Answer:
(a) The utilization rate = 50%
(b) The average down time = 2 hours
(c) Average number of machines waiting = 0.5 Machines
(d) Pn>1 = 0.25
Explanation:
Given that:
Arrival Rate= λ = 4 per day
Service Rate = μ = 8 hour per day
Now,
a)
The utilization rate of this service system is given as;
The utilization rate = λ / μ
= 4/8
= 0.5 = 50%
b)
The average downtime for a broken machine is calculated as;
The average down time = 1/( μ- λ)
= 1/(8-4)
= 1/4
= 0.25 days
It is given that work day = 8 hours
Therefore, 0.25*8 = 2 hours
c)
Average number of machines waiting to be serviced at any given time is calculated as;
Average number of machines waiting = λ²/(μ*(μ-λ))
= 4²/(8*(8-4))
= 16/32
= 0.5 Machines
d) The probability that more than 1 machine is in the system is calculated as;
Pn>k = (λ/μ)^k+1
where k number of machine = 1 machine
Pn>1 = (4/8)¹⁺¹
=(4/8)²
= 0.5²
= 0.25
