Citi Bike tracks the performance of its bicycle fleet based on an estimated ‘mea
ID: 3048562 • Letter: C
Question
Citi Bike tracks the performance of its bicycle fleet based on an estimated ‘mean trips between failure’ (MTBF) per bicycle and per bicycle component. If you were to see a dip in the MTBF per bicycle for the past month, what are some approaches you could use to better understand the source and scale of the problem, and what potential solutions could you suggest? Assuming you have access to any data sets, what in particular would you be looking for and how would you want it to be structured to make analysis as straightforward as possible? (please respond to this prompt in 250 words or less)
Explanation / Answer
Mean trips between failures is the measure of probability of the number successful trips and the probability of the length of the time the trip is successful. First point here is whether the bicycle starts the trip successfully. It means the number of trouble free successful starts. Second is the length of each trip. Duration of the each trouble free trip lasts for a stipulated period of time.
Our objective here is to study the trend or inclination or slope of the expected number of failures in a typical time interval. Say for example the expected number of bicycle starting trouble in the past one month is the count of the number of failures in sample data of 30 bicycles or more. The bicycle and its components performance as per its design intend through the trouble free starts and last its operation for a stipulated time period without any breakdown is the scope of the experiment to pinpoint the mean time between failures.
Probability of success is the measure of product of the probability of the all the independent components function properly. And we need to understand the system and subsystems in the bicycle that means the probability of success of at least one independent system or component function properly is the probability of 1 plus or 1 minus the probability of the independent component multiplied by the probability of success of other independent component in the system.
In the past month data, if you do the analysis of the number of failures and mean time between the failure, Mean trips between failures can be modeled using a negative exponential distribution. The rate of failure is a function of time between failures.
For the past one month data, we need to analyze the number of failures occurred in day one, day two, day 3 extra till the 30 th day of the month. For example, there are suppose the two bicycles failed in the day one of the past month and 0 failed in day 2, etc,.. We can calculate the mean trips between failures. The probability (nothing but the reliability of the trips) is calculated using the negative exponential distribution of the length of service(T) before failure and the mean trips between failures(MTBF). Then the probability, P(no failure before T) = (exp(-T/MTBF)).