Question

Title Consider a system with three components in series. The components have constant failure rates ? 1 ,. Description Consider a system with three components in series. The components have constant failure rates λ1, λ2, and λ3. The failure rate of the third component is three times the failure rate of the second component, and the failure rate of the second component is twice that of the first component. It is desired to achieve a system reliability of 0.95 at time t = 100 hours. Determine (a) The failure rates of the components; (b) The MTTF of the system; (c) The probability of having 0, 1, and 2 failures in 100 hours of operation; and (d) The failure rates of the components if a reliability of 0.95 is desired at the MTTF.​

Answer 1

Answer:

BASIC PROBABILITY THEORY: Rules for combining probability, Probability Distri

butions, Random variables, density and distribution functions. Mathematical

expectation. Binominal distribution, Poisson distribution, normal distribution,

exponential distribution, Weibull distribution.

2

RELIABILITY: Definition of Reliability. Significance of the terms appearing in the

definition. Component reliability, Hazard rate, derivation of the reliability function in

terms of the Hazarad rate, Hazard models.

FAILURES: Causes of failures, types of failures, Modes of failure, Bath tub curve, Effect

of preventive maintenance. Measures of reliability: mean time to failure and mean

time between failures.

3

CLASSIFICATION OF ENGINEERING SYSTEMS: Series, parallel, series-parallel, parallel-

series and non-series-parallel configurations. Expressions for the reliability of the

basic configurations.

RELIABILITY LOGIC DIAGRAMS: Reliability evaluation of Non-series-parallel

configurations: minimal tie-set, minimal cut-set and decomposition methods.

Deduction of the minimal cut sets from the minimal path sets.

4

DISCRETE MARKOV CHAINS: General modeling concepts, stochastic transitional

probability matrix, time dependent probability evaluation and limiting state

probability evaluation. Absorbing states.

CONTINUOUS MARKOV PROCESSES: Modeling concepts, State space diagrams,

Stochastic Transitional Probability Matrix, Evaluating limiting state Probabilities.

Reliability evaluation of repairable systems.

5

SERIES SYSTEMS AND PARALLEL SYSTEM: Series systems, parallel systems with two

and more than two components, Network reduction techniques. Minimal cut

set/failure mode approach

UNIT-I