Can we measure the resistor if it is installed in circuit board?
Ans) You can calculate a resistor in a circuit but the circuit will most likely affect the value read (generally making it look lower in resistance). A simple example would be if there were two resistors in parallel in the circuit. If you calculate one, you will get the resistance of the two in parallel, and maybe other effects of the rest of the circuit.
Most resistors have markings on them, and they rarely fail unless they are cooked by too much power. That is the simple way. If they are not marked, you want to know the value, and it is in a circuit, then it is hard to figure out the value. It might be simpler to unsolder one end of it and then calculate it.