Example of Inverse Cumulative Distribution Function (ICDF)

A reliability engineer for an appliance manufacturer investigates failure times for the heating element within the company's toasters. The engineer wants to determine the time at which specific proportions of heating elements fail in order to set the warranty period. Heating element failure times follow a normal distribution, with a mean of 1000 hours and a standard deviation of 300 hours.

The engineer uses the inverse CDF to determine the time by which 5% of the heating elements fail, the times between which 95% of all heating elements fail, and the time at which only 5% of the heating elements continue to function.

Note

This example uses the normal distribution. However, these steps are similar for any distribution that you select.

  1. In an empty worksheet column, such as C1, type 0.05, 0.95, 0.025 , and 0.975 into separate rows. These values are the probabilities for which the data values will be calculated.
  2. Open the Inverse Cumulative Distribution Function (ICDF) dialog box.
    • Mac: Statistics > Probability Distributions > Inverse Cumulative Distribution Function
    • PC: STATISTICS > CDF/PDF > Inverse Cumulative Distribution Function
  3. From Form of input, select A column of values.
  4. From Values in, select C1.
  5. From Distribution, select Normal.
  6. In Mean, enter 1000.
  7. In Standard deviation, enter 300.
  8. Under Output, select Display a table of inverse cumulative probabilities. If you prefer to store the values in the worksheet, select Store inverse cumulative probabilities in a column.
  9. Click OK.

Interpret the results

If the distribution of heating element failures follows a normal distribution with a mean of 1000 and a standard deviation of 300, then the following are true:
  • The time by which 5% of the heating elements are expected to fail is the inverse CDF of 0.05, or approximately 507 hours.
  • The time at which only 5% of the heating elements are expected to continue to function is the inverse CDF of 0.95, or 1493 hours.
  • 95% of all heating elements are expected to fail between 412 hours and 1588 hours, which is the inverse CDF of 0.025 and the inverse CDF of 0.975.
Summary
Input
Mean
Standard deviation
Inverse of the Cumulative Probability
P(X ≤ x)
x
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