Reliability Engineering Fundamentals
Core definitions and measures
Reliability is the probability that an item performs its required function under stated conditions for a stated period. Every word matters: probability (so it is a random variable, expressed 0-1 or as a percentage), required function (defined by a specification), stated conditions (stress, environment, duty cycle), and stated period (time, cycles, miles). Questions frequently strip one qualifier and ask whether a statement is a valid reliability definition; the correct answer usually restores the missing condition.
The bathtub curve and failure rate
Know the three regions: decreasing early failures (infant mortality, screened by burn-in), roughly constant random failures (described by the exponential distribution, memoryless), and increasing wear-out failures (described by normal or Weibull with shape > 1). The bathtub curve describes populations, not individual units, and not every product shows all three regions.
Key relationships
- Exponential: R(t) = e^(-lambdat), MTBF = 1/lambda, and F(t) = 1 - e^(-lambdat).
- Reliability and unreliability are complements: R + F = 1.
- For series systems, R_system = product of component reliabilities; for parallel (active redundancy), R_system = 1 - product of (1 - R_i).
- Hazard rate h(t) = f(t)/R(t); only the exponential has constant h(t).
Traps to watch
Confusing MTBF with MTTF (repairable vs non-repairable), assuming exponential when wear-out is present, and treating reliability as a deterministic pass/fail property. Also watch unit mismatches (hours vs cycles) and the temptation to average reliabilities in series instead of multiplying.
Worked rule of thumb
Two independent components in series with R = 0.95 each give 0.95 x 0.95 = 0.9025. Adding an identical parallel path to the whole series string gives 1 - (1 - 0.9025)^2 = 0.9905. Redundancy at the system level buys more than redundancy inside one component when the string is long.