II. A. 3. a. The Four Functions

II. Probability and Statistics for Reliability
A. Basic concepts

3. Discrete and continuous probability distributions (Analyze)

Compare and contrast various distributions (binomial, Poisson, exponential, Weibull, normal, log-normal, etc.) and their functions (e.g., cumulative distribution functions (CDFs), probability density functions (PDFs), hazard functions), and relate them to the bathtub curve.

This lesson takes a close look at the four common functions used with statistical distributions.

 

Additional References

The Four Functions (article)

Reliability Function (article)

Reliability from Hazard step function (article)

PDF to CDF with Brief Calculus Refresher (article)

Quick Quiz

1-12. Identify which of the following are normally accepted reliability engineering tools.

I.   probability density function
II.  hazard rate function
III. conditional reliability function
IV. mean life function
V.   cumulative distribution function

(A) I and II only
(B) I, II, and III only
(C) II, III, IV, and V only
(D) I, II, III, IV, and V

Answer Discussion

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1-20. The hazard rate function h(t) as a function of time t in hours for a device is

h(t) = 0, for t ≤ 0 and 0.66t, for t > 0

Determine the reliability of this device at t = 3 hours?

(A) 0.0.00263
(B) 0.0.0513
(C) 0.138
(D) 0.372

Answer Discussion