Bulb Replacement Problem: Lighting on exit ramp 167 on I-55 consists of a cluster of 3...

 
 

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Bulb Replacement Problem: Lighting on exit ramp 167 on I-55 consists of a cluster of 3 bulbs. Safety regulations require that whenever a bulb fails, it must be immediately replaced. Cost of the bulb is $450 per unit. Cost of making the trip to replace one or more bulbs is $900 (independent of the number of bulbs replaced). Based on past experience, a bulb's life is described by the following probability distribution. Use only the random numbers provided. Duration (life of bulb) in months Probability Cumulative Probability 2 0.2 3 0.3 4 0.3 0.2 Highway department wants to investigate two possible alternative policies- i) replace a bulb when it fails, or ii) replace all bulbs whenever one or more bulbs fail – no matter when that bulb was installed. Simulate the system (alternative-1 for 25 months and alternative-2 for 25 months). A) Which policy the department should use. B) What is the optimum monthly average cost of operating the system? C) Can you suggest yet third alternative policy which may be worthwhile investigating? Alternative 1: Replace only bulb that fal Bulb 1 Bulb 2 Bulb 3 Time RA RA RM 1 3. 9 9 1 3. 6. 6 1 6. 2 Simulate Alternative 1 for 26 months. Alternative 2: Replace all three bulbs w Bulb 1 Bulb 2 Bulb 3 Time RA RA RN 4 8 1 1 1 1 6 4 4. 1. 4 2 1. 1 1 6. 1 4. 1 1 Simulate Alternative 2 for 25 months. Bulb Replacement Problem: Lighting on exit ramp 167 on I-55 consists of a cluster of 3 bulbs. Safety regulations require that whenever a bulb fails, it must be immediately replaced. Cost of the bulb is $450 per unit. Cost of making the trip to replace one or more bulbs is $900 (independent of the number of bulbs replaced). Based on past experience, a bulb's life is described by the following probability distribution. Use only the random numbers provided. Duration (life of bulb) in months Probability Cumulative Probability 2 0.2 3 0.3 4 0.3 0.2 Highway department wants to investigate two possible alternative policies- i) replace a bulb when it fails, or ii) replace all bulbs whenever one or more bulbs fail – no matter when that bulb was installed. Simulate the system (alternative-1 for 25 months and alternative-2 for 25 months). A) Which policy the department should use. B) What is the optimum monthly average cost of operating the system? C) Can you suggest yet third alternative policy which may be worthwhile investigating? Alternative 1: Replace only bulb that fal Bulb 1 Bulb 2 Bulb 3 Time RA RA RM 1 3. 9 9 1 3. 6. 6 1 6. 2 Simulate Alternative 1 for 26 months. Alternative 2: Replace all three bulbs w Bulb 1 Bulb 2 Bulb 3 Time RA RA RN 4 8 1 1 1 1 6 4 4. 1. 4 2 1. 1 1 6. 1 4. 1 1 Simulate Alternative 2 for 25 months.