Certified Quality Engineer (CQE) Practice Exam 2025 - Comprehensive All-in-One Study Guide for Exam Success!

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The overall reliability of a process has a mean time between failures (MTBF) of 16.5 hours. If the failures follow an exponential distribution and the total run time is 30 hours, what is the process reliability?

0.1623

To determine the process reliability in this context, we use the information about the mean time between failures (MTBF) and the total run time. Given that the failures follow an exponential distribution, the reliability function can be calculated with the formula:

Reliability (R) = e^(-t/MTBF)

where "t" is the total run time and "MTBF" is the mean time between failures.

In this scenario, the MTBF is 16.5 hours and the total run time is 30 hours:

1. Calculate t/MTBF:

t/MTBF = 30 hours / 16.5 hours = 1.8182

2. Now, we apply this to the reliability formula:

R = e^(-1.8182)

Calculating e raised to the power of negative 1.8182 gives us approximately 0.1623.

Thus, the process reliability calculated results in 0.1623, which aligns with the first choice given in the options. This means there is roughly a 16.23% probability that the process will operate without failure over the 30-hour run time, which is consistent with the characteristics of an exponential distribution where events occur randomly over time.

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0.5500

0.5769

0.8377

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