Math Solutions

(Step-by-Step) A new component is placed in service and nine spares are available. The times to failure in days are independent exponential variables, Ti ~

Question: A new component is placed in service and nine spares are available. The times to failure in days are independent exponential variables, Ti ~ EXP (100).

  1. What is the distribution of the sum from i=1 to 10 of Ti?
  2. What is the probability that successful operation can be maintained for at least 1.5 years? Hint: Use theorem that says: If X ~ GAM (theta, k), then Y = 2X/theta ~ Chi-squared (2k).
  3. How many spares would be needed to be 95% sure of successful operation for at least two years?

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Solution: The downloadable solution consists of 7 pages
Deliverable: Word Document


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