Question

Your company is starting to prepare for potential impact of an earthquake on operations worldwide. You have been assigned to a team that has been tasked with exploring ways to prepare your plant site for a possible natural disaster caused by a major earthquake. The objective is to minimize damage to the plant and to keep the employees safe. The options include reinforcing structures, putting power and telephone lines underground, improving evacuation routes, etc.

The company management has developed two potential damage scenarios (options A and B). The resulting distributions of damage estimates are listed and compared with the do-nothing alternative (see Table below).

Determine the expected value of damage estimates and coefficients of variation for all three options and make a recommendation how to proceed.

Probability Damage- Do Nothing Damage- Option A Damage – Option B 0.01 $ 950,000 $ 600,000 $ 500,000 0.10 $ 500,000 $ 300,000 $ 200,000 0.19 $ 250,000 $ 100,000 $   70,000 0.20 $ 100,000 $   75,000 $   30,000 0.20 $   75,000 $   50,000 $   10,000 0.30 $   50,000 $     5,000 $     1,000

Answer 1

There are three types of damages, Nothing, Option A and Option B.

The expected mean is calculated as  , where p_i is the probability and x_i is the damage.

The expected mean of damage nothing = _nothing= (0.01* 950000 + 0.10 * 500000 + 0.19 * 250000 + 0.20 * 100000 + 0.20 * 75000 + 0.30 * 50000) = 157000

The expected mean of damage A = A ₌ (0.01* 600000 + 0.10 * 300000 + 0.19 * 100000 + 0.20 * 75000 + 0.20 * 50000 + 0.30 * 5000) = 81500

The expected mean of damage B = B ₌ (0.01* 500000 + 0.10 * 200000 + 0.19 * 70000 + 0.20 * 30000 + 0.20 * 10000 + 0.30 * 1000) = 81500

The standard deviation is calculated as: .​

The standard deviation for damage nothing = (0.01* 950000^2 + 0.10 * 500000 ^2+ 0.19 * 250000 ^2 + 0.20 * 100000^2 + 0.20 * 75000^2 + 0.30 * 50000^2) - 157000^2 = 50125.6.

The cofficient of variation of damage nothing = (sd / ) * 100 = (50125.6 / 157000) * 100 = 31.93%.

The standard deviation for damage A = (0.01* 600000^2 + 0.10 * 300000^2+ 0.19 * 100000^2 + 0.20 * 75000^2 + 0.20 * 50000^2 + 0.30 * 5000^2)- 81500^2 = 97417.9.

The cofficient of variation of damage A = (sd / ) * 100 = (97417.9 / 81500) * 100 = 119.53%.

The standard deviation for damage B = (0.01* 500000^2 + 0.10 * 200000^2 + 0.19 * 70000^2 + 0.20 * 30000^2+ 0.20 * 10000^2 + 0.30 * 1000^2) - 81500^2 = 31449.16

The cofficient of variation of damage B = (sd / ) * 100 = (31449.16 / 81500) * 100 = 38.58%.

Among the 2 damage plans A and B, the one with the least coefficent of variation is the precise plan. So, as compared to damange nothing, plan damage B is precise and start executing that plan.