Measurement strategy From all possible combinations of source data involved in the measurement/test, select such combination that gives the maximum mutual information, minimum information loss at the same time. For the optimum combination, all results should be equally probable (see P1), Repeat this step k times.
A system of ten bulbs connected in series and supplied from voltage source is not emitting light. Accepting an assumption that one faulty bulb (open circuit) is causing the problem and that it can be any bulb with equal probability, locate faulty bulb using a voltmeter, at minimum number of measurements.
The source entropy: [bit].
Each measurement gives possible readings: - supply voltage; - no voltage. Then, maximum information provided by single measurement:
[bit].
From (3.1.6) it is clear, that measurements are necessary to locate the faulty bulb.
Measurement strategy:
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1 st measurement: Voltmeter is connected to the first 5 bulbs. The obtained information: [bit].
2 nd measurement: Voltmeter is connected to the first/last 3 bulbs, if reading of the 1 st measurement is 1 or
to the 4 th /6 th bulb, if reading of the 1 st measurement is 0. In the first, less advantageous case, the obtained information:
[bit].
3 rd measurement: Voltmeter is connected to the first/last 2 bulbs, if reading of the 2 nd measurement is 1 or
to the 3 rd /8 th bulb, if reading of the 2 nd measurement is 0. In the first, less advantageous case, the obtained information:
[bit].
4 th measurement: Voltmeter is connected to the 1 st /9 th 5 bulb. The obtained information:
[bit].
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