Question

Consider a simple two-stage assembly line that has two identical robot arms (one for each stage). The system is functioning if a part can receive processing (i.e. the robot arm is working) in both stages of an assembly line. Your supervisor knows that a pure series system is not the most reliable and has authorized the purchase of two additional arms to be used to add redundancy to the system. However, she is unsure of the best way to set up the additional components to maximize system reliability. There are two options being considered:

Assume the individual component reliability for all 4 arms is R.

1. Put an additional arm in each stage so that the arms in a single stage operate in parallel.

2. Set up an additional two-stage assembly line that will operate in parallel with the original line.

(a) What is the system reliability of the first option in terms of R?

(b) What is the system reliability of the second option in terms of R?

(c) On the same graph, plot the system reliabilities of both options when R = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.

(d) Based on your graph, what recommendations can you make to your supervisor about how to add redundant components to a system under different values of R?

Answer 1

c) Graph

d) Table for the both option is as follows:-

R	Option 1 (Reliability)	Option 2 (Reliability)
0	0	0
0.1	0.0361	0.0199
0.2	0.1296	0.0784
0.3	0.2601	0.1719
0.4	0.4096	0.2944
0.5	0.5625	0.4375
0.6	0.7056	0.5904
0.7	0.8281	0.7399
0.8	0.9216	0.8704
0.9	0.9801	0.9639
1	1	1

So from the System Reliability we can easily observe that Option 1 is more reliable than Option 2 so we can make recommendation to supervisor as "Put an additional arm in each stage so that the arms in a single stage operate in parallel" is more reliable option.