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Крючков Фундаменталс оф Нуцлеар Материалс Пхысицал Протецтион 2011
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T = Trf – T a < 0 |
(8.4) |
for the respective operational situation. Here, T is the guard force slack time; and Trf and Ta are the response force and attacker action times (from the alarm signal arrival time) respectively.
The probabilities of seizure are assessed by the expression |
|
P( T = Trf – T a < 0) = F(–x ), |
(8.5) |
where F(x) is the standard normal random quantity distribution function; and x is the mathematical expectation of the given response force slack time found from the expression:
х= |
M [Trf |
]− M [Тa |
] |
, |
(8.6) |
|
D[T |
|
]+ D[Т |
] |
|||
|
rf |
a |
|
|
|
where M[T] and D[T] are the mathematical expectation and the variance of the response force and attacker times respectively.
The attacker and response force time values are combined out of the components relating to different phases of their actions (PB defeat time for the attacker, and assembly time, movement time, perimeter length examination time and others for the response force). The mathematical expectations and variances of the attacker and response force action times are calculated based on the relation for the sum of independent random
I
quantities according to which, where T = ∑ti , we have:
i =1 |
|
I |
|
M[T] = ∑M [ti] , |
(8.7) |
i =1 |
|
I |
|
D[T] = ∑D[ti] , |
(8.8) |
i =1 |
|
where ti, i=1,...,I are separate random values; and M[ti] and D[ti] are mathematical expectations and variances of quantities ti.
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