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Normal Distribution

The normal distribution can be used to model the reliability of items that experience wearout failures. Given a mean life, μ and standard deviation, σ, the reliability can be determined at a specific point in time (t). The normal distribution probability density function, reliability function and hazard rate are given by:

Normal Distribution PDF Equation Probability Density Function

Normal Distribution PDF Equation Reliability Function

Normal Distribution PDF Equation Hazard Rate

For example, given a mean life of a light bulb of μ=900 hours, with a standard deviation of σ=300 hours, the reliability at the t=700 hour point is 0.75, as represented by the green shaded area in the picture below.
Normal Distribution

Calculation Inputs:

1. Mean life (μ):
2. Standard deviation (σ):
3. Time period of interest (t):
4. Units associated with inputs #1, #2 and #3 above:
5. Decimal places:
6. Options:

Table
f(t) chart
R(t) chart
F(t) chart
h(t) chart

Title (optional):



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References:

  1. MIL-HDBK-338, Electronic Reliability Design Handbook.
  2. Bazovsky, Igor, Reliability Theory and Practice.
  3. O'Connor, Patrick, D. T., Practical Reliability Engineering.
  4. http://en.wikipedia.org/wiki/Normal_distribution
  5. Khan Academy, Introduction to the Normal Distribution.
  6. Khan Academy, Normal Distribution Excel Exercise.