major stressors associated with the catch-and-release of recreationally angled fish are exercise and air exposure. This study investigated the combined effects of exercise and air exposure duration on the congeneric largemouth bass Micropterus salmoides and smallmouth bass M. dolomieu, two of the most popular sportfish in North America. We simulated angling by exercising the fish (i.e., chasing by hand) for either 20 or 180 s and then immediately exposed fish to air for random durations ranging from 0 to 10 min. To assess the combined effects of increased exercise and air exposure durations, and the time needed to recover, we monitored several behavioral responses for both species. For largemouth bass, we also measured hematological variables (i.e., lactate, glucose, and hematocrit). Never did exercise and air exposure have a significant effect on the same response measured in the same species, suggesting that there are two separate responses occurring: likely an exercise response and a stress response associated with hypoxia. Our results also indicate that largemouth bass recover from combined exercise and air exposure faster than smallmouth bass. Smallmouth bass took longer to regain equilibrium, to stop leaning, and to return to very shallow (i.e., normal) ventilation depth, as a result of the treatments of exercise and air exposure, than the largemouth bass. This is likely due in part to behavioral and habitat differences between the two species as well as their different aerobic capacities and sensitivities to hypoxia. Interestingly, no mortality was observed despite air exposure durations of up to 10 min. It is still unclear how air exposure interacts with environmental stressors, such as water temperature. We conclude, based on these findings and as suggested from other studies, that air exposure is a significant stressor, and that species-specific guidelines are needed for catch-and-release practices to be most effective, and to best insure the sustainability of fisheries.

Mission reliability analysis of fault-tolerant multiple-phased systems

Fault-tolerant multiple-phased systems (FTMPS) are defined as systems whose critical components are independently replicated and whose operational life can be partitioned into a set of disjoint periods, called “phases”. Because of their deployment in critical applications, their mission reliability analysis is a task of primary relevance to validate the designs. This paper is focused on the reliability analysis of FTMPS with random phase durations, non-exponentially distributed repair activities and different repair policies. For self-repairable FTMPS with a component-level reconfiguration architecture, we derive several efficient formulations from the underlying structure characteristics for their intraphase behavior analysis. We also present a uniform solution framework of the mission reliability for FTMPS with generally distributed phase durations. Compared with existing methods based on deterministic and stochastic Petri nets or Markov regenerative stochastic Petri nets, our approach is more simple in concept and powerful in computation. Two examples of FTMPS are analyzed to illustrate the advantages of our approach.

A two-stage stochastic programming approach for project planning with uncertain activity durations

This paper investigates the problem of setting target finish times (due dates) for project activities with random durations. Using two-stage integer linear stochastic programming, target times are determined in the first stage followed by the development of a detailed project schedule in the second stage. The objective is to balance (1) the cost of project completion as a function of activity target times with (2) the expected penalty incurred by deviating from the specified values. It is shown that the results may be significantly different when deviations are considered, compared to when activities are scheduled as early as possible in the traditional way. For example, the optimal target completion time for a project may be greater than the makespan of the early-start schedules under any scenario. To find solutions, an exact algorithm is developed for the case without a budget constraint and is used as a part of a heuristic when crashing is permitted. All computational procedures are demonstrated on a set of 150 benchmark problems consisting of 90 activities each.

Optimal booking of machines in a virtual job-shop with stochastic processing times to minimize total machine rental and job tardiness costs

We treat a virtual job-shop problem of sequencing n jobs on m unique machines. Each machine is outsourced with known renting cost per time unit. The job-operation processing times have random durations, and each job has its tardiness penalty function. The objective is to determine in advance the machine booking schedule that maximizes an economic gain. We present a simulation based on a cyclic coordinate descent search- algorithm and greedy priority dispatching rule that delivers a rent timetable that minimizes the expected total cost.

A SHOCK TUBE?BASED FACILITY FOR IMPACT TESTING

Abstract : Many dynamic testing techniques use gas guns as a pressure generator. The pressure generated from the gas guns is often of low velocity and low energy and has a relatively random or short duration of a uniform pressure level. This kind of pressure is not well defined and cannot be converted into other application conditions. With aims at improving experimental capability and expanding the research horizon, a shock tube was designed and constructed; and innovative applications were explored. With proper adjustments of gas components and gas pressures, well-defined pressure sources could be produced. With appropriate designs of a force transformer, various testing parameters required for different, dynamic experiments could also be simulated. In this paper, a piston-like impactor was inserted into the shock tube as a pressure transformer. The feasibility of using the shock-tube-based facility for impact testing was demonstrated.