What is a commonly used model for times to failure (or survival times)?

What is a commonly used model for times to failure (or survival times)?

• A. Normal distribution
• B. Exponential distribution
• C. Weibull distribution
• D. Poisson distribution

Answer: (C)

Times to failure, or survival times, are nonnegative and often show a changing failure rate over time. The Weibull distribution is especially useful here because its hazard function can increase, decrease, or stay constant depending on its shape parameter, making it flexible for different wear‑out or infant-mortality scenarios. The probability density is f(t) = (k/λ) (t/λ)^{k-1} exp[-(t/λ)^k] for t > 0, where k is the shape and λ the scale. When k = 1, it reduces to the exponential distribution, which has a constant hazard (memoryless). Normal distributions aren’t appropriate for survival times because they can produce negative values and don’t capture skew, and Poisson is for counting events in a fixed interval rather than modeling continuous time until failure. So the Weibull is the standard, flexible choice for modeling survival or time-to-failure data.

Times to failure, or survival times, are nonnegative and often show a changing failure rate over time. The Weibull distribution is especially useful here because its hazard function can increase, decrease, or stay constant depending on its shape parameter, making it flexible for different wear‑out or infant-mortality scenarios. The probability density is f(t) = (k/λ) (t/λ)^{k-1} exp[-(t/λ)^k] for t > 0, where k is the shape and λ the scale. When k = 1, it reduces to the exponential distribution, which has a constant hazard (memoryless). Normal distributions aren’t appropriate for survival times because they can produce negative values and don’t capture skew, and Poisson is for counting events in a fixed interval rather than modeling continuous time until failure. So the Weibull is the standard, flexible choice for modeling survival or time-to-failure data.