TRISOFailureProbabilityIntegration

Compute TRISO failure probability by integration.

Description

TRISOFailureProbabilityIntegration computes TRISO failure probability using a direct integration approach. This VectorPostprocessor returns a vector that includes SiC failure probability due to internal pressure, IPyC cracking probability, SiC failure probability due to IPyC cracking and SiC overall failure probability.

The total failure probability is given as:

$var element = document.getElementById("moose-equation-7b99934d-9916-47fb-bf72-8ffdd86c8bcc");katex.render("P_f = \\frac{1}{\\sqrt{2\\pi}^nD_jD_k...}\\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}...e^{-\\frac{(v_j-\\mu_j)^2}{2D_j^2}}e^{-\\frac{(v_k-\\mu_k)^2}{2D_k^2}}...\\left[ 1-e^{-\\left(\\frac{\\sigma(v_j,v_k...)}{\\sigma_{ms}}\\right)^m} \\right]\\text{d} v_k \\text{d} v_j...", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-86440e82-73ee-425e-9308-83d88d2abbd9");katex.render("v_k,v_j...", element, {displayMode:false,throwOnError:false});$ are random parameters and $var element = document.getElementById("moose-equation-ee4a79cb-0dd3-4d93-8ae0-6ec5d8f9c71c");katex.render("D_k, D_j", element, {displayMode:false,throwOnError:false});$ are their standard deviations.

A quadrature rule is needed to perform the integration. Two quadrature samplers are available: tensor grid and Smolyak sparse grid. The sparse grid option is preferred because it requires a much smaller number of samples when random variable dimensions become large.

Example Input Syntax

[VectorPostprocessors<<<{"href": "../../syntax/VectorPostprocessors/index.html"}>>>]
  [failure_results]
    type = StochasticResults<<<{"description": "Storage container for stochastic simulation results coming from a Postprocessor.", "href": "../vectorpostprocessors/StochasticResults.html"}>>>
    parallel_type<<<{"description": "Set how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is performed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function."}>>> = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration<<<{"description": "Compute TRISO failure probability by integration.", "href": "TRISOFailureProbabilityIntegration.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
    sampler<<<{"description": "Name of the sampler used for integration of SiC failure probability."}>>> = quadrature_triso_1d
    failure_results_vpp<<<{"description": "The name of Vectorpostprocessor that stores failure results at each quadracture point."}>>> = failure_results
    ipyc_cracking_results_vector<<<{"description": "Name of vector in the vectorpostprocessor with results of IPyC cracking."}>>> = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector<<<{"description": "Name of vector in the vectorpostprocessor with results of SiC failure due to IPyC cracking."}>>> = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector<<<{"description": "Name of vector in the vectorpostprocessor with results of SiC failure due to pressure."}>>> = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

Input Parameters

failure_results_vppThe name of Vectorpostprocessor that stores failure results at each quadracture point.
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of Vectorpostprocessor that stores failure results at each quadracture point.

Required Parameters

contains_complete_historyFalseSet this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
Default:False
C++ Type:bool
Controllable:No
Description:Set this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
ipyc_cracking_results_vectorName of vector in the vectorpostprocessor with results of IPyC cracking.
C++ Type:std::string
Controllable:No
Description:Name of vector in the vectorpostprocessor with results of IPyC cracking.
parallel_typeREPLICATEDSet how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is performed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
Default:REPLICATED
C++ Type:MooseEnum
Options:DISTRIBUTED, REPLICATED
Controllable:No
Description:Set how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is performed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
samplerName of the sampler used for integration of SiC failure probability.
C++ Type:SamplerName
Controllable:No
Description:Name of the sampler used for integration of SiC failure probability.
sic_failure_due_to_ipyc_cracking_results_vectorName of vector in the vectorpostprocessor with results of SiC failure due to IPyC cracking.
C++ Type:std::string
Controllable:No
Description:Name of vector in the vectorpostprocessor with results of SiC failure due to IPyC cracking.
sic_failure_due_to_pressure_results_vectorName of vector in the vectorpostprocessor with results of SiC failure due to pressure.
C++ Type:std::string
Controllable:No
Description:Name of vector in the vectorpostprocessor with results of SiC failure due to pressure.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(examples/TRISO/failure_probability_direct_integration/direct_integration_2d_2d.i)
(examples/TRISO/failure_probability_direct_integration/direct_integration_1d_2d.i)
(examples/TRISO/failure_probability_direct_integration/direct_integration_1d.i)
(test/tests/triso_failure/triso_failure_probability_integration.i)

(test/tests/triso_failure/triso_failure_probability_integration.i)

[StochasticTools]
  auto_create_executioner = false
[]

[Distributions]
  [normal_kernel_r]
    type = Normal
    mean = 213.35e-6
    standard_deviation = 4.4e-6
  []
  [normal_buffer_t]
    type = Normal
    mean = 98.9e-6
    standard_deviation = 8.4e-6
  []
  [normal_ipyc_t]
    type = Normal
    mean = 40.4e-6
    standard_deviation = 2.5e-6
  []
  [normal_sic_t]
    type = Normal
    mean = 35.2e-6
    standard_deviation = 1.2e-6
  []
  [normal_opyc_t]
    type = Normal
    mean = 43.4e-6
    standard_deviation = 2.9e-6
  []
[]

[Samplers]
  [quadrature_triso_1d]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
[]

[MultiApps]
  [triso_1d]
    type = SamplerFullSolveMultiApp
    input_files = triso_1d_ipyc_weibull_probability.i
    sampler = quadrature_triso_1d
    mode = batch-reset
  []
[]

[Transfers]
  [transfer_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_IPyC
  []
  [transfer_sic_failure_due_to_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC_crackedIPyC
  []
  [transfer_sic_failure_due_to_pressure]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC
  []
[]

[Controls]
  [cmdline_triso_1d]
    type = MultiAppSamplerControl
    multi_app = triso_1d
    sampler = quadrature_triso_1d
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
[]

[VectorPostprocessors]
  [failure_results]
    type = StochasticResults
    parallel_type = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration
    execute_on = timestep_end
    sampler = quadrature_triso_1d
    failure_results_vpp = failure_results
    ipyc_cracking_results_vector = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = 'TIMESTEP_END'
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  perf_graph = true
[]

(examples/TRISO/failure_probability_direct_integration/direct_integration_2d_2d.i)

[StochasticTools]
  auto_create_executioner = false
[]

[Distributions]
  [normal_kernel_r]
    type = Normal
    mean = 213.35e-6
    standard_deviation = 4.4e-6
  []
  [normal_buffer_t]
    type = Normal
    mean = 98.9e-6
    standard_deviation = 8.4e-6
  []
  [normal_ipyc_t]
    type = Normal
    mean = 40.4e-6
    standard_deviation = 2.5e-6
  []
  [normal_sic_t]
    type = Normal
    mean = 35.2e-6
    standard_deviation = 1.2e-6
  []
  [normal_opyc_t]
    type = Normal
    mean = 43.4e-6
    standard_deviation = 2.9e-6
  []
[]

[Samplers]
  [quadrature_asphericity]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
  [quadrature_ipyc_cracking]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
[]

[MultiApps]
  [asphericity]
    type = SamplerFullSolveMultiApp
    input_files = asphericity.i
    sampler = quadrature_asphericity
    mode = batch-reset
  []
  [ipyc_cracking]
    type = SamplerFullSolveMultiApp
    input_files = ipyc_cracking.i
    sampler = quadrature_ipyc_cracking
    mode = batch-reset
  []
[]

[Transfers]
  [transfer_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = asphericity
    sampler = quadrature_asphericity
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_IPyC
  []
  [transfer_sic_failure_due_to_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = ipyc_cracking
    sampler = quadrature_ipyc_cracking
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC_crackedIPyC
  []
  [transfer_sic_failure_due_to_pressure]
    type = SamplerPostprocessorTransfer
    from_multi_app = asphericity
    sampler = quadrature_asphericity
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC
  []
[]

[Controls]
  [cmdline_asphericity]
    type = MultiAppSamplerControl
    multi_app = asphericity
    sampler = quadrature_asphericity
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
  [cmdline_ipyc_cracking]
    type = MultiAppSamplerControl
    multi_app = ipyc_cracking
    sampler = quadrature_ipyc_cracking
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
[]

[VectorPostprocessors]
  [failure_results]
    type = StochasticResults
    parallel_type = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration
    execute_on = timestep_end
    sampler = quadrature_asphericity
    failure_results_vpp = failure_results
    ipyc_cracking_results_vector = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = 'TIMESTEP_END'
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  perf_graph = true
[]

(examples/TRISO/failure_probability_direct_integration/direct_integration_1d_2d.i)

[StochasticTools]
  auto_create_executioner = false
[]

[Distributions]
  [normal_kernel_r]
    type = Normal
    mean = 213.35e-6
    standard_deviation = 4.4e-6
  []
  [normal_buffer_t]
    type = Normal
    mean = 98.9e-6
    standard_deviation = 8.4e-6
  []
  [normal_ipyc_t]
    type = Normal
    mean = 40.4e-6
    standard_deviation = 2.5e-6
  []
  [normal_sic_t]
    type = Normal
    mean = 35.2e-6
    standard_deviation = 1.2e-6
  []
  [normal_opyc_t]
    type = Normal
    mean = 43.4e-6
    standard_deviation = 2.9e-6
  []
[]

[Samplers]
  [quadrature_triso_1d]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
  [quadrature_ipyc_cracking]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
[]

[MultiApps]
  [triso_1d]
    type = SamplerFullSolveMultiApp
    input_files = triso_1d.i
    sampler = quadrature_triso_1d
    mode = batch-reset
  []
  [ipyc_cracking]
    type = SamplerFullSolveMultiApp
    input_files = ipyc_cracking.i
    sampler = quadrature_ipyc_cracking
    mode = batch-reset
  []
[]

[Transfers]
  [transfer_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_IPyC
  []
  [transfer_sic_failure_due_to_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = ipyc_cracking
    sampler = quadrature_ipyc_cracking
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC_crackedIPyC
  []
  [transfer_sic_failure_due_to_pressure]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC
  []
[]

[Controls]
  [cmdline_triso_1d]
    type = MultiAppSamplerControl
    multi_app = triso_1d
    sampler = quadrature_triso_1d
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
  [cmdline_ipyc_cracking]
    type = MultiAppSamplerControl
    multi_app = ipyc_cracking
    sampler = quadrature_ipyc_cracking
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
[]

[VectorPostprocessors]
  [failure_results]
    type = StochasticResults
    parallel_type = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration
    execute_on = timestep_end
    sampler = quadrature_triso_1d
    failure_results_vpp = failure_results
    ipyc_cracking_results_vector = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = 'TIMESTEP_END'
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  perf_graph = true
[]

(examples/TRISO/failure_probability_direct_integration/direct_integration_1d.i)

[StochasticTools]
  auto_create_executioner = false
[]

[Distributions]
  [normal_kernel_r]
    type = Normal
    mean = 213.35e-6
    standard_deviation = 4.4e-6
  []
  [normal_buffer_t]
    type = Normal
    mean = 98.9e-6
    standard_deviation = 8.4e-6
  []
  [normal_ipyc_t]
    type = Normal
    mean = 40.4e-6
    standard_deviation = 2.5e-6
  []
  [normal_sic_t]
    type = Normal
    mean = 35.2e-6
    standard_deviation = 1.2e-6
  []
  [normal_opyc_t]
    type = Normal
    mean = 43.4e-6
    standard_deviation = 2.9e-6
  []
[]

[Samplers]
  [quadrature_triso_1d]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 3
    sparse_grid = smolyak
  []
[]

[MultiApps]
  [triso_1d]
    type = SamplerFullSolveMultiApp
    input_files = triso_1d.i
    sampler = quadrature_triso_1d
    mode = batch-reset
  []
[]

[Transfers]
  [transfer_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_IPyC
  []
  [transfer_sic_failure_due_to_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC_crackedIPyC
  []
  [transfer_sic_failure_due_to_pressure]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC
  []
[]

[Controls]
  [cmdline_triso_1d]
    type = MultiAppSamplerControl
    multi_app = triso_1d
    sampler = quadrature_triso_1d
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
[]

[VectorPostprocessors]
  [failure_results]
    type = StochasticResults
    parallel_type = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration
    execute_on = timestep_end
    sampler = quadrature_triso_1d
    failure_results_vpp = failure_results
    ipyc_cracking_results_vector = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = 'TIMESTEP_END'
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  perf_graph = true
[]

(test/tests/triso_failure/triso_failure_probability_integration.i)

[StochasticTools]
  auto_create_executioner = false
[]

[Distributions]
  [normal_kernel_r]
    type = Normal
    mean = 213.35e-6
    standard_deviation = 4.4e-6
  []
  [normal_buffer_t]
    type = Normal
    mean = 98.9e-6
    standard_deviation = 8.4e-6
  []
  [normal_ipyc_t]
    type = Normal
    mean = 40.4e-6
    standard_deviation = 2.5e-6
  []
  [normal_sic_t]
    type = Normal
    mean = 35.2e-6
    standard_deviation = 1.2e-6
  []
  [normal_opyc_t]
    type = Normal
    mean = 43.4e-6
    standard_deviation = 2.9e-6
  []
[]

[Samplers]
  [quadrature_triso_1d]
    type = Quadrature
    distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
    execute_on = PRE_MULTIAPP_SETUP
    order = 1
    sparse_grid = smolyak
  []
[]

[MultiApps]
  [triso_1d]
    type = SamplerFullSolveMultiApp
    input_files = triso_1d_ipyc_weibull_probability.i
    sampler = quadrature_triso_1d
    mode = batch-reset
  []
[]

[Transfers]
  [transfer_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_IPyC
  []
  [transfer_sic_failure_due_to_ipyc_cracking]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC_crackedIPyC
  []
  [transfer_sic_failure_due_to_pressure]
    type = SamplerPostprocessorTransfer
    from_multi_app = triso_1d
    sampler = quadrature_triso_1d
    to_vector_postprocessor = failure_results
    from_postprocessor = weibull_failure_probability_SiC
  []
[]

[Controls]
  [cmdline_triso_1d]
    type = MultiAppSamplerControl
    multi_app = triso_1d
    sampler = quadrature_triso_1d
    param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
  []
[]

[VectorPostprocessors]
  [failure_results]
    type = StochasticResults
    parallel_type = REPLICATED
  []
  [failure_probability]
    type = TRISOFailureProbabilityIntegration
    execute_on = timestep_end
    sampler = quadrature_triso_1d
    failure_results_vpp = failure_results
    ipyc_cracking_results_vector = transfer_ipyc_cracking:weibull_failure_probability_IPyC
    sic_failure_due_to_ipyc_cracking_results_vector = transfer_sic_failure_due_to_ipyc_cracking:weibull_failure_probability_SiC_crackedIPyC
    sic_failure_due_to_pressure_results_vector = transfer_sic_failure_due_to_pressure:weibull_failure_probability_SiC
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
  exodus = false
  execute_on = 'TIMESTEP_END'
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
  perf_graph = true
[]

Description
Example Input Syntax
Input Parameters
Input Files