NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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SCREEN | NESC1002/01 | Tested | 19-NOV-1985 |

Machines used:

Package ID | Orig. computer | Test computer |
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NESC1002/01 | IBM 3033 | IBM 3084Q |

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3. DESCRIPTION OF PROGRAM OR FUNCTION

SCREEN is a statistical sensitivity analysis procedure for ranking input data of large computer codes in the order of sensitivity importance. The problem is to determine a group of the most important input parameters of a computer code when the total number of input variables is large, so large that standard sensitivity evaluations varying each input variable (one or two at a time) would be prohibitively expensive.

SCREEN is a statistical sensitivity analysis procedure for ranking input data of large computer codes in the order of sensitivity importance. The problem is to determine a group of the most important input parameters of a computer code when the total number of input variables is large, so large that standard sensitivity evaluations varying each input variable (one or two at a time) would be prohibitively expensive.

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4. METHOD OF SOLUTION

SCREEN selects values for the input parameters of a deterministic computer program from input-specified regions of interest. The regions are defined by probability distributions and confidence intervals. The program arranges these input values into combinations called 'knot-points' that serve as input for the deterministic code that calculates the values of interesting output variables (consequences) for the specified knot-points.

The output/consequence values for the knot-points are then used to determine (1) which input variable are most correlated with the output/consequence values, using stagewise correlation analysis, (2) which input variables are most likely to contribute to discontinuities or threshold effects in the output values, using statistical tests for subset characteristics, and (3) which group of input parameters yields the best significant regression model, using quadratic models and successive regression analyses with an increasing number of parameters. The regression part of SCREEN evaluates all regressions of two variables using the principle of stepwise regression analysis for a large number of variables. Both residual errors and special sensitivity/spuriousness indices can be used to select seed input variables for each step of the regression analysis. The significance of each added parameter of a model can be assessed by F-statistics for regression models. Student t-statistics and extreme value statistics are used for testing threshold effects.

SCREEN selects values for the input parameters of a deterministic computer program from input-specified regions of interest. The regions are defined by probability distributions and confidence intervals. The program arranges these input values into combinations called 'knot-points' that serve as input for the deterministic code that calculates the values of interesting output variables (consequences) for the specified knot-points.

The output/consequence values for the knot-points are then used to determine (1) which input variable are most correlated with the output/consequence values, using stagewise correlation analysis, (2) which input variables are most likely to contribute to discontinuities or threshold effects in the output values, using statistical tests for subset characteristics, and (3) which group of input parameters yields the best significant regression model, using quadratic models and successive regression analyses with an increasing number of parameters. The regression part of SCREEN evaluates all regressions of two variables using the principle of stepwise regression analysis for a large number of variables. Both residual errors and special sensitivity/spuriousness indices can be used to select seed input variables for each step of the regression analysis. The significance of each added parameter of a model can be assessed by F-statistics for regression models. Student t-statistics and extreme value statistics are used for testing threshold effects.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Maxima of -

1000 input parameter variables

6 output/consequence variables

When selecting the cases to be run (knot-points), eight optional distributions are available for the input parameters, including uniform, exponential, normal, truncated normal, log-normal, and beta distributions.

Maxima of -

1000 input parameter variables

6 output/consequence variables

When selecting the cases to be run (knot-points), eight optional distributions are available for the input parameters, including uniform, exponential, normal, truncated normal, log-normal, and beta distributions.

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6. TYPICAL RUNNING TIME

Running time depends strongly on the size of the problem, i.e., number of input parameters, knot-points, and the number of regression steps needed to complete the screening. For small problems where the number of input parameters and knot-points are both less than 50, the total running time is typically a few CPU seconds on an IBM370/195. Large problems, with approximately 500 input parameters and 50 knot-points, take several minutes of CPU time per consequence on an IBM370/195. NESC executed the sample problem in 2 CPU seconds on an IBM3033.

Running time depends strongly on the size of the problem, i.e., number of input parameters, knot-points, and the number of regression steps needed to complete the screening. For small problems where the number of input parameters and knot-points are both less than 50, the total running time is typically a few CPU seconds on an IBM370/195. Large problems, with approximately 500 input parameters and 50 knot-points, take several minutes of CPU time per consequence on an IBM370/195. NESC executed the sample problem in 2 CPU seconds on an IBM3033.

NESC1002/01

NEA-DB executed the test case included in this package on IBM 3084Q in 2 seconds of CPU time.[ top ]

7. UNUSUAL FEATURES OF THE PROGRAM

Compared to other screening techniques available, SCREEN has the following somewhat unique features: (a) the values of the input parameters (knot-point coordinates) are selected from a continuous distribution rather than from discrete levels; (b) quadratic regression models rather than linear models are used; (c) the total number of input variables may be much larger than the number of cases and no prior elimination of variables by judgment is necessary; (d) the regression analysis in SCREEN is more extensive than the standard stepwise regression analysis procedure; and (e) extreme value and t-tests are used to identify parameters important to threshold (discontinuity) effects.

Compared to other screening techniques available, SCREEN has the following somewhat unique features: (a) the values of the input parameters (knot-point coordinates) are selected from a continuous distribution rather than from discrete levels; (b) quadratic regression models rather than linear models are used; (c) the total number of input variables may be much larger than the number of cases and no prior elimination of variables by judgment is necessary; (d) the regression analysis in SCREEN is more extensive than the standard stepwise regression analysis procedure; and (e) extreme value and t-tests are used to identify parameters important to threshold (discontinuity) effects.

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8. RELATED AND AUXILIARY PROGRAMS

The SCREEN code can be used in conjunction with any separate deterministic code (typically an accident-analysis code such as SAS3D) that provides data for screening. It can also be used to generate input data in the correct format for the response-surface analysis code PROSA2 (NESC Abstract 778).

The SCREEN code can be used in conjunction with any separate deterministic code (typically an accident-analysis code such as SAS3D) that provides data for screening. It can also be used to generate input data in the correct format for the response-surface analysis code PROSA2 (NESC Abstract 778).

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10. REFERENCES

- J.K. Vaurio,

Response Surface Techniques Developed for Probabilistic Analysis

of Accident Consequences, Proceedings of the American Nuclear

Society Topical Meeting on Probabilistic Analysis of Nuclear

Reactor Safety, Los Angeles, California, May 8-10, 1978.

- J.K. Vaurio,

Methods for Statistical Determination of Effective Input

Variables,

Transactions of the American Nuclear Society, Vol. 32, pp.

296-297, 1979.

- J.K. Vaurio,

Statistical Determination of Threshold Variables,

Transactions of the American Nuclear Society, Vol. 35, pp.

263-264, 1980.

- J.K. Vaurio,

Response Surface Techniques Developed for Probabilistic Analysis

of Accident Consequences, Proceedings of the American Nuclear

Society Topical Meeting on Probabilistic Analysis of Nuclear

Reactor Safety, Los Angeles, California, May 8-10, 1978.

- J.K. Vaurio,

Methods for Statistical Determination of Effective Input

Variables,

Transactions of the American Nuclear Society, Vol. 32, pp.

296-297, 1979.

- J.K. Vaurio,

Statistical Determination of Threshold Variables,

Transactions of the American Nuclear Society, Vol. 35, pp.

263-264, 1980.

NESC1002/01, included references:

- J.K. Vaurio:Statistical Identification of Effective Input Variables.

ANL-82-57 (September 1982)

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NESC1002/01

The test case was run on IBM 3084Q in 2ooK bytes of main storage.[ top ]

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

SCREEN

contains some FORMAT statements which use the T edit descriptor and READ statements which use the ERR= and END= error and end-of-file specifiers. Subroutines ABEND, ALLOC2, FLTRNF, FREE2, and LOC are written in Basic Assembly Language. FLTRNF, ALLOC2, and FREE2 are Argonne National Laboratory computing environment routines. The FLTRNF function statement U=FLTRNF(0) returns uniform random numbers U, between 0 and 1. Subroutines ALLOC2 and FREE2 dynamically allocate and release space for the arrays used in the regression analysis. Subroutine SASIN, which prepares input for an external deterministic code that calculates consequences, is to be supplied by the user. Versions of SASIN appropriate for the VENUS2 and SAS3D computer programs are included in the package.

SCREEN

contains some FORMAT statements which use the T edit descriptor and READ statements which use the ERR= and END= error and end-of-file specifiers. Subroutines ABEND, ALLOC2, FLTRNF, FREE2, and LOC are written in Basic Assembly Language. FLTRNF, ALLOC2, and FREE2 are Argonne National Laboratory computing environment routines. The FLTRNF function statement U=FLTRNF(0) returns uniform random numbers U, between 0 and 1. Subroutines ALLOC2 and FREE2 dynamically allocate and release space for the arrays used in the regression analysis. Subroutine SASIN, which prepares input for an external deterministic code that calculates consequences, is to be supplied by the user. Versions of SASIN appropriate for the VENUS2 and SAS3D computer programs are included in the package.

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NESC1002/01

File name | File description | Records |
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NESC1002_01.003 | INFORMATION FILE | 53 |

NESC1002_01.004 | SCREEN SOURCE PROGRAM (FORTRAN) | 4570 |

NESC1002_01.005 | SCREEN ASSEMBLER ROUTINES | 344 |

NESC1002_01.006 | SCREEN JCL TO RUN SAMPLE PROBLEM | 35 |

NESC1002_01.007 | SCREEN SAMPLE PROBLEM INPUT DATA | 179 |

NESC1002_01.008 | SCREEN SAMPLE PROBLEM PRINTED OUTPUT | 2003 |

NESC1002_01.009 | SUBROUTINE SASIN FOR SAS3D PROGRAM | 928 |

Keywords: accidents, correlations, least square fit, probability, randomness, regression analysis, risk assessment, safety, sensitivity analysis, statistics.