Lifetime of a device of several components

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Let's consider the following example: A piece of electronic equipment is composed of six components A to F. They have the following mean time between failures:

The components are in serial and parallel configuration as shown below:

What is the probability that the machine will fail within 250 hours?

We first assume that the components will fail with a constant probability per unit time, i.e. that their times to failure will be exponentially distributed, which is a reasonable assumption implied by the MTBF figure. The problem belongs to reliability engineering. Components in series make the machine fail if any of the components in series fail. For parallel components, all components in parallel must fail before the machine fails. Thus, according to the figure above, the machine will fail if A fails, or B, C and D all fail, or E and F both fail. The figure below shows the spreadsheet modelling the time to failure.

Running a simulation with 10 000 iterations on Cell D16 gives an output distribution of which 63.5% of the trials were less than 250 hours.

The spreadsheet of this model is reached here: Lifetime of a device.