Nuclear power plants. which depend on the functioning of many designed numerous

Question

Nuclear power plants. which depend on the functioning of many designed numerous components, are with redundancies. Assume, for simplicity. that during a particular, major, design level of earthquake. shutdown of the reactor depends on the proper functioning of the control system. the cooling system, and the primary containment Assume that there are three redundant control systems, two redundant cooling systems, and a single, steel primary containment with two critical necessary components A and B. Block model the system and calculate the system reliability with respect to shutdown in terms of component reliabilities. Assume independence of component performances. There will be no major accident if either the shutdown is controlled or the reinforced concrete secondary containment vessel performs properly. Model the total system with respect to major accident reliability A safety system consists of 3 monitors. A plant abnormal state requiring shutdown occurs with probability of 0.2. lf the safety system fails to shut down, $10,000 is lost. Each spurious (or false) shutdown costs S4000. Determine the optimal m-out-of-three safety system using as data. Pr(monitor shutdown failure, abnormal plant) = 0.01 Pr(monitor spurious signal I normal plant) - 0.05 Assume statistically independent failures.

Explanation / Answer

Back-up Theory

Reliability of A = 1 – P(A’s failure)

Now, to work out solution,

Let

Reliability of Control System, RN = N;    Reliability of Cooling System, RL = L;

Reliability of Primary Containment Vessel, RV = V      

Reliability of Critical Component A of Primary Containment Vessel, RA = A;

Reliability of Critical Necessary Component B of Primary Containment Vessel, RB = B;

Now, V = P(both A and B function) = AxB.

Since there is redundancy of 3 in Control System, it fails only if all 4 (main + 3 redundant) fail and hence

N = {1- (1 - N)4}

Similarly, L = {1- (1 - L)3}

Part (a)(i): System reliability with respect to shutdown.

Since controlled shutdown depends on the proper functioning of all three,

System reliability with respect shutdown = AB{1- (1 - N)4}{1- (1 - L)3} ANSWER

Part (a)(ii) System reliability with respect to major accident.

P(major accident) = P(controlled shutdown fails and Secondary Containment Vessel fails)

= [1- AB{1- (1 - N)4}{1- (1 - L)3}](1 - AB)

= (1 - AB)2 + AB(1 - AB){1- (1 - N)4}{1- (1 - L)3} ANSWER

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