PDUs awarded

First Mars flight is approaching. Let's see how to plan the final phase with MonteCarloProject.

We are on the 1st of January 2025. OK, a bit optimistic, but let's go on. The WBS (work breakdown structure) for the MARS1 project consisting of final preparations and checks for the first Mars flight is shown on the picture 1.

MARS1 WBS

Picture 1. WBS for MARS1 project.

AC = attitude control

GNC = Guidance, navigation and control

TC = Thermal control

LV = Launch vehicle

We need to give cost and duration probability distributions and related parameters for each task in the MARS1 project In order to simulate how much this final phase would cost and how long it would take. Following table shows these distributions and parameters.

Table 1. Probability distributions and related parameters for MARS1 project's tasks.

Name Distribution Cost       Duration              
    Minimum Most probable Maximum Stand. dev. Minimum   Most probable   Maximum   Stand. dev.  
Spacecraft                          
Equpment                          
Check training eq. Normal   $200   $100     1 d     4 h
Check scientific instr. Beta $700 $1 000 $5 000   3 d 1 w 5 w    
Systems                          
Check attitude control Normal   $200   $100     1 d     4 h
Check GNC Beta $200 $300 $1 500   1 d 2 d 2 w    
Check thermal control Beta $300 $500 $2 500   2 d 3 d 3 w    
Check propulsion Beta $300 $500 $2 500   2 d 3 d 3 w    
Check life support Beta $700 $1 000 $4 000   3 d 1 w 4 w    
Check comms Triangular $500 $700 $3 500   2 d 3 d 3 w    
Check power Beta $700 $1 000 $3 000   3 d 1 w 3 w    
Check launch vehicle Triangular $300 $500 $2 500   2 d 3 d 3 w    
Load testing of structures Beta $300 $500 $1 500   2 d 3 d 2 w    
Supplies                          
Food & water                          
Stock food Beta $300 $500 $1 000   2 d 3 d 1 w    
Stock water Beta $300 $500 $1 000   2 d 3 d 1 w    
Stock medical supplies Beta $700 $1 000 $2 000   3 d 1 w 2 w    
Stock sanitary supplies Beta $700 $1 000 $2 000   3 d 1 w 2 w    
Stock personal supplies Beta $700 $1 000 $2 000   2 d 3 d 1 w    
Check supplies Beta $700 $1 000 $2 000   3 d 1 w 2 w    
Mission                          
Trajectory                          
Plan Triangular $1 000 $2 000 $6 000   1 w 2 w 6 w    
Simulate Triangular $700 $1 000 $3 000   3 d 1 w 3 w    
Review research plan Normal   $500   $100     3 d     1 d
Ground segment                          
Control center                          
Check comms Triangular $700 $1 000 $4 000   3 d 1 w 4 w    
Plan staffing Normal   $300   $100     2 d     1 d
Launch facilities                          
Fuelling                          
Check system Normal   $300   $100     2 d     1 d
Fuel spacecraft Beta $100 $200 $1 000   4 h 1 d 1 w    
Launch pad                          
Prepare pad Triangular $1 000 $2 000 $8 000   1 w 2 w 8 w    
Check pad Beta $700 $1 000 $4 000   3 d 1 w 4 w    
Crew                          
Review training Normal   $2 000   $500     2 w     1 w
Health & safety                          
Safety checks Normal   $300   $100     2 d     1 d
Medical checks Beta $700 $1 000 $3 000   3 d 1 w 3 w    
Public relations                          
Plan reporting Normal   $500   $100     3 d     1 d
Publish reporting plan Normal   $300   $100     2 d     1 d
Project management                          
Mission control meeting Beta $4 000 $5 000 $20 000   5 h 1 d 4 d    
Final control meeting Beta $4 000 $5 000 $15 000   4 h 1 d 3 d    

 

In the MARS1 project task specific probability distributions fall into one of the following types:

Probability distributions are characterized by following parameters:

  • minimum, most probable and maximum cost and duration for beta-PERT and triangular distributions
  • most probable cost and duration and their standard deviation for the normal distribution

For example majority of the tasks in spacecraft system checks might cost much more and last a lot longer than the most probable cost or duration, but the minimum cost and duration are quite close to the most probable estimates. Same applies to communication checks and launch pad related tasks in the 'Ground segment' section.

Following schedule (picture 2) shows task dependency relationships (i.e. predecessors and successors), which are also required for simulating the project duration.

MARS1 schedule no durations

Picture 2. MARS1 schedule.

We can see that tasks under 'Spacecraft', 'Supplies', 'Mission' and 'Ground segment' need to be done before the 'Mission control meeting'. After the meeting tasks related to 'Public relations' and 'Crew' can be done. They are followed by the 'Final control meeting'.

Let's look at the results after running the Monte Carlo simulation with 500 rounds in MonteCarloProject. MARS1 project's total cost and duration distributions are shown in pictures 3 and 4. A separate article highlights the use of Monte Carlo method in project modeling.

MARS1 total cost distribution

Picture 3. Histogram and cumulative probability curve for MARS1 project's cost.

Having a look at the cumulative probability curve in picture 3 we can see that there's a 33% probabilty of project costing no more than roughly $40 500 and a very high probability (98%) of project's total cost staying under roughly $52 000.

MARS1 total duration distribution

Picture 4. Histogram and cumulative probability curve for MARS1 project's duration.

Having a look at the cumulative probability curve in picture 4 we can see that there's a 49% probabilty of project finishing by the 19th of February 2025 and a very high probability (97%) of it finishing by the 15th of March 2025. Information is useful when targeting a certain launch window.

MonteCarloProject shows also the hits (cost and duration) for each simulation round in a scatter chart (see picture 5).

MARS1 cost duration scatter chart

 

Picture 5. Results of MARS1 project's simulation rounds.

Scatter chart is useful when finding out a probability of staying simultaneously below a certain total cost and duration for the MARS1 project.

Bon voyage!