A system has three components, each of which has a current reliability as shown below. The...
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A system has three components, each of which has a current reliability as shown below. The company has received a PhP 12 M budget that can be used to buy additional units. Since these are new units, their reliabilities are way higher than the older components. These can be used as backup to the existing components. Multiple backup units can be bought per component subject to the budget limitation. Details are provided in the next table. Component 1 2 3 Component 1 2 3 System Total Existing Reliability 0.74 Existing Reliability, r 0.74 0.82 0.77 0.467236 0.82 0.77 The company wishes to determine the number of additional units that it should buy per component that would maximize the total system reliability. Sample computations are shown below. No. Bought 2 0 1 3 Cost (PhP), Ci 3 M 4 M 5 M Additional Unit Additional Units Cost 6 M OM 5 M 11 M Reliability Reliability, p 0.88 0.95 0.96 Net Reliability 1-0.12²=0.98561-(0.26)(0.0144) = 0.996256 1-0.05⁰=0.0000 1-(0.18)(1.0000) = 0.820000 1-0.04¹=0.9600 1-(0.23)(0.0400) = 0.990800 0.996256*0.820000*0.990800 = 0.809414 1. Define the stage, state, alternative, and recursive function of the DP. 2. Complete the DP table. Find the optimal decision of the company with the use of DP. The following must be defined / completed to get full points. 3. Setup the mathematical expression for the recursive function. 4. Summarize the corresponding action of the company including the final system reliability. A system has three components, each of which has a current reliability as shown below. The company has received a PhP 12 M budget that can be used to buy additional units. Since these are new units, their reliabilities are way higher than the older components. These can be used as backup to the existing components. Multiple backup units can be bought per component subject to the budget limitation. Details are provided in the next table. Component 1 2 3 Component 1 2 3 System Total Existing Reliability 0.74 Existing Reliability, r 0.74 0.82 0.77 0.467236 0.82 0.77 The company wishes to determine the number of additional units that it should buy per component that would maximize the total system reliability. Sample computations are shown below. No. Bought 2 0 1 3 Cost (PhP), Ci 3 M 4 M 5 M Additional Unit Additional Units Cost 6 M OM 5 M 11 M Reliability Reliability, p 0.88 0.95 0.96 Net Reliability 1-0.12²=0.98561-(0.26)(0.0144) = 0.996256 1-0.05⁰=0.0000 1-(0.18)(1.0000) = 0.820000 1-0.04¹=0.9600 1-(0.23)(0.0400) = 0.990800 0.996256*0.820000*0.990800 = 0.809414 1. Define the stage, state, alternative, and recursive function of the DP. 2. Complete the DP table. Find the optimal decision of the company with the use of DP. The following must be defined / completed to get full points. 3. Setup the mathematical expression for the recursive function. 4. Summarize the corresponding action of the company including the final system reliability.
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Define the stage state alternative and recursive function of the DP Stage Each stage represents the selection of additional units for a specific component State The state variables represent the remai... View the full answer
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