A Crew of Mechanics at the Highway Department Garage Repair

question 133

Essay

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the utilization rate for this service system?
b. What is the average time before the facility can return a breakdown to service?
c. How much of that time is spent waiting for service?
d. How many vehicles are likely to be in the system at any one time?

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Definitions:

Independent Variable

An experimental variable that is changed or controlled to test its effects on dependent variables.

Coefficient Of Determination

A metric in statistics that evaluates the percentage of variability in the outcome variable that can be explained by the predictor variable(s).

SSE

Sum of Squared Errors, a measure used in statistics to quantify the discrepancy between data points and a model's predictions.

SSR

Sum of Squares due to Regression, a measure indicating how well a regression model fits the data.