GAMMA.INV

Application:

Scheduling Preventive Maintenance

Scenario: A factory manager is responsible for a critical machine whose components are subject to wear and tear. The time to failure, in days, for a specific component is known to follow a Gamma distribution. The manager wants to establish a preventative maintenance schedule that replaces the component before 90% of them are expected to fail. This proactive approach minimizes unexpected downtime and costly emergency repairs.

Given Data:

The Gamma distribution for the component's time-to-failure has the following parameters:

• Alpha (α): 8 (This is the shape parameter, representing the complexity or number of stages of wear leading to failure.)
• Beta (β): 60 (This is the scale parameter, representing the average time in days for each stage.)
• Probability (p): 0.90 (This is the cumulative probability we are interested in. We want to find the time value where the cumulative probability of failure is 90%.)

The GAMMA.INV Function:

The GAMMA.INV function is used to calculate the inverse of the cumulative Gamma distribution. It takes a probability and the distribution's parameters and returns the corresponding value from the distribution. The syntax is typically:

GAMMA.INV(probability, alpha, beta)

Calculation:

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

GAMMA.INV(0.90, 8, 60)

Result:

The result of this calculation is approximately 706.25.

Interpretation:

This result means that there is a 90% probability that a component will fail at or before 706.5 days of operation. The factory manager can use this information to set a preventative maintenance schedule, such as replacing the component every 700 days, to ensure the machine continues to operate reliably and avoid the vast majority of potential failures.

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