PSI - Issue 22

S.V. Belodedenko et al. / Procedia Structural Integrity 22 (2019) 51–58 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

53

3

as P EXP = exp (-a ). In operational safety strategies, first of all, high-risk elements are considered, for which the deterministic damage, as a rule, does not exceed 0.25. Then, with an error of not more than 5%, you can take P EXP = 1- а. It follows that a = Q . Taking into account the definition of the individual resource safety index (RSI) β Pik and (4) get the RSI for systems (Belodedenko & Bilichenko, 2015):

1



u

 

  



lg  

 

10 Pik ik 

P

. (5) Guided by the same considerations, we can find the rule for amalgamating the safety indexes for the reliability functions described by the Lindley law P LND = (1 + a) P EXP . Then they are represented in the form P LND = (1 + a) (1 - a) = 1 - a 2 . From this it follows that a 2 = Q . Then, analogously to (5), we obtain:

1



u

 

  



lg  

 

2 10 Pik ik 

PLND

. (6) The individual RSI β Pik of the systems element is the logarithm of the guaranteed margin of lifetime n TP for safety P . The safety index decreases linearly with the operating time t . When the RSI reaches zero value it indicates that the object is used with the unacceptable risk. 3. Comparative analysis of the amalgamation rules The comparison of the amalgamation rules is carried out by constructing the reliability function of the mechanical system. In Section 3, such a function is constructed in the relative operating time λt . To verify the effectiveness of the amalgamation for RSI to get the reliability function in real-time t . From the defining equation for RSI it can be seen that essentially the safety index is а lifetime distribution function (LDF) of the lognormal type. Thi s function is inversed to the reliability function P(t) (although P(lgt) is more correct), which makes it possible to compare the rules of amalgamating different reliability indicators. In this case, it is the PS and the RSI. On the basis of RSI approach, two possible algorithms for constructing a amalgamated reliability function arise. First, based on the rules for combining statistical samples in the form of LDF of individual elements of the lgT Pik , one can obtain the general LDF of the system lgT PΣ . To do this, after finding the mean value β 0Σ = lgT Σ , we need to find the general of the standard deviation (SD) S lgT . Parameters of the general LDF of the system for the considered example are given in the last bottom line of Table 1. Secondly, it is possible to get individual functions of lgT Pik , conditionally considering the start of operation moment lgt = 0 :   2 0 lg lg lg lg 1.15 ik ik Pik Pik ik T P T T T S U S      , (7) where U P is quantile of standard normal distribution (for PS> 0.5 , U P <0 ). Table 1. To constructing of the system reliability function based on the method of RSI.. ik n λ,[un.time ]-1 T 0 , [un.time] β 0 S lgTik u ik

1-3 4-6

3 3 4

0,1 0,2 0,3

10

0,946 0,217 0,645 0,217 0,464 0,217 0,563 0,295

1 1 1

5

7-10 Σ=1 -

3,3

10

2,1*

0,48*

-