Reliability Modeling and Prediction
Block diagrams and models
A reliability block diagram (RBD) represents the logic of success, not necessarily the physical layout. Series blocks are all required; parallel blocks provide redundancy. Candidates must translate a described system into an RBD and compute system reliability. Traps: confusing physical series with reliability series, and forgetting that a standby unit needs a switch model.
Distributions
- Exponential: constant hazard, MTBF = 1/lambda; used for random failures.
- Weibull: shape beta sets behavior (beta < 1 infant mortality, beta = 1 random, beta > 1 wear-out); scale eta is the characteristic life at 63.2% failure.
- Normal and lognormal: wear-out and time-to-repair modeling. Know how to read a Weibull plot: slope gives beta, and the 63.2% intersection gives eta.
Markov and fault tree models
Markov models handle state transitions and repair; fault trees use gates (AND, OR) to link basic events to a top event. Minimal cut sets identify single points of failure. Traps include double-counting dependent events and ignoring repair in availability models.
Worked example
Three components in parallel, each R = 0.9: R_system = 1 - (1 - 0.9)^3 = 1 - 0.001 = 0.999. If a switch with R = 0.99 is required for each standby unit, multiply the redundancy benefit by the switch reliability; the gain shrinks fast.
Prediction cautions
Prediction models assume constant hazard and generic environments. Use them for comparison and allocation, then confirm with test and field data. Do not present a prediction as a demonstrated value.