Present practices and future plans for MIL-STD-781

MIL-STD-781 specifies reliability acceptance test procedures based on both fixed-length tests and probability ratio sequential tests. The assumption underlying MIL-STD-781 is a constant mean time between failures (MTBF) and typical practice applies MIL-STD-781 to electrical, electronic, and mechanical equipment. This article discusses some of the difficulties that have prompted the C and D revisions of MIL-STD-781. In addition, it discusses the relationship of MIL-STD-781 with MIL-STD-1635(EC) which deals with reliability growth testing. The article concludes with a discussion of needed research in reliability growth testing, in support of MIL-STD-781, and in the area of stress and its impact of MTBF.     

Warranty analysis and renewal function estimation

Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.     

An application of empirical bayes techniques to the simultaneous estimation of many probabilities

Consider the following situation: Each of N different combat units is presented with a number of requirements to satisfy, each requirement being classified into one of K mutually exclusive categories. For each unit and each category, an estimate of the probability of that unit satisfying any requirement in that category is desired. The problem can be generally stated as that of estimating N different K-dimensional vectors of probabilities based upon a corresponding set of K-dimensional vectors of sample proportions. An empirical Bayes model is formulated and applied to an example from the Marine Corps Combat Readiness Evaluation System (MCCRES). The EM algorithm provides a convenient method of estimating the prior parameters. The Bayes estimates are compared to the ordinary estimates, i.e., the sample proportions, by means of cross validation, and the Bayes estimates are shown to provide considerable improvement.     

A note on a model for evasive vehicle movement along a fixed path

A model for a vehicle moving evasively along a fixed path is defined in terms of a two- state semi-Markov process. An important feature of this model is the continuous movement of the vehicle as a function of time. One potential application of this model is the development of a strategy for the deployment of long-range missiles on long underground tracks.     

An application of servomechanisms to inventory

In recent years, some attention has been devoted to the application of techniques of control theory to inventory management. In particular, H. Vassian (1955) developed a model for a periodic review inventory system utilizing techniques of discrete variable servomechanisms to analyze the system in a cost-free structure. The resulting model is inherently deterministic, however, and emphasizes the control of inventory fluctuation about a safety level by selecting an appropriate order policy. Such an order policy is defined only up to an arbitrary method of forecasting customer demands. The present paper is a continuation of the model developed by Vassian in which exponential smoothing is used as a specific forecasting technique. Full recognition of the probabilistic nature of demand is taken into account and the requirement of minimizing expected inventory level is imposed. In addition, explicit formulas for the variance in inventory are derived as functions of the smoothing constant and the tradeoff between small variance and rapid system response is noted. Finally, in an attempt to remove the bias inherent in exponential smoothing, a modification of that technique is defined and discussed as an alternate forecasting method.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

Monotone failure rates for multivariate distributions

It is shown that the monotone multivariate failure rates of Brindley and Thompson have no natural analog involving the multivariate failure rate function of Basu for absolutely continuous distributions. Quantities related to the multivariate failure rate function are used to define monotone failure rates. It is shown that these are equivalent to the monotone failure rates of Brindley and Thompson. Based on these quantities, the loss of memory property of Marshall and Olkin is characterized.     

Some simple scheduling algorithms

This paper considers situations in which jobs require only one operation on a single machine, or on one of a set of identical machines. Penalty-free interruption is allowed. Some simple algorithms are given for finding optimum schedules to minimize maximum lateness and total delay, for the single-machine case, and maximum lateness for a restricted multi-machine case. A simple flow problem formulation permits minimizing maximum lateness for the more general multimachine case.