Question

A hydraulic system is comprised of five components (serially) having the following constant failure rates (times are in days): λ1 = 0.001, λ2 = 0.005, λ3 = 0.0007, λ4 = 0.0025, and λ5 = 0.00001.

(a) Find the system MTTF and standard deviation

Answer 1

The MTTF for the given hydraulic system with serial components is approximately 108.577 days, and the standard deviation is similarly 108.577 days, as both are derived from the sum of the constant failure rates.

Step-by-step explanation:

The Mean Time To Failure (MTTF) for a series hydraulic system can be calculated by taking the inverse of the sum of all failure rates in the system. In this case, with constant failure rates λ1 = 0.001, λ2 = 0.005, λ3 = 0.0007, λ4 = 0.0025, and λ5 = 0.00001, the system MTTF is found by summing these rates and taking the inverse:

• Total failure rate, λ = λ1 + λ2 + λ3 + λ4 + λ5
• λ = 0.001 + 0.005 + 0.0007 + 0.0025 + 0.00001 = 0.00921
• MTTF = 1 / λ = 1 / 0.00921 = 108.577 days approximately

Standard deviation (σ) for a system with a constant failure rate is equal to the MTTF, so the standard deviation is also 108.577 days approximately.