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Question 4 (30 Marks) The main power supply for a high-rise construction site is through a 415-volt busbar. This busbar is normally connected to the city's electricity grid. However, the site also has a diesel generator backup to ensure continuous power supply for crucial operations. For power to come from the electricity grid: ▪ The grid must be operational. ▪ It must be properly connected to the construction site. For the backup generator to provide power: ▪ The generator must be functional. ▪ It must be connected. ▪ The isolator switch must be operational. (a) Draw a fault tree for the head event “No power on the 415 busbar” using the following basic events: ▪ City grid failure (P=0.03) ▪ City grid inadvertently disconnected (P=0.02) ▪ Diesel generator failure (P=0.04) ▪ Diesel generator disconnected (P=0.05) ▪ Diesel generator isolator switch failure (P=0.02). (5 marks) ChatGPT ChatGPT A fault tree is a graphical representation of the logical relationships between events that can lead to a specific undesired event, in this case, "No power on the 415 busbar." Basic events are the lowest level events that contribute to the top event. Here's a simplified fault tree for the given scenario: scss Copy code No power on the 415 busbar (Top Event) / | | | \ City grid failure City grid inadvertently Diesel generator Diesel generator (P= 0.03 ) disconnected (P= 0.02 ) failure (P= 0.04 ) disconnected (P= 0.05 ) ___________________ ______________ ______________ | | | | | | / \ / \ / \ / \ / \ / \ / \ / \/ \ / \ \ / \ City City Grid Grid Diesel Diesel Diesel Diesel grid grid dis. dis. gen. gen. iso. iso. failure disc. (P= 1 ) (P= 1 ) gen. disc. switch switch (P= 1 ) (P= 1 ) (P= 1 ) (P= 1 ) (P= 0.02 ) (P= 0.02 ) Explanation:

● "No power on the 415 busbar" is the top event. ● The four main branches represent the four primary ways in which the top event can occur. ● Each box represents a basic event, and the lines connecting them indicate the logical relationships between events. ● "City grid failure" and "City grid inadvertently disconnected" are parallel events leading to the top event. ● Similarly, "Diesel generator failure," "Diesel generator disconnected," and "Diesel generator isolator switch failure" are parallel events leading to the top event. Note: The probabilities (P values) have been omitted in the graphical representation for clarity. The values should be included in your final fault tree, and the probabilities for parallel events should be combined using appropriate logic (e.g., OR gate). You Determine the probability that there will be no power on the 415-volt busbar. (5 marks) The busbar supplies power for several critical site operations including a tower crane and a dewatering pump for the foundation pit. The construction site is in an area that experiences stable weather for 60% of the year and heavy rainfall for the remaining 40%. The tower crane is operational 15% of the time during stable weather and 5% during rainy conditions. The dewatering pump operates 30% of the time during heavy rainfall and 5% during stable weather. ChatGPT ChatGPT To determine the probability that there will be no power on the 415-volt busbar, we can use the fault tree and calculate the probability of each path leading to this top event. Let's denote the events: ● A: City grid failure ● B: City grid inadvertently disconnected ● C: Diesel generator failure ● D: Diesel generator disconnected ● E: Diesel generator isolator switch failure The probability of "No power on the 415 busbar" can be calculated using the fault tree and the probabilities associated with each event. ("No power on the 415 busbar")= ( + )+ ( + + ) � � � � � � � � P ("No power on the 415 busbar")= P ( A + B )+ P ( C + D + E )

● X: No power on the 415-volt busbar ● Y: Tower crane operation halted ● Z: Dewatering pump operation halted The event tree can be constructed as follows: scss Copy code X / \ / \ / \ / \ Y Z / \ / \ Stable Heavy weather rainfall / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ Y Z Y Z / \ / \ / \ / \ / \ / \ \ / \ Tower Tower Pump Pump Tower Pump Pump crane crane halt halt crane halt halt ( 15% ) ( 85% ) ( 70% ) ( 30% ) ( 5% ) ( 95% ) ( 5% ) Explanation: ● The top event is "No power on the 415-volt busbar" (X). ● The two branches represent the possible outcomes given the absence of power on the 415-volt busbar: Tower crane operation halted (Y) or Dewatering pump operation halted (Z). ● The next level represents the different scenarios based on weather conditions: Stable weather or Heavy rainfall. ● The final level represents the probability of the crucial operations being halted given the specific weather condition and the absence of power on the 415-volt busbar. The probabilities in parentheses represent the conditional probabilities based on the given information. For example, the probability of the tower crane operation being halted given that there's no power on the 415-volt busbar during stable weather is 85%. You

Determine this conditional probability. (5 marks) ChatGPT ChatGPT To determine the conditional probability that one of the crucial operations (tower crane or dewatering pump) will be halted given that there's no power on the 415-volt busbar, we need to consider the probabilities along the paths in the event tree. Let's denote the events: ● X: No power on the 415-volt busbar ● Y: Tower crane operation halted ● Z: Dewatering pump operation halted The conditional probability we want to find is �(� or � �) ∣ P ( Y or Z ∣ X ) . Using the event tree, we can express this as: �(� or � �)=�(� �)+�(� �) ∣ ∣ ∣ P ( Y or Z ∣ X )= P ( Y ∣ X )+ P ( Z ∣ X ) Now, we need to calculate the conditional probabilities along each path: �(� �) ∣ P ( Y ∣ X ) - Probability of the tower crane operation being halted given that there's no power on the 415-volt busbar. ● �(� �)=0.15 ∣ ● P ( Y ∣ X )=0.15 (from the event tree). �(� �) ∣ P ( Z ∣ X ) - Probability of the dewatering pump operation being halted given that there's no power on the 415-volt busbar. ● �(� �)=0.70 ∣ ● P ( Z ∣ X )=0.70 (from the event tree). Now, we can calculate the conditional probability: �(� or � �)=�(� �)+�(� �) ∣ ∣ ∣

Now, we know that: �(� or �)=�(�)+�(�)−�(� and �) P ( Y or Z )= P ( Y )+ P ( Z )− P ( Y and Z ) Since the events Y and Z are mutually exclusive (the tower crane and dewatering pump cannot be halted simultaneously), ( and )=0 � � � P ( Y and Z )=0 . So, the formula simplifies to: �(Both operational)=1−�(�)−�(�) P (Both operational)=1− P ( Y )− P ( Z ) Now, we can use the information from the event tree: �(Both operational)=1−�(�)−�(�) P (Both operational)=1− P ( Y )− P ( Z ) =1−0.15−0.70 =1−0.15−0.70 =0.15 =0.15 Therefore, the overall probability that the tower crane or dewatering pump will be non-operational is 0.15 0.15 or

15% 15% .