Original practice · fully worked
Original variant: field-sensor failure classes
A sensor fleet is divided among sheltered, standard, and harsh sites in proportions 0.20, 0.50, and 0.30. A standard-site sensor is three times as likely to fail during a year as a sheltered-site sensor, while a harsh-site sensor is twice as likely to fail as a standard-site sensor. The annual failure probability for a randomly selected sensor is 0.028. Calculate the annual failure probability at a standard site.
- A
0.80% - B
1.40% - C
2.40% - D
2.80% - E
4.80%
Answer and calculation
Write the sheltered and harsh failure rates as one-third and twice the standard-site rate. The weighted fleet equation gives a standard-site probability of 0.024, so the answer is C.
Setup
Setup
Let s be the standard-site annual failure probability and express the other two rates relative to it.
qsheltered=3s,qstandard=s,qharsh=2s Model
Model
Average the three rates with the fleet proportions.
0.20(3s)+0.50s+0.30(2s)=0.028 Compute
Compute
The coefficient is 7/6, so the standard-site rate follows directly.
(151+21+53)s=67s=0.028 s=0.028(76)=0.024 Answer
Answer
The standard-site annual failure probability is listed in choice C.
s=0.024(C) 