<p> plot(data,char,size,clr) </p>

8f4a32a2-9e1c-4d2c-a631-6e699dbfd493 29 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

T 20307180116246311379384421458495497499141 mat :

length _T n 14 :

'N' number of units under test over 'T' N 130 :

log vraisemblance
log likelyhood α β x L n α β * ln * β 1 - (T i el ln i 1 n sum * + (α T i el β^i 1 n sum * - :

partial derivatives and
1rst order conditions. α β x L α diff n α / T i el (β^i 1 n sum - ≡ (0 ≡ α β x L β diff n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - ≡ (0 ≡ 21 sys

system n α / T i el (β^i 1 n sum - 0 ≡ n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - 0 ≡ 21 mat :

init α 40 ≡ β 0.9 - ≡ 21 mat :

α β sol system init FindRoot :

α β 21 mat α β sol : 55.4246 0.8558 - 21 mat

sanity n α / T i el (β^i 1 n sum - n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - 21 mat : 0.000000001 0.000000192 21 mat

55.4246 0.8558 - 21 mat

The life cycle analysis starts with n=130 units under test for time_test=499 days. Use a Weibull probability destiny distribution function.

Weibull  log likely
probability PDF x β W β 1 el β 2 el * x β 2 el 1 - (^β 1 el x β 2 el^* - exp * (* :

β 55.4246 0.8558 - 21 mat :

i 1 T rows range Y i el N T i el β W (* eval : for XY T Y - augment : 21 line

data XY o 5 black plot :

Rate of survivals of all units under test over the observation period T The other way around: at ~ 400 days, almost no more units will fail ...

data N x β W ( * abs 2 1 sys

day 'T' T 400 :

@ 400 days, 0.0658 % 
of units have survived N T β W abs * 0.0658