CMRP Reliability Data Analysis and Statistics 2

Question 1

What are the two primary parameters of a two-parameter Weibull distribution?

Accepted Answer

Shape (β) and scale (η)

Answer

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?

Accepted Answer

Infant mortality failures with a decreasing failure rate

Answer

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?

Accepted Answer

Exponential distribution

Answer

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?

Accepted Answer

The characteristic life at which 63.2% of units have failed

Answer

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?

Accepted Answer

Wear-out failures approximating a normal distribution

Answer

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.

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CMRP - Certified Maintenance and Reliability Professional Practice Test

CMRP Reliability Data Analysis and Statistics 2