🚀 go-pugleaf

The data :

-          A temporal serie : (x1, x2, ., xn)

-          Time between two observations : delta

-          specification : X < b

How i can change delta to be able to react enough early to not have a point
out of the specification?

Intuitively, if I increase the frequency , i can react more quickly.

But.

Formelly

Hypothesis : random observations

The variable X has a mean m and a standard deviation sigma.

Notations :

X =  variable

delta = time between two consecutive observations

lambda = failure parameter

L = lenght before OS (Out of Specification)

The expectation of L is:  1/p where p=P(X>b).

For simplicity, I suppose that the only failure is a shift of the mean where
the mean pass from m0 to m1 = m + lambda* sigma.

The average time before an OS if no failure (lambda = 0) is : Delta * E0(L).

For a failure lambda, the average time before an OS is: Delta * E(L;lambda).

If the frequency change from Delta to Delta1 = c* Delta, the average time
before an OS is :Delta1* E(L;lambda) = c *Delta* E(L;lambda).

If the variable has a large deviation, or is too close of the specification,
the average time before an OS is little.  So, intuitively, I increase the
frequency of the observations.  But the observations are independent, so the
average length before an OS is constant and the average time before an OS
decreases !

Where is the bug ?