A technique which combines modified pattern search methods with composite designs and polynomial constraints to solve constrained optimization problems

This paper presents a method of selecting design parameters which optimizes a specific measure (aircraft design example: minimum weight, maximum mission effectiveness) and guarantees designated levels of response in specified areas (such as combal ceiling, acceleration time). The method employs direct search optimization applied to a nonlinear functional constrained by nonlinear surfaces. The composite design technique is combined with regression methods to determine adequate surface representations with a minimum of required data points. A sensitivity analysis is conducted at the optimum set of design parameters to test for uniqueness.     

On the use of standard tables to obtain Dodge-Romig LTPD sampling inspection plans

Procedures are described which yield single and double sample Dodge-Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge-Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific “process average” and lot size rather than a compromise plan designed to cover intervals on these two parameters.     

On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

An empirical bayes estimator for the scale parameter of the two-parameter weibull distribution

An empirical Bayes estimator is given for the scale parameter in the two-parameter Weibull distribution. The scale parameter is assumed to vary randomly throughout a sequence of experiments according to a common, but unknown, prior distribution. The shape parameter is assumed to be known, however, it may be different in each experiment. The estimator is obtained by means of a continuous approximation to the unknown prior density function. Results from Monte Carlo simulation are reported which show that the estimator has smaller mean-squared errors than the usual maximum-likelihood estimator.     

Minimax inspection strategies for single unit systems

A model for proper scheduling of inspections is considered, if system failures can be detected only by checking. Two cases are analyzed: replacement and no replacement of a failed system. On condition that no or only partial information on the lifetime distribution of the system is available, minimax inspection strategies are obtained with respect to cost criterions.     

Remarks on a univariate shock model with some bivariate generalizations

In a 1973 paper J. D. Esary, A. W. Marshall, and F. Proschan [5] considered a shock model giving rise to various nonparametric classes of life distributions of interest in reliability theory. A number of authors have extended these results in a variety of directions. In this paper, alternative proofs of the increasing failure rate (IFR) and decreasing mean residual life (DMRL) results are given which do not make use of the theory of total positivity. Some bivariate extensions are then obtained using a shock model similar to that originally used by H. W. Block, A. S. Paulson, and R. C. Kohberger [2] to unify various bivariate exponential distributions.     

A dynamic inventory system with recycling

This paper deals with a periodic review inventory system in which a constant proportion of stock issued to meet demand each period feeds back into the inventory after a fixed number of periods. Various applications of the model are discussed, including blood bank management and the control of reparable item inventories. We assume that on hand inventory is subject to proportional decay. Demands in successive periods are assumed to be independent identically distributed random variables. The functional equation defining an optimal policy is formulated and a myopic base stock approximation is developed. This myopic policy is shown to be optimal for the case where the feedback delay is equal to one period. Both cost and ordering decision comparisons for optimal and myopic policies are carried out numerically for a delay time of two periods over a wide range of input parameter values.