The Use of Lagrangian Multipliers for Optimum Reliability Allocation

Abstract

The paper develops a method to allocate reliability to system elements where a system reliability requirement must be met or a total cost constraint is imposed. Parallel and serially arranged elements are considered with each element's probability density function of time to failure being approximated by the two parameter Weibull distribution. The problem is approached as a minimization of total system cost or system unreliability and Lagrange multipliers prove to be useful as a solution technique. A cost function is developed to relate the cost of and element to the reliability level achieved in that element. Both the element's cost function and reliability expression must be continuous variables. Numerical examples are shown for each allocation model.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1972
Accession Number
AD0768585

Entities

People

  • Robert A. Davison

Organizations

  • United States Army Materiel Command

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Computer Programs
  • Computers
  • Digital Computers
  • Engineering
  • Equations
  • Linear Programming
  • Mathematics
  • Optimization
  • Probability
  • Probability Density Functions
  • Redundancy
  • Reliability
  • Simplex Method
  • Simultaneous Equations
  • Standards

Fields of Study

  • Engineering

Readers

  • Operations Research
  • Regression Analysis.
  • Statistical inference.