Yoshio Hattori

Optimal Reliability Allocation by Branch-and-Bound Technique

The paper presents an efficient method for finding the exact optimal solutions of reliability allocation problems that are formulated as an integer nonlinear programming problem generalized to handle nonlinear constraints and nonseparable problems. The method is based on branch-and-bound and developed by considering separation and relaxation techniques.

An Efficient Bottom-up Algorithm for Enumerating Minimal Cut Sets of Fault Trees

The paper improves the conventional bottom-up algorithm for enumerating minimal cut sets of fault tree. It is proved that, when the logical product of two reduced sum-of-product forms is expanded by the distribution rule, one need only check if each resulting term is absorbed by some terms of two original sum-of-product forms. The algorithm for executing this process is presented and illustrated by an example. The entire computer program is given in a supplement and the computational results for several examples are presented to demonstrate the efficiency of the algorithm.

Reliability Optimization with Multiple Properties and Integer Variables

The paper considers the problem of determining an optimal design of a reliability system with multiple properties and integer variables. This problem is formulated as a multiobjective nonlinear pure-integer programming problem. The method for solving this problem consists of three techniques: 1) narrowing a given feasible region if the region is too wide, 2) obtaining exactly the set of Pareto-optimal solutions, and 3) selecting the best one for decision makers from the set of Pareto-optimal solutions. An increase in the number of objective functions scarcely affects the size of problem. An example is included.

Reliability of All Possible Series-Parallel Redundant Structures of M I.I.D. Units with Two Failure Modes

The paper presents a method for generating systematically and exactly all possible series-parallel (s-p) structures for several i.i.d. units. The method is modified in order to calculate the failure probabilities and reliabilities of all the possible s-p redundant structures for the i.i.d. units with two failure modes. Included is an example of finding an optimal s-p redundant structure subject to four constraints for reliability (two for failure probabilities and two for fail-safe).

Transient Characteristics of Constant Velocity Faraday-Type MHD Generator

Transient characteristics of an open-cycle constant velocity Faraday-type MHD generator comparable to the size of Russian U·25 (MHD Experimental Generator at the Institute for High Temperatures, Moscow) are presented. Transient responses to start-up, shutdown and load changes of a subsonic MHD generator are numerically calculated solving unsteady magnetohydrodynamic equations. Results show that the MHD generator can attain another steady state within ten times the gas residence time for most of load changes. When loads locally change, shock waves occur to cause considerable fluid property change. The most dangerous transient characteristics are due to very large transient Hall fields at the start-up, which leads to breakdown between adjacent electrodes, particularly, the down-stream region of the generator. For local short-circuiting or load changes throughout the generator, no serious problems arise except for those associated with current density increase.

Discussion of ``Optimization by Integer Programming of Constrained Reliability Problems with Several Modes of Failure''

Tillmans 1969 treatment for components with several modes of failure and series (or parallel) redundancy using the components is discussed. This note claims that his treatment is wrong. Author replies and further discussion are provided.

OPTIMAL CONTROL OF STEADY STATE NEUTRON FLUX DISTRIBUTION IN SLAB REACTORS.

The algorithm is presented for seeking optimal control of the steady state neutron flux distribution making use of Pontryagins Maximum Principle, for a one group model of the bare slab reactor as well as for a two group model of the reflected slab reactor, both of which are homogeneous except for the control material. The performance criterion to be minimized is the spatial square integral error between the thermal flux distribution and the desired flux shape, and the control variable is the cross section of the absorbing material. A numerical example is given for the bare reactor where the desired shape is assumed to be uniformly flat. The non-linear nature of the problem imparts a complex aspect to the algorithm concerning the steepest descent method, as indicated by the numerical example. The results show that, as the bounds of the control variable are relaxed, the number of switchings is increased and a better performance criterion is obtained but this is accompanied by a higher hot spot factor.