hello please how I can create a matrix for 2 variables Tp and Na or I change each time the variable Tp and see the series of variable Na and finally see the minimum value of t

Modèle analytique Hassan

Description:

The system is working and may crash randomly. For a breakdown we pay a CMC cost and an average repair time MTTRc. Each Tp we check the number of alarms. If the number of alarms reaches a threshold na * I do an MP action of cost CMP and average duration MTTRp if not I do nothing. Each Xp ut a check is made on the finished product in order to decide whether to trigger an alarm or not.

Digital data:

CMC=3000

CMP=700

MTTRc=30

MTTRp=10

Xa= 5 ;

Ca: cost of intervention in the event of an alarm

Weibull-type degradation law (shape = 2, scale 100)

q = the number of alarms detected on the date Tp

The number of alarms that appear follows the binomial law of parameters p = 0.1 and N = int (Tp / Xa)

(int = whole part)

(N represents the total number of alarms that we can have over a period [0, Tp])

Analytical development:

Detail :

The probability of having an alarm on the date Tp

with N= int(Tp/Xa)

So :

Simplified final model

Resolution:

So it remains to work on Matlab to find the values (Tp *, na *) which minimize the total cost.

1-You can start by making a matrix where you vary Tp and na

na = [1,2, ………… ..int (Tp / Xa)]

Tp = [10, 20, 30 ………………………… .300]

2- you can look on Matlab for the command that gives you the minimum of a 2-variable function