Course Archives: Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, Bangalore

Course Archives Statistical Quality Control & Operations Research Unit

Course: Reliability, Maintainability And Safety I
Level: Postgraduate
Time: Currently not offered

Syllabus: Probability:
Concept and Definition: Sample space and events; basic properties with union and intersection of events; conditional probability Bayes rule.
Discrete random variables: Binomial, Geometric, Negative Binomial, Poisson; Poisson approximation to Binomial distribution; independent random variables and their sum; moments expectation, variance; Chebychevs inequality.
Continuous random variables: Distribution function and density function; Uniform, Normal, Exponential, Gamma, Weibull their moments; change of variable formula.
Jointly distributed random variables: Conditional distribution; correlation coefficient; order statistics; Central Limit Theorem.
Reliability, Maintainability and Safety:
Concept of Reliability: Definition of reliability and related measures; concept of failure; quality and reliability; importance of reliability.
Failure Patterns Probability Models: Hazard models bath tub curve; causes of early failure; failure time distributions: exponential, Weibull, normal, log normal, gamma; their properties and uses.
System Reliability Computation: Series, parallel, series parallel, bridge and r out of n configurations: reliability block diagram; determination of reliability through combinatorial methods of inspection, events space, cut set and tie set; strength and stress distribution safety factor and reliability.

Reference Texts:
1. Introduction to Probability Theory: By Hoel P.G., Port S.C. and Stone C.J. (1971), Houghton Mifflin Company.
2. An Introduction to Probability Theory and its Applications (Vol. I): By Feller W. (1957), John Wiley & Sons.
3. An Introduction to Probability Theory and its Applications (Vol. II): By Feller W. (1966), John Wiley & Sons.
4. A first Course in Probability: By Ross S.M. (2005), Prentice Hall.
5. Reliability in Engineering Design: By Kapur K.C. and Lamberson L.R. (1977), John Wiley & Sons, Inc.
6. Statistical Methods for Reliability Data: By Meeker W.Q. and L.A. Escobar L.A. (1998), John Wiley & Sons, Inc.
7. Statistical Models and Methods for Lifetime Data: By Lawless J.F. (1982), John Wiley & Sons, Inc.
8. System Reliability Theory: By Hoyland A. and Rausand M. (1994), John Wiley & Sons, Inc.

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