CMRP Reliability Data Analysis and Statistics 2 — Questions and Answers
Question 1: What are the two primary parameters of a two-parameter Weibull distribution?
- Mean and standard deviation
- Shape (β) and scale (η) (Correct answer)
- Location and dispersion
- Failure rate and repair rate
Correct answer: Shape (β) and scale (η)
The two-parameter Weibull distribution uses the shape parameter (β) and scale parameter (η, characteristic life) to model failure behavior across a wide range of failure types.
Question 2: In Weibull analysis, what does a shape parameter (β) value of less than 1 indicate about the failure pattern?
- Wear-out failures with increasing failure rate
- Random failures at a constant rate
- Infant mortality failures with a decreasing failure rate (Correct answer)
- Bimodal failures from two competing failure modes
Correct answer: Infant mortality failures with a decreasing failure rate
β < 1 indicates a decreasing failure rate, characteristic of infant mortality where weak items fail early and the surviving population becomes more reliable over time.
Question 3: When the Weibull shape parameter (β) equals exactly 1, the Weibull distribution reduces to which distribution?
- Normal distribution
- Lognormal distribution
- Exponential distribution (Correct answer)
- Gamma distribution
Correct answer: Exponential distribution
β = 1 produces a constant failure rate, which is the defining characteristic of the exponential distribution used for random, memoryless failures.
Question 4: What does the eta (η) parameter represent in a Weibull distribution?
- The minimum guaranteed life before any failure
- The characteristic life at which 63.2% of units have failed (Correct answer)
- The median time to failure
- The maximum expected service life
Correct answer: The characteristic life at which 63.2% of units have failed
The scale parameter η (characteristic life) is the time at which exactly 63.2% of units have failed, regardless of the value of the shape parameter β.
Question 5: A Weibull shape parameter (β) of approximately 3.5 is often associated with which type of failures?
- Random electronic failures
- Infant mortality defects
- Wear-out failures approximating a normal distribution (Correct answer)
- Corrosion-induced sudden failures
Correct answer: Wear-out failures approximating a normal distribution
β ≈ 3.5 produces a symmetrical, bell-shaped failure distribution that closely approximates the normal distribution, typically seen in mechanical wear-out and fatigue failures.
Question 6: Which graphical technique is most commonly used to estimate Weibull parameters from failure data?
- Scatter plot with linear regression
- Weibull probability paper with median rank plotting (Correct answer)
- Histogram with normal curve overlay
- P-chart with control limits
Correct answer: Weibull probability paper with median rank plotting
Median rank plotting on Weibull probability paper (or software equivalent) linearizes the Weibull CDF so that slope and intercept yield the shape and scale parameters.
Question 7: The lognormal distribution is best suited to model which reliability scenario?
- Electronic components with a constant failure rate
- Repair times and failures due to fatigue or corrosion crack growth (Correct answer)
- Catastrophic failures in safety-critical systems
- Infant mortality defects caught during burn-in
Correct answer: Repair times and failures due to fatigue or corrosion crack growth
The lognormal distribution is commonly applied to repair times and cumulative-damage failure mechanisms such as fatigue, corrosion, and stress-corrosion cracking.
CMRP Reliability Data Analysis and Statistics 2
What are the two primary parameters of a two-parameter Weibull distribution?