This paper makes use of the concept and theory of fuzzy number in fuzzy mathematics, to research for the response time of operator in accident of Chinese nuclear power plant. Through the quantitative analysis for the performance shape factors (PSFs) which influence the response time of operators, the formula of the operator response time is obtained based on the possibilistic fuzzy linear regression model which is used for the first time in this kind of research. The research result shows that the correct research method can be achieved through the analysis of the information from a small sample. This method breaks through the traditional research method and can be used not only for the reference to the safe operation of nuclear power plant, but also in other areas.

The reliability research of nuclear power plant (NPP) operators is focused on the non-response probability of NPP operators under the restrained time. The response time to the accidents is very important. It can be influenced by the performance shape factors (PSFs). Since PSFs include many factors and uncertainties, it is very difficult to be processed quantitatively. Based on the probability distribution of the response time on human cognitive reliability (HCR) model, in order to solve the uncertainty problem on the nonresponse probability, the response time is supposed to be a single-point value. This is the traditional research method of HCR model. However, because the uncertainty of the median time to the accidents on HCR model can be influenced by PSF, it is not completed to regard the response time as only a simple-point value. In another word, the response time should be a range or an uncertain number.

The paper makes use of the related method of fuzzy mathematics and does the research of the NPP operator response time distribution related to PSF. The method describes the linear relations between the response time and PSF. The relations can be described by the fuzzy definition of PSF that can set up a linear fuzzy system equation and makes use of fuzzy linear regression to estimate the related fuzzy parameters. Furthermore, the possibilistic distribution function of the response time to the accidents of NPP operators can be obtained.

A linear system model whose parameters are defined by possibility distributions, not defined by probability functions, is called a possibilistic linear regression system model. Here, a possibility distribution is represented by a fuzzy number that has a membership function to surround its central value.

A possibilistic linear system can describe the system model that is influenced by many complicated and uncertain factors [

The fuzzy output

Based on formula (

For the estimation of the parameters in the possibilistic linear fuzzy regression model, if there is a model for producing an upper set covering the fuzzy observed value, a lower set covered by the observed value, or a set intersected with the observed value, it could give estimates of the fuzzy parameters.

The given data are represented as

The possibilistic linear distribution can be described by fuzzy number

Our idea is to obtain the fuzzy parameters

The formulations derived from formula (

The objective that we do the research on fuzzy numbers is that fuzzy numbers can describe not only a sample point but also a relevant range. The method can be used in reliability cognitive model of NPP operators. The individual NPP operator cognitive model is relevant to the related fuzzy number.

The mutual relations given by formula (

The concepts of three problems.

Min problem is

Subject to formula (

Among the mutual relations of the Min, Max, and Conjunction problems, the Min problem has the widest contents.

For instance, if there is an upper fuzzy set

Among three kinds of fuzzy number problems, Min problem method can be selected to do application in NPP operator reliability cognitive research. The reliability cognitive model of NPP operator can be described by using the widest range fuzzy number.

The cognitive response time of NPP operator can be affected by varied PSF such as psychology, stress, procedure, cognitive complexity, and environments. The response time can be described by mathematics equations. The possibilistic linear regression model supplies PSF quantitative method to the complicated problem such as NPP operator accident response time.

Based on the data of the experimental accident response time of Chinese NPP operators, it is assumed that the response times can be represented by the fuzzy numbers which have symmetrical possibility distributions around the observed values. That is, each observed value becomes a center point having the possibility of 1, and the possibility distribution is symmetrically spread from the center point based on

Symmetrical fuzzy number.

In this paper, we only use one accident: the loss of coolant accident (LOCA) as the research example so as to decrease the data volume. The response time of the LOCA accident on the Chinese NPP operators can be studied through the possibilistic linear fuzzy regression model. Table

LOCA accident experimental result and the Chinese NPP operators data.

Crew | Group | Age (year) | Experience inside/outside a control room (year) | Education (year) | LOCA accident response time (sec) |
---|---|---|---|---|---|

1 | 1 | 25 | 0/4 | 14 | 10 |

2 | 1 | 24.84 | 0/3 | 15 | 26 |

3 | 1 | 27 | 0/6 | 15 | 18 |

4 | 2 | 27.5 | 0/4 | 17 | 48 |

5 | 2 | 25 | 0/4 | 14 | 14 |

6 | 2 | 25.42 | 0/3 | 16 | 82 |

7 | 3 | 24.33 | 0/3 | 15 | 129 |

8 | 3 | 25 | 0/3 | 16 | 82 |

9 | 3 | 23.67 | 0/4 | 14 | 47 |

10 | 4 | 25.33 | 0/4 | 14 | 33 |

11 | 4 | 25 | 0/3 | 15 | 19 |

12 | 4 | 24.67 | 0/3 | 15 | 26 |

13 | 5 | 23.5 | 0/2 | 14 | 88 |

14 | 5 | 25 | 0/3 | 14 | 10 |

15 | 5 | 24.17 | 0/2 | 15 | 50 |

16 | 6 | 23.5 | 0/2 | 14 | 42 |

17 | 6 | 25.25 | 0/3 | 15 | 60 |

18 | 6 | 25.67 | 0/3 | 15 | 60 |

19 | 7 | 30 | 0/10 | 15 | 49 |

20 | 7 | 23.5 | 0/2 | 15 | 126 |

21 | 7 | 28.25 | 0/7 | 15 | 19 |

22 | 8 | 25.33 | 0/2 | 15 | 76 |

23 | 8 | 25 | 0/5 | 14 | 41 |

24 | 8 | 26.33 | 0/3 | 15 | 59 |

In Table

The related data represented by fuzzy numbers of LOCA accident of 24 Chinese NPP operators in 8 groups are shown in Table

Fuzzy parameters of LOCA accident of Chinese NPP operators.

Response time (sec) | Age (year) | Experience inside/outside a control room (year) | Education (year) |
---|---|---|---|

25.6 | 0/4.33 | 14.67 | |

26.0 | 0/3.67 | 15.67 | |

24.3 | 0/3.33 | 15.0 | |

25.0 | 0/3.33 | 14.67 | |

24.2 | 0/2.33 | 14.33 | |

24.8 | 0/2.67 | 14.67 | |

27.3 | 0/6.33 | 15.0 | |

25.6 | 0/3.33 | 14.67 |

In Table

Since all the 24 of the crew have no experience inside control room, thus the relevant factor can be omitted. The possibilistic linear model for the response time

When using the Min problem, referring to formulas (

Through Table

Thus, the possibilistic linear regression model for the response time

Based on formula (

In order to verify the fitting result of the model, the experimental data of the response time of NPP operators can be used for estimation. Using formula (

Figure

Fuzzy estimates versus data bound.

We also can determine if the failure probability plots of the fuzzy estimated upper and lower values were close to the failure probability based on experimental data in Table

Failure probability curves.

Figure

Comparison of the differences between upper and lower limits.

The possibilistic linear fuzzy regression model supplies the research method arriving at target rapidly under the small samples. This will do good to the research of the reliability of Chinese NPP operators.

Doing research on operator failure probabilities based on the fuzzy regression model in HRA can provide a well-fitted relationship between PSF (e.g., age, experience outside a control room, and education) and operator response time. Although because of different experiment conditions we can obtain different results, it is believed that the fuzzy regression model can play an important role, providing analysts with approximated failure probabilities. Therefore, the research method of fuzzy mathematics is a very useful tool to study NPP operator cognitive model.

The paper for the first time utilizes possibilistic linear fuzzy regression model to do the theory analysis and the quantitative calculation under small samples on the accident response time of Chinese NPP operators. The results are satisfied. The research method not only has important significance to the further research on Chinese NPP operators but also supplies good reference for the applications in other areas in the future.