Using the information from table 1 below, what is the aggregate RDF for a vehicle configuration using 3 strap-on boosters?
Assume a 'series' combination of the launch elements shown for your calculation.
Vehicle subsystem subsystem reliability Replacement cost
1st stage liq engine 0.991 $25.4M
2nd Stage liq engine 0.995 $17.1M
payload section/fairing 0.993 $12.7M
Strap-on Booster 0.997 $4.2M
I assumed that an aggregate RDF would mean to work this is as a simple series combination. I was not sure if I needed to include all the components in the series or just the 3 strap-on booster rockets. I included all components and worked it this way:
Reliability = 1st stage x 2nd stage x payload section x booster 1 x booster 2 x booster 3
= .991 x .995 x .993 x .997 x .997 x .997 = 0.97035 = 0.970
RDF = 1-reliability = 1 - .97035 = 0.02965 = 0.0230
Is this correct? Please let me know. I have to have this right in order to work the other problems.