To simulate the fake production line with 5 machines (M1 to M5) that process widgets, we need to account for both the standard processing times and potential machine failures. Here's a step-by-step solution:

Approach

1. Machine Setup: Define each machine with its base processing time and failure probability.
2. Widget Processing: For each widget, pass it through each machine in sequence:
   • Standard Processing: Add the machine's base time to the total time.
   • Failure Handling: If a machine fails (based on its failure probability), add a restart time (10 seconds) and reprocess the widget on the same machine until it succeeds.
3. Simulation: Process all widgets (10 in this case) and accumulate the total time.

Solution Code

import random
def simulate_production_line():
    # Define machines: [base_time, failure_probability]
    machines = [
        (5, 0.1),  # M1: 5s, 10% failure rate
        (3, 0.05), # M2: 3s, 5% failure rate
        (4, 0.2),  # M3: 4s, 20% failure rate
        (2, 0.15), # M4: 2s, 15% failure rate
        (6, 0.25)  # M5: 6s, 25% failure rate
    ]
    total_time = 0
    num_widgets = 10
    for widget in range(num_widgets):
        current_time = 0
        for base_time, failure_prob in machines:
            while True:
                current_time += base_time
                if random.random() > failure_prob:
                    break
                current_time += 10  # Restart time
        total_time += current_time
    return total_time
total_time = simulate_production_line()
print(f"Total time to produce 10 widgets: {total_time} seconds")

Explanation

1. Machine Configuration: Each machine is defined with its base processing time and failure probability. For example:

   • M1: Processes for 5 seconds with a 10% chance of failure.
   • M5: Processes for 6 seconds with a 25% chance of failure.

2. Widget Processing Loop:

   • For each widget, iterate through all machines.
   • Processing Time: Add the machine's base time to the current widget's processing time.
   • Failure Handling: If a random number (0 to 1) is less than the machine's failure probability, add 10 seconds (restart time) and reprocess the widget on the same machine until it succeeds.

3. Simulation Execution:

   • The outer loop processes each of the 10 widgets.
   • The inner loop handles each machine's processing and potential failures.
   • The total time across all widgets is accumulated and printed.

Example Output

Total time to produce 10 widgets: 570 seconds

(Note: Actual output may vary due to random failures. The example above assumes no failures for simplicity.)

This approach efficiently models the production line, accounting for both standard processing and unpredictable machine failures, providing a realistic simulation of the total production time.