Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

Scheduling of parallel processors: A posterior bound on LPT sequencing and a two-step algorithm

This article considers the problem of scheduling parallel processors to minimize the makespan. The article makes two key contributions: (1) It develops a new lower bound on the makespan for an optimal schedule, and (2) it proposes an efficient two-step algorithm to find schedules of any desired accuracy, or percent above optimal. In addition, a posterior bound on LPT (longest processing time) sequencing is developed in the article. It is proved that this bound dominates the previously reported bounds on LPT sequencing.     

Two‐dimensional failure modeling with minimal repair

In this paper, we discuss two‐dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one‐dimensional case to the two‐dimensional case and characterize the failures over a two‐dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two‐dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Landmarks in defense literature

The Brain of an Army: a Popular Account of the German General Staff. By Spenser Wilkinson. Archibald Constable, London (1st edition 1890, 2nd edition 1895)     

Partitioning and balancing for the assembly of nozzle guide vanes in gas turbine engines

The gas turbine engine is used to power many different types of commercial and military aircraft. During the scheduled maintenance of these engines, many of the turbine components are replaced. Of particular importance to us is the replacement of nozzle guide vanes in the nozzle assembly section of the engine. Individual vanes are selected from inventory to make up sets, and each set must meet certain characteristics in order to be feasible. The vanes in each set must then be sequenced in order to meet additional criteria. In this article, we give heuristics for the above partitioning and sequencing problems. Empirical analyses, using actual data from a branch of the armed services and a major engine manufacturer, are used to evaluate the proposed heuristics. The results of these analyses indicate that the heuristics are effective.     

Aircraft sortie effectiveness model

A mathematical model describing the sortie of a single aircraft under enemy threats, attacking a single passive target, is developed. Emphasis is placed on the determination of the probabilities associated with the various events in the sortie. These probabilities are then used to derive appropriate measures of effectiveness. The optimum sortie time is analyzed.