Let calculate the mtbf after hours failure rate hourstherefore

(b) 2500 pieces of the same device were installed and put into service. Estimate the reliability and the number of failures after 2 weeks.

Answer

MTBF = 1 / Failure rate

Given:

Failure rate (λ) = 4 / 6000 = 0.0006667 per hour

Now, let's calculate the device's reliability (R) and unreliability (U) after 500 hours:

= 1 - 0.3297

≈ 0.6703

Therefore, after 500 hours of testing, the device's reliability is approximately 0.6703, unreliability is approximately 0.3297, failure rate is 0.0006667 per hour, and the MTBF is approximately 1500 hours.

(b) To estimate the reliability and the number of failures after 2 weeks (336 hours), we can use the same formulas as above with the updated testing time:

≈ 0.1984

Reliability (R) = 1 - Unreliability (U)

≈ 561.60

Therefore, after 2 weeks (336 hours), the estimated reliability of the 2500 installed pieces is approximately 0.8016, and the estimated number of failures is approximately 561.