Ok, I came across this question when studying for my exam and was hoping I could get some explanation here.

A Flow Measurement System for dispensing medications evenly to patients consists of an Orifice Plate (with failure rate of

λ = 0.75), a Differential Pressure Transmitter (λ = 1.0), a Square Root Extractor (λ = 0.1) and a Recorder (λ = 0.1) all connected in series. Calculate the probability of losing the flow measurement after 0.5 years for the following configurations;

- A single Flow Measurement System as shown; (Just shows a series system of the above compnents in the order they are shown..)

So the solution I have is as follows:

1. Calculate the overall failure rate: 0.75 + 1.0 + 0.1 + 0.1 = 1.95

2. Calculate the probability of a system failure within 0.5 years:

FSyst(t) = 1 - e^-λsyst(t)

= 1- e^1.95(.5)

= 1-e^-0.975

= 1-0.377

Now, I understand everything up until the 0.377 figure. Where does this come out of? The above is the solution from the book (Bentley; An introduction to reliability & quality engineering).

Can anyone explain the .377 to me? Sorry if this is a very basic question...