Optimal mission abort policy for phased-mission systems

For safety-critical systems such as aircrafts and submarines, mission abort is commonly deployed to enhance system survivability at the cost of reducing mission success probability. In addition to mission abort, protective device can also mitigate the failure risk of safety-critical systems by reducing the magnitude of external shocks. Considering the effect of protective device on system failure behavior, this article proposes a condition-based mission abort policy where a mission is terminated and rescue procedure starts immediately if the state of system is worse than a control limit. Based on the developed mission abort policy, mission reliability and system survivability are evaluated to analyze the risk of mission failure and system failure. The optimal mission abort threshold balancing the tradeoff between mission reliability and system survivability is investigated. Furthermore, the joint optimization of mission abort and protective device selection policies is explored by simultaneously optimizing the defensive factor and abort threshold. A numerical example on a hydraulic system is presented to illustrate the applicability of the proposedpolicies.

Optimal mission abort policy for systems subject to random shocks based on virtual age process

Reliability modeling for balanced systems considering mission abort policies

The balanced system often performs key missions in many fields, such as aerospace, new energy storage, and the military. However, the failure of the system can cause major losses. Therefore, the mission needs to be aborted when the risk of system failure is higher. In this paper, the optimal mission abort policy for a k‐out‐of‐n: F balanced system is studied. The system with a restricted mechanism consists of m sectors and there are n components in each sector, in which the components fail due to two situations: internal failure or external shocks. If the number of working components in m sectors is the same, the system is balanced. If one component fails, the system will force down or resume a component with a probability to keep balance. The model of the mentioned system is established, and the Markov process imbedding approach is used for deriving the reliability indices. Two optimization models are established according to two competitive abort criteria. Finally, an unmanned aerial vehicle performing a mission is discussed to illustrate the proposed mission abort policy.

Optimizing time-varying performance and mission aborting policy in resource constrained missions

This paper presents a fuzzy graph evaluation and review technique (GERT) analytic model for multi-phased mission systems that provides a new approach to calculate mission performance of phased-mission system (PMS). The model extends traditional analytic models of PMS using logic diagram method (such as Fault Trees and Binary Decision Diagram) and state transition method (such as Markova Model). By using fuzzy GERT based on grey number, we provide a stochastic network to build the model of phased-mission which avoids the difficulty to give exact logic relation in reliability analysis method based on logic diagram and the state space explosion and the mapping problems that are encountered by the Markov chain approach, and at the same time, we use gray number to describe the phased-mission transition probability which is more easier to determine than traditional models. In this model, as the key performance indicators of PMS, mission cycle and success probability are solved. Finally, a computation study of typical carrier operational mission is given to illustrate how to apply the approach to calculate mission reliability of PMS. Furthermore, sensitivities of mission cycle and success probability in the model are analyzed.

This paper models a real-time warm standby system that has to accomplish a specified amount of task by a hard deadline. The system is subject to corrective replacements (CRs) upon failure of its operating element. It can also be renewed according to a predetermined schedule through preventive replacements (PRs). To facilitate an effective recovery of system operation after replacements, periodic backups are performed so that warm standby elements, upon being activated, can take over the mission task from the last backup point instead of from scratch. This paper presents a novel integrated model that considers effects of periodic backups, CRs and PRs in analyzing and optimizing real-time warm standby systems. Mission success probability and expected mission completion time are evaluated. Impacts of different mission and element parameters on mission success probability, optimal backup and PR policies, and optimal element activation sequence are investigated. It is shown that in warm standby systems with periodic backups and tight deadlines, PRs can improve the mission success probability even when they take the same time as CRs. When the maximum allowed mission time exceeds a certain level, PRs become ineffective and the optimal policy can involve only periodic backups.

The problem of off-line inspection is of both practical and theoretical interest. It has been the subject of research in somewhat simplistic scenarios. In this paper, the theoretical coverage of this problem is extended to include inspection errors. In particular, a process which is subject to random failures that sequentially produces a batch of units is investigated. After the batch is complete, off-line inspections are performed. In the proposed model it is these inspections that are subject to errors. The optimal inspection policy, i.e., which units should be inspected and the inspection order so as to minimize the expected number of inspections, is determined. The considered objective function is to find the point at which the machine fails with a given confidence level. The optimal policy is found by a dynamic programming algorithm and four different heuristic policies are investigated. An extensive computational study that examines the behavior of both the optimal and heuristic policies is presented. In particular, the effect of the model parameters on the behavior of the optimal policy is analyzed. The heuristic policies are computationally studied with the goal of comparing their quality to the optimal solution, and also to compare the heuristics themselves.

We study lot-size policies in a serial, multistage manufacturing/inventory system with two key generalizations, namely (1) random yields at each production stage and (2) an autoregressive demand process. Previous research shows that the optimal policies in models with random yields (even in models with a single installation) lack the familiar order-up-to structure and are not myopic. Thus, dynamic programming algorithms are needed to compute optimal policies, and one encounters the “curse of dimensionality”; this is exacerbated here by the need to expand the size and dimension of the state space to accommodate the autoregressive demand feature. Nevertheless, although our model is more complex, we prove that there is an optimal policy with the order-up-to feature and, more importantly, that the optimal policy is myopic. This avoids the computational burden of dynamic programming. Our results depend on two assumptions concerning the stochastic yield, namely that the expected yield at a work station is proportional to the lot size, and the distribution of the deviation of the yield from its mean does not depend on the lot size. We introduce the concept of echelon-like variables, a generalization of Clark and Scarf's classical concept of echelon variables, to derive the structure of optimal policies. Furthermore, we show that the same kind of policy is optimal for several criteria: infinite-horizon discounted cost, infinite-horizon long-run average cost, and finite-horizon discounted cost (with the appropriate choice of the salvage value function).

Optimal mission abort and selective replacement policies for multi-state systems

The stagecoach problem is a special type of network analysis problem in which the cities (nodes) are arranged in stages. By such human or natural arrangement, a journey from City 1 in stage 1 to City n in stage n involves visiting only one city in each intermediate stage. The stagecoach problem involves the determination of the minimum cost flow in which basically two methods have been in use. One of the methods is by listing all possible routes, computing their corresponding costs and selecting the minimum cost route. This procedure entails much computational effort. The second procedure is to determine the suboptimal cost of routes between any two consecutive stages. Though this second approach has less computational effort, its overall optimal policy could be wrong because the choice of a least expensive route at one stage may result in our adopting a more expensive route at a later stage. In this paper we present a recursive dynamic programming algorithm for solving the stagecoach problem. The algorithm is computationally more efficient than the first method as it obtains its minimum total cost using the suboptimal policies of the different stages without computing the cost of all the routes. By the dynamic programming algorithm of this paper, the possibility of missing the minimum cost route is ruled out as could happen in the second approach. The dynamic programming algorithm for obtaining the minimum cost path in a stagecoach problem is numerically illustrated Keywords : Network analysis, stagecoach, dynamic programming algorithm Global Journal of Mathematical Sciences Vol. 7 (1) 2008: pp. 15-20

Data backups play an important role in effective recovery of system operations, especially, those in computing and Information Technology-related applications. By saving copies of information associated with the completed part of a mission task, a failed system, upon being repaired, can resume its operation from the latest backup point instead of having to repeat the entire work from scratch. This paper considers a repairable, real-time system performing a sequence of nonperiodic full backup (FB) and incremental backup (IB) procedures during its mission. The mission succeeds if a specified amount of work can be accomplished by the system within a deadline. New contributions of this paper are twofold. First, a numerical recursive method is proposed to model effects of the nonperiodic, mixed backup strategy in assessing mission success probability, and expected completion time of the considered system. The method is applicable to any distribution of FBs and IBs and has no limitation on system time-to-failure distributions. Second, the optimal backup policy problem is formulated and solved, which finds the distribution of FBs and IBs maximizing the mission success probability. Examples are provided to illustrate the proposed methodology as well as influence of different parameters on the optimal solution. Advantages of adopting nonperiodic backups over periodic ones are also illustrated.

Optimal radio access technology selection on heterogeneous networks

Dynamic programming for optimal ship refueling decision

This paper models a type of vendor-managed inventory (VMI) agreement that occurs in practice called a (z, Z) contract. We investigate the savings due to better coordination of production and delivery facilitated by such an agreement. The optimal behavior of both the supplier and the retailer are characterized. The optimal replenishment and production policies for a supplier are found to be up-to policies, which are shown to be easily computed by decoupling the periods when the supplier outsources from those when the supplier does not outsource. A simple application of the newsvendor relation is used to define the retailer's optimal policy. Numerical analysis is conducted to compare the performance of a single supplier and a single retailer operating under a (z, Z) VMI contract with the performance of those operating under traditional retailer-managed inventory (RMI) with information sharing. Our results verify some observations made in industry about VMI and show that the (z, Z) type of VMI agreement performs significantly better than RMI in many settings, but can perform worse in others.