Assume that there is a requirement for a new system with a specified performance
ID: 3229828 • Letter: A
Question
Assume that there is a requirement for a new system with a specified performance capacity and reliability of 70% in response to an invitation to bid", three supplier configuration have been proposed and are reflected in the figures marked "Configuration A" Configuration B" and "Configuration C". The Component reliability factors are noted in "Table 1" A. Determine the system reliably for configuration A B. Determine the system reliability for configuration B C. Determine the system reliability for configuration C The winning proposal would be producing and delivering 250 systems. Calculate what the bid price would be for D) Configuration A, E) Configuration B, F Configuration C Which configuration would you choose, why?Explanation / Answer
Part (A)
Let the top part of Configuration A be X and the bottom part be Y. Then, Configuration A works if
A works and at least one of X and Y works and F works or equivalently,
A works and neither X nor Y fails and F works and hence R = RA x {1 – (1- RX)(1 - RY)} x RF …. (1)
Now, X works if B works and at least one of D and E works and C works or equivalently,
B works and neither D nor E fails and C works and hence RX = RB x {1 – (1- RD)(1 – RE)} x RC
= 0.85 x (1 – 0.0221) x 0.93 = 0.7731………………………………………………………….. …. (2)
Y works if C works and at least one of F and B works and A works or equivalently,
C works and neither F nor B fails and A works and hence RY = RC x {1 – (1- RF)(1 – RB)} x RA
= 0.93 x (1 – 0.0225) x 0.89 = 0.8091………………………………………………………….. …. (3)
(1), (2) and (3) => R = 0.89 x {1 – (0.2269 x 0.1909)} x 0.85 = 0.7237
Thus, reliability of Configuration A = 0.7237 ANSWER
Part (B)
Similarly, reliability of Configuration B
= 0.89 x {1 – (0.15 x 0.07)} x {1 – (0.11 x 0.17 x 0.13 x 0.15)} x 0.83 x 0.84 = 0.6503
Thus, reliability of Configuration B = 0.6503 ANSWER
Part (C)
Following the steps of Part (A), reliability of Configuration B
= 0.89 x {1 – (0.2819 x 0.2323)} x 0.85 = 0.7089
Thus, reliability of Configuration C = 0.7089 ANSWER
Parts (D, E and F)
Configuration
Number of Components (Price in $’000)
Total
Price
A (28)
B(15.2)
C(20)
D(17.5)
E(19)
F(12)
A
2
2
2
1
1
2
184.9
B
3
1
1
2
1
1
185.5
C
1
2
1
4
1
1
179.4
Part (G)
To decide on the configuration to buy, a thumb rule could be price per reliability which is
$ 255.49 for A, $285.25 for B and $253.78 for C.
253.78 being the lowest, choice should be Configuration C ANSWER
Configuration
Number of Components (Price in $’000)
Total
Price
A (28)
B(15.2)
C(20)
D(17.5)
E(19)
F(12)
A
2
2
2
1
1
2
184.9
B
3
1
1
2
1
1
185.5
C
1
2
1
4
1
1
179.4