Tabular aids for fitting weibull moment estimates

Moment estimators for the parameters of the Weibull distribution are considered in the context of analysis of field data. The data available are aggregated, with individual failure times not recorded. In this case, the complexity of the likelihood function argues against the use of maximum-likelihood estimation, particularly for relatively large sets of data, and moment estimators are a reasonable alternative. In this article, we derive the asymptotic covariance matrix of the moment estimators, and provide listings for BASIC computer programs which generate tables useful for calculation of the estimates as well as for estimating the asymptotic covariance matrix using aggregated data.     

A measure of effectiveness for sensors and strategies

This paper discusses a possible measure of effectiveness for information sensing equipment, such as radar or sonar, based on its ability to provide information. It is shown that such a measure is particularly appropriate for situations where a sequence of similar limited engagements may occur, as on antisubmarine patrol, for example. In this case the measure expresses the expected rate of gain per engagement of the relative resources of the participants. Rates are calculated for the optimal and certain simpler, but suboptimal, strategies. The measure is illustrated by an exact analysis of a gambling problem and a qualitative treatment of an anti-missile missile allocation problem.     

A comparison of several attribute sampling plans

The purpose of this research is to examine several types of procedures for attribute sampling inspection-the widely used Military Standard 105D plans [8], the lesser known Double Zero plans as developed by Ellis [4] and the Narrow Limit gaging plans of Ott and Mundel [9]. Each of the procedures is described with an effort made to illuminate their more subtle features. Then the plans are compared, whence it is revealed that (i) Narrow Limit gaging plans have a serious weakness in comparison to the others and (ii) Double Zero plans tend to be essentially conservative, but that sufficiently tight Military Standard 105D plans can be selected to achieve comparable performance in all ways.     

Statistical auditing of large-scale management information systems

In recent years many large government and commercial organizations have developed large-scale management information systems. During the early phases of any system development, questions are likely to be raised concerning the criteria of completeness and accuracy of the data. How to respond to these questions is difficult, and represents the general subject of this paper. In particular, this paper describes the application of statistical techniques, namely, various kinds of multivariate data analysis, to the problem of assessing the quality of a large-scale data collection system in the U. S. Navy. Results of using these techniques are described and indicate their usefulness as auditing procedures. While the discussion is placed in a particular context, the procedures should be of value for other large-scale information systems.     

A graph theoretic interpretation of the sufficiency conditions for the contiguous-binary-switching (CBS)-rule

A sufficient condition for the optimality of the CBS-rule due to W. Smith is given a graphic interpretation in terms of ‘convex’ graphs. A convex graph is uniquely constructed (except for a homomorphism), and has the property that the optimum is achieved from any starting point.     

Three-machine flowshop stochastic scheduling to minimize distribution of schedule length

This article studies a special case of stochastic three-machine, permutation flowshop scheduling. It is proved that a sequence where processing times on the first and third machines are in a monotone nondecreasing and nonincreasing order of the likelihood ratio, respectively, and on the second machine are equally distributed, minimizes distribution of schedule length.     

A note on optimal switching between two activities

Let f₁ and f₂ map [0, T] into the real numbers. A system is following either f₁ or f₂ and earning the associated reward ∫ f₁ or ∫ f₂, respectively. It is possible at any time to switch from f_i to f_j by paying a switching cost b > 0. We determine a switching policy which maximizes the total reward. Conditions which guarantee a planning horizon are established.     

A note on values and multilinear extensions

An axiomatic formulation is given of a class of values for cooperative games. This class includes the Shapley value and the Banzhaf index, and is related to the multilinear extension of a game.     

The mixed ordering policy in periodic review stochastic multi-commodity inventory systems

In multi-commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two-commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K₁, or K₂, where max (K₁, K₂) ≤ K ≤ K₁ + K₂, This paper considers a two-commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.