Problem # 2 A manufacturing company is modernizing its operations for which it i

Question

Problem # 2 A manufacturing company is modernizing its operations for which it is planning to upgrade a man operation with a robotic cell that will work around the clock. The following information is given for the new robotic cell: Time required for the robot to complete an assembly is always exactly 100 minutes. Expected mean time between failures is 500 minutes. Expected mean time between repairs is on average 5 minutes with a standard deviation of 3 minutes. The CV of job inter-arrival times into the system is 1. Average throughput is 10 parts per day. The robot operates 24 hours a day. . . Provide values for the following parameters (assume that the robotic cell is a G/G/1 system): 1) Availability (A) of the robot 2) C 3) ?

Explanation / Answer

First, try o write what all are given -

t0 = natural processing time = 100 min
C0 = CV of natural processing time = 0
mf = mean time to failure = 500 min
mr = mean time to repair = 5 min
Sr = SD of repair time = 3 min
Ca = CV of interarrival times = 1
TH = average throughput = 10 per day = 10/(24*60) = 0.00694 per minute

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(1)

Availability (A) = mf / (mf + mr) = 500 / (500+5) = 0.99

(2)

Cr = CV of repair time = Sr / mr = 3/5 = 0.60

(3)

Ce2 = Co2 + (1+Cr2)A(1 - A)(mr / t0) = 0 + (1+0.6^2)*0.99*(1 - 0.99)*(5/100) = 0.000673

(4)

te = t0 / A = 100 / 0.99 = 101.01 min
ta = average interarrval time = 1/TH = 144 min

Utilization (u) = te / ta= 101.01/144 = 0.7015

(5)

CTq = {(Ca2 + Ce2)/2} x {u.te / (1 - u)} = ((1+0.000673)/2)*(0.7015*101.01/(1 - 0.7015)) = 118.8 minutes

(6)

CT = CTq + te = 118.8 + 101.01 = 219.81 minutes

(7)

WIPq = CTq x TH = 118.8 x 0.00694 = 0.825

(8)

WIP = CT x TH = 219.81 x 0.00694 = 1.53

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