profust_reliability

Compute the profust reliability according to the research in [1].

Syntax

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profust_reliability(s, msf)

Description

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R = profust_reliability(s, msf)

Compute the profust reliability according to the research in [1].

s is an array of system state vectors if msf is not None. Otherwise, s is an array of the degree of membership of system states, and the msf specifies the membership function.

Suppose that the system is in a specific state $S_q$$S_q$ at time $t_0$$t_0$ for certain, and the system is in a specific state $S_j$$S_j$ at time $t$$t$ for certain.

Then the profust reliability is

More details and the proof are available in [1].

Examples

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>>> from OpenHA.assessment.attribute import profust_reliability, trapezoidal_membership_func
>>> import numpy as np
>>> import pandas as pd
# TODO: the way to load dataset
>>> x = pd.read_csv(r'E:\OpenHA_\test\examples\data_zzy.csv', header=None)
# select the data of the last column
# the height of a multicopter
>>> x = x[3]
# parameters for the trapezoidal membership function
>>> a = 9.8
>>> c = 9.95
>>> d = 10.05
>>> b = 10.2
# construct the membership function
>>> f = lambda x: trapezoidal_membership_func((a, b, c, d), x)
# call the function
>>> y = profust_reliability(x, f)

Input Arguments

s —— An array of system state vectors if msf is not None. Otherwise, its an array of the degree of membership of system states.

f —— The membership function, specified as a callble object, or just None.

The membership function represents the degree of membership between an element and a set. In fuzzy mathematics, the degree of membership is in $[0,1]$$[0,1]$.

Properties of Arguments

References

[1] Z. Zhao, Q. Quan, K.-Y. Cai, "A modified profust-performance-reliability algorithm and its application to dynamic systems," Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 643-660, 2017. DOI: 10.3233/JIFS-152544.