Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

The impotence of conventional arms control: why do international regimes fail when they are most needed?

Amid tensions with the West over Ukraine, Russia pulled out of the Treaty on Conventional Armed Forces in Europe in March 2015. The Russian case is another example of a country disengaging from conventional arms control when relations with other member states deteriorate. This raises an important question: can arms control regimes aimed at preventing conflict survive periods of tension and preserve peace? This article argues no. It demonstrates that the prospect and stability of conventional arms control regimes depend on healthy international relations. In times of tension, governments rely on military institutions for advice and absorb military biases incompatible with arms control. Therefore, these regimes fail when most needed and are impotent as instruments of peace. Beyond conventional arms control, the article hints at the fragility of nuclear agreements such as the 2015 Iran deal and the 2010 New START between the United States and Russia.     

The Just Warrior Ethos: A Response to Colonel Riza

In 2014, Colonel M. Shane Riza published an article in this journal arguing that remotely piloted aircraft (RPA) and robotic weapons threaten the US Air Force’s warrior ethos. Riza has clearly articulated the sentiments of one side of a vibrant debate within our service. This paper presents an alternative view; a view held by some who have experienced these new forms and tools of war, and who have wrestled with their implications first-hand. In this paper, we address some methodological concerns with Riza’s approach and then engage some misunderstandings about RPA’s relationship to military history and to risk. The second part of this paper takes a close look at some of the early Just War thinkers to determine what implications the tradition may have on the warrior ethos. We propose, as an alternative to Riza’s position, a return to an ethos grounded in humility, charity, and a conception of war as a last resort; in short, a return to the Just Warrior Ethos.     

Transient analysis of multiple-unit reliability systems

A general Markovian model representing several multiple-unit redundant repairable systems is proposed and its transient behavior is studied. Specifically, for multiple-unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.     

On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

Bounds and properties of the expected value of sample information for a project-selection problem

In this article we extend the work of Mehrez and Stulman [5] on the expected value of perfect information (EVPI) to the expected value of sample information (EVSI) for a class of economic problems dealing with the decision to reject or accept an investment project. It is shown that shifting the mean of the underlying a priori distribution of X, the project's monetary value from zero in either direction will decrease the associated EVSI of Y, the random sampled information. A theorem is then presented which gives an upper bound on the EVSI over all distributions of Y, as well as the structure of the posterior mean E[X|Y] for which this upper bound is achieved. Finally, the case where E[X|Y] is linear in Y is discussed and its performance compared with that of the optimal case.     

Herdsmen militancy and humanitarian crisis in Nigeria: A theoretical briefing

This article explores the phenomenon of herdsmen militancy as a new trajectory for the farmer–herder crisis in Nigeria, with reference to its humanitarian implications. Relying on a systematic analysis of secondary data and aligning with the analytical anchorage of liberal political ecology theory, the article posits that herdsmen militancy depicts a contradiction in agrarian relations in the context of a national security crisis which has been complicated by salient socio-ecological factors such as climate change, armed violence, and identity politics. In view of the dire humanitarian consequences of this situation, the article submits that herdsmen militancy constitutes a major threat to human and national security in Nigeria. It makes a case for a pragmatic policy capable of mitigating the myriad socio-ecological factors that tend to trigger herdsmen militancy, with prohibition on open grazing in critical hotbeds of herder–farmer conflict as a strategic measure.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

Optimal maintenance policies for constantly monitored systems

A multistate system is assumed to be constantly monitored; i.e., the state of the system is always known with certainty. Damage to the system accumulates via a continuous-time Markov process. A model of the system including restoration costs and state occupation costs is developed. It is shown that under certain conditions the optimal restoration policy for the system is a control limit rule. A control limit rule is a policy which requires restoration of the system whenever the damage exceeds a certain level. Examples are presented to show that there are several situations in which, perhaps surprisingly, control limit rules are not optimal.     

Linear search with bounded resources

A point is placed at random on the real line according to some known distribution F, and a search is made for this point, beginning at some starting points s on the line, and moving along the line according to some function x(t). The objective of this article is to maximize the probability of finding the point while traveling at most d units. Characterizations of simple optimal searches are found for arbitrary distributions, for continuous distributions with continuous density everywhere (e.g., normal, Cauchy, triangular), and for continuous distributions with density which is continuous on its support (e.g., exponential, uniform). These optimal searches are also shown to be optimal for maximization of the expected number of points found if the points are placed on the line independently from a known distribution F.