Formula to detect non uniformity noise I have this line profile, how is the best way to detect this kind of non uniformity?

I must detect a sudden change, as opposed to the last section that decreases slowly..
But the sudden difference might be smaller than in this example so I need a threshold and the overall noise across the line might be a little bit higher difficulting the find..
P.S.: it seems this graph is non linear on the left, don't mind that issue, assume that it is more the less constant all the way until 12335K
 A: Let $X_t$ denote your $t$ sample and let $Y_t := X_t - X_{t-1}$. If you have a segment of data without these non-uniformities, e.g. $\{0,1,2,...,T\}$, consider the empirical distribution of $Y_t, 1\leq t \leq T$; You have a list of numbers that represent typical changes in $X_t$. This is the empirical distribution for $Y_t$ (true is $Y_t \perp Y_s, s \neq t$ which is probably false but still useful even without that assumption). Denote this distribution $D$. For a new sample $X_p$, take the null hypothesis $H_0: X_p - X_{p-1} \sim D$ and $H_1: X_p - X_{p-1} \not \sim D$. Choose a threshold $\alpha$ (e.g. $\alpha = 10^{-2}$ or $\alpha = 10^{-3}$). Now you reject the null $H_0$ if ($|A|$ is the size of the set $A$):
$$
\frac{  |\{1 \leq t \leq T| X_p - X_{p-1} > Y_t \}| }{T} > 1-\alpha.
$$
Rejecting the null $H_0$ means the observed difference $X_p - X_{p-1}$ size is significant, so you say there is a jump (nonuniformity) at the significance level $\alpha$. This is a fairly standard hypothesis testing approach to solve your problem, only thing is it uses your data to construct the null, as opposed to (e.g.) normal or student-T distributions. As long as you understand the basics mechanics of hypothesis testing, you can modify above procedure as you please (e.g. use absolute values to detect non-uniformities in both directions).
A: After adjusting for pulses ...and your pattern suggests many pulses. the next step might be to ignore pulses and to test for variance change ( which is visually obvious) . I have implemented and tested Tsay's procedures into AUTOBOX a piece of software that I have helped to develop. If you wish to try and do it yourself pursue https://pdfs.semanticscholar.org/09c4/ba8dd3cc88289caf18d71e8985bdd11ad21c.pdf
