Stat 567:Statistical Reliability
Twenty Third Class (December 3, 1997)

Models of System Reliability

Class Objectives:

• Learn to use reliability block diagrams in reliability calculations
• Learn the difference between cold and hot standby redundancy
• Learn approximate techniques of reliability calculation

Homework Assignments:

• Take a look at Military Reliability Standards and Handbooks to learn about MIL-STD-217 and other military reliability standards.
• A system is to be designed with an overall reliability of .999 using components having individual reliabilities of .7. What is the minimum number of componets that must be connected in parallel?

Class Outline and Main Points:

• Reliability
  • Mission reliability (Mil-Std-721)
    • The mission reliability is the probability that an item will perform an intended function under stated conditions for a stated period of time
    • User viewpoint
  • Basic reliability (Mil-Std-721)
    • The basic reliability is the probability that an item will perform with no troubles requiring repair under stated conditions for a stated period of time
    • repairperson viewpoint
• Coherent systems
  • Increasing binary function
  • Every component is relevant to the system
  • An unnecessarily abstract presentation of a simple idea.
• Reliability Block Diagrams (RBD)
  • Series systems
  • Parallel systems
  • k-out-of-n system
  • PBX example
• Formulas for calculations of system reliability
  • Series system
    • System reliability is the product of the component reliabilities
    • System reliability rapidly decreases as the number of components increase
    • Unreliabilities add up when you have a moderate number of highly reliable components
    • Reliability budgets
    • Example: Old Christmas tree lights
    • The system failure rate is the sum of the component failure rates
  • Parallel system
    • System unreliability is the product of the component unreliabilities
    • Hot-standby
    • Example: New Christmas tree lights
  • Series-parallel systems
    • PBX example
  • k-out-n system
• Conditional probability approach for calculating system reliability
  • Wheatstone bridge
• Cut set method of approximate reliability calculations
  • Cut sets
  • Minimum cut sets
  • Calculation technique
• Cold-standby redundancy
  • Perfect switching
  • Inperfect switching
  • Switches must be very reliable
• Sample questions from the Certified Reliability Engineering (CRE) exam
  • Certified Reliability Engineer (CRE): Certification Requirements
  • Certified Reliability Engineer (CRE) Body of Knowledge
  • The CRE Examination Study Guide by B. L. Dodson and
  • Practical Reliability Engineering. Second Edition. (1985) Patrick D. T. O' Connor.
  • The CRE Examination Study Guide

Study Questions

• What is the difference between cold and hot standby redundancy?
• Why must a switch be very reliable?
• Why is it better to do a system budgets using unreliabilities than reliabilities?
• What should you read to prepare for the CRE exam?

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