#mang #reliability 

if a tyre bursts on an aircraft landing gear, the remaining tyres now have to handle the extra load
this has Implications because failure is a function of load
who up chaining they reactions

# load sharing systems
$n$ thingymajigs sharing a load
no longer statistically independant
the system has failed when there is nothing left
$L$ is the load per component
$F(L)$ is the failure distribution as a function of load
$G_n(L)$ is the probability of the whole system of $n$ components failing

## 2 components
can fail when number 1 fails under load $L$ and then number 2 fails under load $2L$
can also happen when the things are swapped around
$$G_2(l) = 2F(L)F(2L) - F(L)^2$$

## 3 components
all fail under $L$, $F(L)^3$

2 components fail under $L$ and the last under $3L$ = $F(L)^2 + F(3L)$
this can happen in 3 different ways

1 fails under $L$ and the other fail between $L$ and $\frac32L$

1 fails under $L$, the other under $\frac32L$ and the last under $3L$
![[Pasted image 20251030162045.png]]

# n components
![[Pasted image 20251030162116.png]]
after $r$ failures there is a load of $\frac{nL}{n-r}$