Question

GM has a 1.4L engine that they put into over 1,000,000 vehicles. This particular engine has a major issue with reliability. The PCV valve can break and it costs roughly $700 to repair. If the vehicle was made in between 2008 and 2014, the powertrain warranty covers this cost for the first 100,000 miles. After that, it’s on the owners, LIKE ME, to pay for it. If the part has a MTTF(mean) of 40,000 miles, answer the following:

i) Using the exponential distribution, calculate the probability it will fail within the first 20,000 miles…. Like mine just did.

Run a simulation with 3 columns and 5,000 random variables, using the function in cells A5, B5, C5 (copy and paste) with mean=40,000. Each column represents the lifetime of a PCV valve.

ii) In column 1, what is the probability of one of these parts failing on the car within 100,000 miles.

P(1 Failure) =

iii) Combine the values in Column 1 and 2. What is the percent of vehicles that have the PCV valve replaced twice within the first 100,000 miles????? LIKE MINE.

P(2 Failures) =

iv) Combine the values in column 1, 2 and 3. What percent of the vehicles have had 3 PCV valve replaced within the first 100,000?

P(3 Failures) =

At a cost of $700/repair, and $300 to install the part initially, how much does it costs GM to fix 1,000,000 1.4L engines?

Total Cost =

GM’s fix for this situation is to drop the powertrain warranty from 100,000 miles to 36,000 miles. What is the total cost to GM if they only replace PCV valves that break in the first 36,000?

Total Cost =

What if GM just made the part better in the first place. Suppose that a part that costs $800 initially has an MTTF of 160,000. What would the total cost be if they used this new part and had the original 100,000mile warranty?

Total Cost =

Answer 1

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