A modified block replacement policy

A well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP is its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution. A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.     

Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

ADVANCED US CONVENTIONAL WEAPONS AND NUCLEAR DISARMAMENT

The Obama administration has made a great effort to increase the role of advanced conventional weaponry in US national security thinking and practice, in part to help reinvigorate the global nuclear disarmament agenda by reducing the role played by nuclear weapons in the US defense posture. However, such a strategy is fundamentally flawed because increases in US conventional superiority will exacerbate US relative strength vis-à-vis other powers, and therefore make the prospect of a nuclear weapon-free world seem less attractive to Washington's current and potential nuclear rivals. Consequently, it is highly likely that the impact of efforts to increase US advanced conventional superiority through ballistic missile defense and a conventional “prompt global strike” program will ensure that the Obama administration is adopting a pathway to nuclear abolition on which it is the sole traveler for the foreseeable future.     

Convoys to combat Somali piracy

As the world becomes increasingly globalized, interruptions to international trade cannot be permitted. Piracy off the coast of Somalia has hampered international trade in the region and poses significant risks to the sailors required to navigate those waters. Over the past three years the global community has attempted, through a number of different naval tactics, to stop these acts of piracy; however, these tactics have proven ineffective. This article looks at historical precedence and military theory to support the concept of using convoys to protect the thousands of cargo vessels traveling round the Horn of Africa every year. This tactic will greatly decrease the number of successful pirate attacks and save countless lives in the process.     

‘Immediate redress’: USS Potomac and the pirates of Quallah Batoo

Maritime interests in the twenty-first century are not immune to the growing number of irregular challenges and hybrid threats that have come to dominate land warfare. In order to better understand these challenges a study of naval history can help provide a vital foundation. In the early 1830s the United States Navy dispatched the frigate USS Potomac to Sumatra to investigate a pirate attack on the spice trader Friendship. Potomac's crew of sailors and Marines conducted a landing at the village Quallah Batoo and fought a pitched battle. As the navies of the world approach naval irregular warfare in the new century, studying past examples like Potomac's mission can help illuminate the principles of successful naval irregular warfare.     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998     

A note on a modified block replacement policy for units with increasing marginal running costs

The model for a modified block replacement policy (MBRP) is extended to include running costs. An illustrative example is worked out for the case when item life is exponentially distributed and marginal running cost per unit time increases linearly with the age of the item.