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 Existing Reliability, 0.74 0.82 0.77 Additional Unit Cost (PhP). Reliability 3M 0.88 4M 0.95 SM 0.96 2 3 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. Component Existing Reliability 0.74 0.82 0.77 0.467236 No. Bought 2 0 2 3 System Total Additional Units Cost Reliability Net Reliability 6 M 1 -0.12 = 0.9856 1-(0.26 0.0144) = 0.996256 OM 1-0.05 = 0.00001 -(0.18)(1.0000) = 0.820000 5M 1 -0.04 = 0.9600 1-(0.23)(0.0400) = 0.990800 11M 0.996256*0.820000*0.990800 = 0.809414 Find the optimal decision of the company with the use of DP. The following must be defined / completed to get full points 1. Define the stage, state, alternative, and recursive function of the DP. 2. Complete the DP table. 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 Existing Reliability, 0.74 0.82 0.77 Additional Unit Cost (PhP). Reliability 3M 0.88 4M 0.95 SM 0.96 2 3 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. Component Existing Reliability 0.74 0.82 0.77 0.467236 No. Bought 2 0 2 3 System Total Additional Units Cost Reliability Net Reliability 6 M 1 -0.12 = 0.9856 1-(0.26 0.0144) = 0.996256 OM 1-0.05 = 0.00001 -(0.18)(1.0000) = 0.820000 5M 1 -0.04 = 0.9600 1-(0.23)(0.0400) = 0.990800 11M 0.996256*0.820000*0.990800 = 0.809414 Find the optimal decision of the company with the use of DP. The following must be defined / completed to get full points 1. Define the stage, state, alternative, and recursive function of the DP. 2. Complete the DP table. 3. Setup the mathematical expression for the recursive function. 4. Summarize the corresponding action of the company including the final system reliability
