Hold-up Tank Model

This notebook will show the basics of using fmdtools to simulate hazards in a system with human-component interactions, including:

• human-induced failure modes

• human responses to component failure modes

• joint human-component failure modes

The system to model is in tank_model.py.

Copyright © 2024, United States Government, as represented by the Administrator of the National Aeronautics and Space Administration. All rights reserved.

The “"Fault Model Design tools - fmdtools version 2"” software is licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0.

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

import fmdtools.sim.propagate as propagate
import fmdtools.analyze as an
from tank_model import Tank
from fmdtools.sim.sample import FaultDomain, FaultSample
from fmdtools.define.architecture.function import FunctionArchitectureGraph

Verifying the nominal state:

In the nominal state, no change in system state should occur and the tank level should remain at 10. For this, track = 'all' is included to record all states of the model. If track = 'all' is ommitted, only values defined in mdl.default_track would be included (see tank_model.py).

mdl = Tank(track='all')
result, mdlhist = propagate.nominal(mdl, desired_result={'graph': FunctionArchitectureGraph})

Here we can see where it is in the Result and then where it is specifically in the result.graph

result

graph: <fmdtools.define.architecture.function.FunctionArchitectureGraph object at 0x000001EEE2C4EE10>

With these results, we can now plot the graph of results resgraph using:

fig = result.graph.draw(figsize=(8,6))

As can be seen, this gives a graphical representation of the functional model with the various flows. Since all of the functions are grey, no faults were accidentally introduced in this run.

A model history is additionally returned given our specified tracking options. If none are provided, the default_track variable in the Model is used (which in this case is set to all). It also shows the datatype for each (all arrays). See below:

mdlhist

m.sub_faults:                  array(21)
flows.wat_in_1.s.effort:       array(21)
flows.wat_in_1.s.rate:         array(21)
flows.wat_in_2.s.effort:       array(21)
flows.wat_in_2.s.rate:         array(21)
flows.wat_out_1.s.effort:      array(21)
flows.wat_out_1.s.rate:        array(21)
flows.wat_out_2.s.effort:      array(21)
flows.wat_out_2.s.rate:        array(21)
flows.valve1_sig.s.indicator:  array(21)
flows.valve1_sig.s.action:     array(21)
flows.tank_sig.s.indicator:    array(21)
flows.tank_sig.s.action:       array(21)
flows.valve2_sig.s.indicator:  array(21)
flows.valve2_sig.s.action:     array(21)
fxns.import_water.s.amt_open:  array(21)
fxns.import_water.m.faults.stuck: array(21)
fxns.import_water.m.sub_faults: array(21)
fxns.guide_water_in.m.faults.clogged: array(21)
fxns.guide_water_in.m.faults.leak: array(21)
fxns.guide_water_in.m.sub_faults: array(21)
fxns.store_water.s.level:      array(21)
fxns.store_water.s.net_flow:   array(21)
fxns.store_water.m.faults.leak: array(21)
fxns.store_water.m.sub_faults: array(21)
fxns.guide_water_out.m.faults.clogged: array(21)
fxns.guide_water_out.m.faults.leak: array(21)
fxns.guide_water_out.m.sub_faults: array(21)
fxns.export_water.s.amt_open:  array(21)
fxns.export_water.m.faults.stuck: array(21)
fxns.export_water.m.sub_faults: array(21)
fxns.human.aa.active_actions:  array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.tank_sig.s.action: array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.flows.           array(21)
fxns.human.aa.acts.l           array(21)
fxns.human.aa.acts.look.m.sub_faults: array(21)
fxns.human.aa.acts.d           array(21)
fxns.human.aa.acts.d           array(21)
fxns.human.aa.acts.d           array(21)
fxns.human.aa.acts.detect.m.sub_faults: array(21)
fxns.human.aa.acts.r           array(21)
fxns.human.aa.acts.reach.m.sub_faults: array(21)
fxns.human.aa.acts.g           array(21)
fxns.human.aa.acts.grasp.m.sub_faults: array(21)
fxns.human.aa.acts.t           array(21)
fxns.human.aa.acts.t           array(21)
fxns.human.aa.acts.turn.m.sub_faults: array(21)
fxns.human.m.sub_faults:       array(21)
time:                          array(21)

We can also look at the history of each function to check if it nominal or faulty. First checking to see if the the store_water function is nominal and then verifying that it is at the constant level throughout these time steps

mdlhist.fxns.store_water.m

faults.leak:                   array(21)
sub_faults:                    array(21)

mdlhist.fxns.store_water.s.level

array([10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,
       10., 10., 10., 10., 10., 10., 10., 10.])

We can further look at the states of the model using History.plot_line. Input the specific graphs you want to see, here showing that water_in == water_out, that the store water value is constant, and that there is no signal from the tank to indicate anything is wrong. Note that units are not included.

fig, ax = mdlhist.plot_line('flows.wat_in_1.s.rate',
                               'flows.wat_out_1.s.rate',
                               'fxns.store_water.s.level',
                               'flows.tank_sig.s.indicator')

History

If we want to see this data in tabular form, we can use mdlhist.as_table(). This also includes indexing on the table to only see parts of it.

This table is a pandas dataframe. We can save this dataframe to a .csv using nominal_histtable.to_csv("filename.csv")

nominal_histtable = mdlhist.as_table()
nominal_histtable[:10] #only displaying 10

	m.sub_faults	flows.wat_in_1.s.effort	flows.wat_in_1.s.rate	flows.wat_in_2.s.effort	flows.wat_in_2.s.rate	flows.wat_out_1.s.effort	flows.wat_out_1.s.rate	flows.wat_out_2.s.effort	flows.wat_out_2.s.rate	flows.valve1_sig.s.indicator	...	fxns.human.aa.acts.detect.m.sub_faults	fxns.human.aa.acts.reach.m.faults.unable	fxns.human.aa.acts.reach.m.sub_faults	fxns.human.aa.acts.grasp.m.faults.cannot	fxns.human.aa.acts.grasp.m.sub_faults	fxns.human.aa.acts.turn.m.faults.cannot	fxns.human.aa.acts.turn.m.faults.wrong_valve	fxns.human.aa.acts.turn.m.sub_faults	fxns.human.m.sub_faults	time
0	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	0.0
1	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	1.0
2	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	2.0
3	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	3.0
4	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	4.0
5	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	5.0
6	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	6.0
7	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	7.0
8	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	8.0
9	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	9.0

10 rows × 55 columns

What happens under component faults?

Here we model a leak of the tank. To compensate for this leak, the operator opens the first valve to a higher setting, maintaining the level of the tank. This is done with propagate.one_fault, which tells the model that a fault has occured and when it did occure. Note that this fault was part of the history earlier as fxns.store_water.m.faults.leak.

Here, the store_water level drops until the indicator turns on and allows for the system to compensate to keep the tank from fully emptying. Blue represents nominal state and red is the fault scenario.

resgraph, mdlhist = propagate.one_fault(mdl,'store_water','leak', time=3,track='all',desired_result=['graph','endclass','endfaults'])

fig, ax = mdlhist.plot_line('flows.valve1_sig.s.action', 'flows.tank_sig.s.indicator',
                            'fxns.store_water.s.level', 'fxns.store_water.s.net_flow',
                            title="Tank response to leak at t=3", time_slice=3, legend_loc=False, title_padding=0.1)

We can also view the model again with highlighed areas to show the faults visually. The draw_from function requires both the time step you’re call (here, it’s at 10 since that is after the fault occured). For more uses of this function, including animations, see Pump_Example_Notebook.ipynb in the pump example folder.

mg = FunctionArchitectureGraph(mdl)
fig, ax = mg.draw_from(10, mdlhist)

Now mdlhist has double the number of entries–those corresponding to the nominal and faulty scenarios.

fault_histtable = mdlhist.as_table()
fault_histtable

	nominal.m.sub_faults	nominal.flows.wat_in_1.s.effort	nominal.flows.wat_in_1.s.rate	nominal.flows.wat_in_2.s.effort	nominal.flows.wat_in_2.s.rate	nominal.flows.wat_out_1.s.effort	nominal.flows.wat_out_1.s.rate	nominal.flows.wat_out_2.s.effort	nominal.flows.wat_out_2.s.rate	nominal.flows.valve1_sig.s.indicator	...	faulty.fxns.human.aa.acts.detect.m.sub_faults	faulty.fxns.human.aa.acts.reach.m.faults.unable	faulty.fxns.human.aa.acts.reach.m.sub_faults	faulty.fxns.human.aa.acts.grasp.m.faults.cannot	faulty.fxns.human.aa.acts.grasp.m.sub_faults	faulty.fxns.human.aa.acts.turn.m.faults.cannot	faulty.fxns.human.aa.acts.turn.m.faults.wrong_valve	faulty.fxns.human.aa.acts.turn.m.sub_faults	faulty.fxns.human.m.sub_faults	faulty.time
0	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	0.0
1	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	1.0
2	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	2.0
3	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	3.0
4	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	4.0
5	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	5.0
6	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	6.0
7	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	7.0
8	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	8.0
9	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	9.0
10	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	10.0
11	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	11.0
12	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	12.0
13	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	13.0
14	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	14.0
15	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	15.0
16	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	16.0
17	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	17.0
18	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	18.0
19	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	19.0
20	False	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	...	False	False	False	False	False	False	False	False	False	20.0

21 rows × 110 columns

Note how, compared to the previos history table, this one does not include all values rather only the component that was affected (IE the store water function. We can further us History.get_degraded_hist compares the results over time so we can see what functions and flows were degraded over time. We can then use the summary to view a list of the functions and flows that were impacted over time.

We can the the view it as a table again, but compared to the previous it only shows if the fault occurs.

deghist = mdlhist.get_degraded_hist(*mdl.fxns, *mdl.flows)
deghist.as_table()

	import_water	guide_water_in	store_water	guide_water_out	export_water	human	wat_in_1	wat_in_2	wat_out_1	wat_out_2	valve1_sig	tank_sig	valve2_sig	total	time
0	False	False	False	False	False	False	False	False	False	False	False	False	False	0	0.0
1	False	False	False	False	False	False	False	False	False	False	False	False	False	0	1.0
2	False	False	False	False	False	False	False	False	False	False	False	False	False	0	2.0
3	False	False	True	False	False	False	False	False	False	False	False	False	False	1	3.0
4	False	False	True	False	False	False	False	False	False	False	False	False	False	1	4.0
5	False	False	True	False	False	False	False	False	False	False	False	False	False	1	5.0
6	False	False	True	False	False	True	False	False	False	False	False	True	False	3	6.0
7	True	False	True	False	False	True	True	True	False	False	True	True	False	7	7.0
8	True	False	True	False	False	True	True	True	False	False	True	True	False	7	8.0
9	True	False	True	False	False	True	True	True	False	False	True	True	False	7	9.0
10	True	False	True	False	False	True	True	True	False	False	True	True	False	7	10.0
11	True	False	True	False	False	True	True	True	False	False	True	True	False	7	11.0
12	True	False	True	False	False	True	True	True	False	False	True	True	False	7	12.0
13	True	False	True	False	False	True	True	True	False	False	True	True	False	7	13.0
14	True	False	True	False	False	True	True	True	False	False	True	True	False	7	14.0
15	True	False	True	False	False	True	True	True	False	False	True	True	False	7	15.0
16	True	False	True	False	False	True	True	True	False	False	True	True	False	7	16.0
17	True	False	True	False	False	True	True	True	False	False	True	True	False	7	17.0
18	True	False	True	False	False	True	True	True	False	False	True	True	False	7	18.0
19	True	False	True	False	False	True	True	True	False	False	True	True	False	7	19.0
20	True	False	True	False	False	True	True	True	False	False	True	True	False	7	20.0

What about human-induced faults?

Here we evaluate what happens if the operator thinks they see a low or high indicator and takes those given actions.

Note that in these cases, because of the indicator/procedures, the operators are able to correct for the fault.

resgraph, mdlhist = propagate.one_fault(mdl,'human.aa.acts.detect','false_low', time=3, track='all',desired_result=['graph','endclass','endfaults'])

fig, ax = mdlhist.plot_line('flows.valve1_sig.s.action',
                       'flows.tank_sig.s.indicator',
                       'fxns.store_water.s.level',
                       'fxns.store_water.s.net_flow',title="False detection low at t=3",time_slice=3,legend_loc=False, title_padding=0.1)

mg = FunctionArchitectureGraph(mdl)
fig, ax = mg.draw_from(10, mdlhist, figsize=(8,6), withlegend=False, rem_ind=2) #set size and remove legend for legibility.

deghist = mdlhist.get_degraded_hist(*mdl.fxns, *mdl.flows)
deghist.as_table()

	import_water	guide_water_in	store_water	guide_water_out	export_water	human	wat_in_1	wat_in_2	wat_out_1	wat_out_2	valve1_sig	tank_sig	valve2_sig	total	time
0	False	False	False	False	False	False	False	False	False	False	False	False	False	0	0.0
1	False	False	False	False	False	False	False	False	False	False	False	False	False	0	1.0
2	False	False	False	False	False	False	False	False	False	False	False	False	False	0	2.0
3	True	False	True	False	False	True	True	True	False	False	True	False	False	6	3.0
4	True	False	True	False	False	True	True	True	False	False	True	False	False	6	4.0
5	True	False	True	False	False	True	True	True	False	False	True	False	False	6	5.0
6	True	False	True	False	False	True	True	True	False	False	True	True	False	7	6.0
7	True	False	True	False	False	True	True	True	False	False	True	True	False	7	7.0
8	True	False	True	False	False	True	True	True	False	False	True	True	False	7	8.0
9	True	False	True	False	False	True	True	True	False	False	True	True	False	7	9.0
10	True	False	True	False	False	True	True	True	False	False	True	True	False	7	10.0
11	True	False	True	False	False	True	True	True	False	False	True	True	False	7	11.0
12	True	False	True	False	False	True	True	True	False	False	True	True	False	7	12.0
13	True	False	True	False	False	True	True	True	True	True	True	True	False	9	13.0
14	True	False	True	False	False	True	True	True	True	True	True	True	False	9	14.0
15	True	False	True	False	False	True	True	True	True	True	True	True	False	9	15.0
16	True	False	True	False	False	True	True	True	True	True	True	False	False	8	16.0
17	True	False	True	False	False	True	True	True	True	True	True	False	False	8	17.0
18	True	False	True	False	False	True	True	True	True	True	True	False	False	8	18.0
19	True	False	True	False	False	True	True	True	True	True	True	True	False	9	19.0
20	True	False	True	False	False	True	True	True	True	True	True	True	False	9	20.0

resgraph, mdlhist = propagate.one_fault(mdl,'human.aa.acts.detect','false_high', time=3, track='all',desired_result=['graph','endclass','endfaults'])

fig, ax = mdlhist.plot_line('flows.valve1_sig.s.action',
                       'flows.tank_sig.s.indicator',
                       'fxns.store_water.s.level',
                       'fxns.store_water.s.net_flow',
                       title="False detection high at t=3",time_slice=3,legend_loc=False, title_padding=0.1)

mg = FunctionArchitectureGraph(mdl)
fig, ax = mg.draw_from(10, mdlhist, figsize=(8,6), withlegend=False) #set size and remove legend for legibility.

Evaluating Joint Component-Human fault modes

To understand where the risks of failure are, we need to find the scenarios, that, with the modelled human controls, still lead to failures. To assess this, we develop a fault sampling strategy using FaultDomain and FaultSample.

fd = FaultDomain(mdl)
fd.add_all()
fs = FaultSample(fd)
fs.add_fault_phases()
fs

FaultSample of scenarios:
 - tank_fxns_import_water_stuck_t0p0
 - tank_fxns_guide_water_in_clogged_t0p0
 - tank_fxns_guide_water_in_leak_t0p0
 - tank_fxns_store_water_leak_t0p0
 - tank_fxns_guide_water_out_clogged_t0p0
 - tank_fxns_guide_water_out_leak_t0p0
 - tank_fxns_export_water_stuck_t0p0
 - tank_fxns_human_aa_acts_look_not_visible_t0p0
 - tank_fxns_human_aa_acts_detect_false_high_t0p0
 - tank_fxns_human_aa_acts_detect_false_low_t0p0
 - ... (30 total)

endclasses, mdlhists = propagate.fault_sample(mdl, fs)

SCENARIOS COMPLETE: 100%|██████████| 30/30 [00:01<00:00, 20.14it/s]

Here we consider all single and joint-fault scenarios in the set of simulations to see which ones lead to failure:

fs.add_fault_phases(n_joint=2)
endclasses, mdlhists=propagate.fault_sample(mdl, fs, track="all")

SCENARIOS COMPLETE: 100%|██████████| 240/240 [00:12<00:00, 19.40it/s]

fmea_tab = an.tabulate.result_summary_fmea(endclasses, mdlhist) #note, this is currently behaving odd even without the joint fault cases
fmea_tab

	degraded	faulty	rate	cost	expected_cost
nominal	[]	[]	1.0	0.0	0.0
faulty	[]	[]	NaN	NaN	NaN
tank_fxns_import_water_stuck_t0p0	NaN	NaN	0.0	0.0	0.0
tank_fxns_guide_water_in_clogged_t0p0	NaN	NaN	0.00001	1000000.0	1000000.0
tank_fxns_guide_water_in_leak_t0p0	NaN	NaN	0.00001	0.0	0.0
...	...	...	...	...	...
tank_fxns_human_aa_acts_reach_unable__tank_fxns_human_aa_acts_turn_cannot_t10p0	NaN	NaN	0.032432	0.0	0.0
tank_fxns_human_aa_acts_reach_unable__tank_fxns_human_aa_acts_turn_wrong_valve_t10p0	NaN	NaN	0.016216	0.0	0.0
tank_fxns_human_aa_acts_grasp_cannot__tank_fxns_human_aa_acts_turn_cannot_t10p0	NaN	NaN	0.005544	0.0	0.0
tank_fxns_human_aa_acts_grasp_cannot__tank_fxns_human_aa_acts_turn_wrong_valve_t10p0	NaN	NaN	0.002772	0.0	0.0
tank_fxns_human_aa_acts_turn_cannot__tank_fxns_human_aa_acts_turn_wrong_valve_t10p0	NaN	NaN	0.03842	0.0	0.0

242 rows × 5 columns

Next, we can filter out non-failures and sort by the failures with the highest expected cost (though rate would give the same results here)

failure_tab = fmea_tab[fmea_tab['cost'] > 1]
failure_tab.sort_values('expected_cost', ascending = False)

	degraded	faulty	rate	cost	expected_cost
tank_fxns_human_aa_acts_detect_false_high_t0p0	NaN	NaN	0.231504	1000000.0	23150399999.999996
tank_fxns_human_aa_acts_detect_false_low_t0p0	NaN	NaN	0.231504	1000000.0	23150399999.999996
tank_fxns_human_aa_acts_detect_false_high__tank_fxns_human_aa_acts_detect_false_low_t10p0	NaN	NaN	0.053594	1000000.0	5359410201.599999
tank_fxns_human_aa_acts_detect_false_high__tank_fxns_human_aa_acts_detect_false_low_t0p0	NaN	NaN	0.053594	1000000.0	5359410201.599999
tank_fxns_human_aa_acts_detect_false_high__tank_fxns_human_aa_acts_turn_wrong_valve_t10p0	NaN	NaN	0.032086	1000000.0	3208645440.0
...	...	...	...	...	...
tank_fxns_import_water_stuck__tank_fxns_guide_water_in_clogged_t10p0	NaN	NaN	-0.0	1000000.0	-3.166667
tank_fxns_export_water_stuck__tank_fxns_human_aa_acts_detect_false_low_t0p0	NaN	NaN	-0.000001	1000000.0	-73309.6
tank_fxns_export_water_stuck__tank_fxns_human_aa_acts_detect_false_high_t0p0	NaN	NaN	-0.000001	1000000.0	-73309.6
tank_fxns_export_water_stuck__tank_fxns_human_aa_acts_detect_false_high_t10p0	NaN	NaN	-0.000001	1000000.0	-73309.6
tank_fxns_export_water_stuck__tank_fxns_human_aa_acts_detect_false_low_t10p0	NaN	NaN	-0.000001	1000000.0	-73309.6

111 rows × 5 columns

One of the top modes is a joint human-component failure mode. Let’s see what happens in this case:

[*mdlhists.keys()]

['tank_fxns_import_water_stuck_t0p0.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_in_1.s.effort',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_in_1.s.rate',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_in_2.s.effort',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_in_2.s.rate',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_out_1.s.effort',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_out_1.s.rate',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_out_2.s.effort',
 'tank_fxns_import_water_stuck_t0p0.flows.wat_out_2.s.rate',
 'tank_fxns_import_water_stuck_t0p0.flows.valve1_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.flows.valve1_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.flows.tank_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.flows.tank_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.flows.valve2_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.flows.valve2_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.fxns.import_water.s.amt_open',
 'tank_fxns_import_water_stuck_t0p0.fxns.import_water.m.faults.stuck',
 'tank_fxns_import_water_stuck_t0p0.fxns.import_water.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_in.m.faults.clogged',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_in.m.faults.leak',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_in.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.store_water.s.level',
 'tank_fxns_import_water_stuck_t0p0.fxns.store_water.s.net_flow',
 'tank_fxns_import_water_stuck_t0p0.fxns.store_water.m.faults.leak',
 'tank_fxns_import_water_stuck_t0p0.fxns.store_water.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_out.m.faults.clogged',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_out.m.faults.leak',
 'tank_fxns_import_water_stuck_t0p0.fxns.guide_water_out.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.export_water.s.amt_open',
 'tank_fxns_import_water_stuck_t0p0.fxns.export_water.m.faults.stuck',
 'tank_fxns_import_water_stuck_t0p0.fxns.export_water.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.active_actions',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.tank_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.tank_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.valve1_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.valve1_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.valve2_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.valve2_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.detect_sig.s.indicator',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.flows.detect_sig.s.action',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.look.m.faults.not_visible',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.look.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.detect.m.faults.false_high',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.detect.m.faults.false_low',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.detect.m.faults.not_detected',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.detect.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.reach.m.faults.unable',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.reach.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.grasp.m.faults.cannot',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.grasp.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.turn.m.faults.cannot',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.turn.m.faults.wrong_valve',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.aa.acts.turn.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.fxns.human.m.sub_faults',
 'tank_fxns_import_water_stuck_t0p0.time',
 'tank_fxns_guide_water_in_clogged_t0p0.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_in_1.s.effort',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_in_1.s.rate',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_in_2.s.effort',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_in_2.s.rate',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_out_1.s.effort',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_out_1.s.rate',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_out_2.s.effort',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.wat_out_2.s.rate',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.valve1_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.valve1_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.tank_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.tank_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.valve2_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.flows.valve2_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.import_water.s.amt_open',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.import_water.m.faults.stuck',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.import_water.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_in.m.faults.clogged',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_in.m.faults.leak',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_in.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.store_water.s.level',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.store_water.s.net_flow',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.store_water.m.faults.leak',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.store_water.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_out.m.faults.clogged',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_out.m.faults.leak',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.guide_water_out.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.export_water.s.amt_open',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.export_water.m.faults.stuck',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.export_water.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.active_actions',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.tank_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.tank_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.valve1_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.valve1_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.valve2_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.valve2_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.detect_sig.s.indicator',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.flows.detect_sig.s.action',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.look.m.faults.not_visible',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.look.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.detect.m.faults.false_high',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.detect.m.faults.false_low',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.detect.m.faults.not_detected',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.detect.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.reach.m.faults.unable',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.reach.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.grasp.m.faults.cannot',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.grasp.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.turn.m.faults.cannot',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.turn.m.faults.wrong_valve',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.aa.acts.turn.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.fxns.human.m.sub_faults',
 'tank_fxns_guide_water_in_clogged_t0p0.time',
 'tank_fxns_guide_water_in_leak_t0p0.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_in_1.s.effort',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_in_1.s.rate',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_in_2.s.effort',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_in_2.s.rate',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_out_1.s.effort',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_out_1.s.rate',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_out_2.s.effort',
 'tank_fxns_guide_water_in_leak_t0p0.flows.wat_out_2.s.rate',
 'tank_fxns_guide_water_in_leak_t0p0.flows.valve1_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.flows.valve1_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.flows.tank_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.flows.tank_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.flows.valve2_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.flows.valve2_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.import_water.s.amt_open',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.import_water.m.faults.stuck',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.import_water.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_in.m.faults.clogged',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_in.m.faults.leak',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_in.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.store_water.s.level',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.store_water.s.net_flow',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.store_water.m.faults.leak',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.store_water.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_out.m.faults.clogged',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_out.m.faults.leak',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.guide_water_out.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.export_water.s.amt_open',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.export_water.m.faults.stuck',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.export_water.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.active_actions',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.tank_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.tank_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.valve1_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.valve1_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.valve2_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.valve2_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.detect_sig.s.indicator',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.flows.detect_sig.s.action',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.look.m.faults.not_visible',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.look.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.detect.m.faults.false_high',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.detect.m.faults.false_low',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.detect.m.faults.not_detected',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.detect.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.reach.m.faults.unable',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.reach.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.grasp.m.faults.cannot',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.grasp.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.turn.m.faults.cannot',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.turn.m.faults.wrong_valve',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.aa.acts.turn.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.fxns.human.m.sub_faults',
 'tank_fxns_guide_water_in_leak_t0p0.time',
 'tank_fxns_store_water_leak_t0p0.m.sub_faults',
 'tank_fxns_store_water_leak_t0p0.flows.wat_in_1.s.effort',
 'tank_fxns_store_water_leak_t0p0.flows.wat_in_1.s.rate',
 'tank_fxns_store_water_leak_t0p0.flows.wat_in_2.s.effort',
 'tank_fxns_store_water_leak_t0p0.flows.wat_in_2.s.rate',
 'tank_fxns_store_water_leak_t0p0.flows.wat_out_1.s.effort',
 'tank_fxns_store_water_leak_t0p0.flows.wat_out_1.s.rate',
 'tank_fxns_store_water_leak_t0p0.flows.wat_out_2.s.effort',
 'tank_fxns_store_water_leak_t0p0.flows.wat_out_2.s.rate',
 'tank_fxns_store_water_leak_t0p0.flows.valve1_sig.s.indicator',
 'tank_fxns_store_water_leak_t0p0.flows.valve1_sig.s.action',
 'tank_fxns_store_water_leak_t0p0.flows.tank_sig.s.indicator',
 'tank_fxns_store_water_leak_t0p0.flows.tank_sig.s.action',
 'tank_fxns_store_water_leak_t0p0.flows.valve2_sig.s.indicator',
 'tank_fxns_store_water_leak_t0p0.flows.valve2_sig.s.action',
 'tank_fxns_store_water_leak_t0p0.fxns.import_water.s.amt_open',
 'tank_fxns_store_water_leak_t0p0.fxns.import_water.m.faults.stuck',
 'tank_fxns_store_water_leak_t0p0.fxns.import_water.m.sub_faults',
 'tank_fxns_store_water_leak_t0p0.fxns.guide_water_in.m.faults.clogged',
 'tank_fxns_store_water_leak_t0p0.fxns.guide_water_in.m.faults.leak',
 'tank_fxns_store_water_leak_t0p0.fxns.guide_water_in.m.sub_faults',
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 'tank_fxns_store_water_leak_t10p0.flows.wat_in_1.s.rate',
 'tank_fxns_store_water_leak_t10p0.flows.wat_in_2.s.effort',
 'tank_fxns_store_water_leak_t10p0.flows.wat_in_2.s.rate',
 'tank_fxns_store_water_leak_t10p0.flows.wat_out_1.s.effort',
 'tank_fxns_store_water_leak_t10p0.flows.wat_out_1.s.rate',
 'tank_fxns_store_water_leak_t10p0.flows.wat_out_2.s.effort',
 'tank_fxns_store_water_leak_t10p0.flows.wat_out_2.s.rate',
 'tank_fxns_store_water_leak_t10p0.flows.valve1_sig.s.indicator',
 ...]

from fmdtools.analyze.history import History
scenhists = History({'nominal':mdlhists.nominal,
            'faulty':mdlhists.get('tank_fxns_guide_water_in_leak__tank_fxns_human_aa_acts_detect_not_detected_t10p0')})
#scenhists.flatten()
fig, axs = scenhists.plot_line('flows.valve1_sig.s.action',
                       'flows.tank_sig.s.indicator',
                       'fxns.store_water.s.level',
                       'fxns.store_water.s.net_flow', time_slice=[10])

In this case, there is a leak, but the operator cannot turn the valve, resulting in the tank filling too high, which is a failure.

To consider the leak again, we can see what happens when the leak is not detected:

scenhists =History({'nominal':mdlhists.nominal, 'faulty':mdlhists.get('tank_fxns_guide_water_out_leak__tank_fxns_human_aa_acts_detect_false_low_t10p0')})
scenhists.flatten()
fig, axs = scenhists.plot_line('flows.valve1_sig.s.action',
                       'flows.tank_sig.s.indicator',
                       'fxns.store_water.s.level',
                       'fxns.store_water.s.net_flow',
                       time_slice=[10])

In this case, there is a leak, but it is not caugh, resulting in a failure again.

Testing different reaction times

The model set up in tank_model is parameterized by the reaction time of the operator. As a result, we can assess how long or short reaction times affect the given scenarios.

mdl_long_reaction_time = Tank(p={'reacttime':10, "store_tstep":1.0}, track='all') #also needs reconfiguring

In this case, we will show the affect of reaction time on the operator’s ability to catch a leak.

result, mdlhist = propagate.one_fault(mdl_long_reaction_time,'store_water','leak', time=3,track="all", desired_result='graph')

fig, axs = mdlhist.plot_line('flows.valve1_sig.s.action',
                       'flows.tank_sig.s.indicator',
                       'fxns.store_water.s.level',
                       'fxns.store_water.s.net_flow')

result.graph.draw()

(<Figure size 1200x1000 with 1 Axes>, <Axes: >)

As shown, the operator does not respond in time, resulting in the tank draining all the way, a failure state. We can further use the propagate.approach function to compare the number of scenarios caught in this system compared with the other.