GAMMAINV

Application:

Predicting Product Lifespan

Scenario: A manufacturer produces a type of electronic component. The lifespan of this component, measured in hours, is known to follow a Gamma distribution. The manufacturer wants to determine the number of hours at which 95% of the components are expected to have failed. This value is crucial for setting warranty periods and predicting replacement part demand.

Given Data:

The Gamma distribution for the component's lifespan has the following parameters:

• Alpha (α): 5 (This is the shape parameter, representing the number of "stages" of failure.)
• Beta (β): 1200 (This is the scale parameter, representing the mean time for each "stage.")
• Probability (p): 0.95 (This is the cumulative probability we are interested in. We want to find the lifespan value where the cumulative probability of failure is 95%.)

The GAMMAINV Function:

The GAMMAINV function is used to calculate the inverse of the cumulative Gamma distribution. In other words, if you know the probability and the distribution's parameters, it tells you the corresponding value. The syntax is typically:

GAMMAINV(probability, alpha, beta)

Calculation:

Using the values from our scenario, we can set up the function call:

GAMMAINV(0.95, 5, 1200)

Result:

The result of this calculation is approximately 10984.22.

Interpretation:

This result means that there is a 95% probability that a component will fail at or before 10984.22 hours of use. The manufacturer can use this value to inform their warranty policy, perhaps setting a warranty period of 10,500 hours to ensure they cover the vast majority of failures while avoiding excessive costs.

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