What is problem reliability design?
Say we are to design 3 stage systems with devices D1, D2, and D3 and costs of $30, $15, and $20, respectively. The cost of this system is to be no more than $105. The reliability of each device type is 0.9, 0.8, and 0.5.
| Cost | Reliability | Max number of devices | |
|---|---|---|---|
| D1 | 30 | 0.9 | 2 |
| D2 | 15 | 0.8 | 3 |
| D3 | 20 | 0.5 | 3 |
Total cost used=Avalialbe amount=
- Maximum number of additional D1 devices we can purchage=
- Maximum number of additional D2 devices we can purchage=
- Maximum number of additional D3 devices we can purchage=
Let S0={(1,0)}
Malfunction of D1 device = 1-0.9=0.1
Relialbillity of two D1 devices = 1- 0.1 * 0.1=0.99
S21= { (0.99,60)}
S1={ (0.9,30), (0.99,60)}
Relialbillity of two D2 devices=1-(1-0.8)2=0.96
S22={(0.864,60)}
The tuple (0.9504,90) is eliminated because we cannot purchase a D3 device with the remaining amount of $15. Reliability of three D2 devices=1-(1-0.8)3=0.992
S32= {(0.8928,75)}
The tuple (0.792,75) is eliminated as the tuple (0.864,60) dominates (0.792,75).
S2={(0.72,45), ((0.864,60), (0.8928,75)}
Reliability of two D3 devices = 1-(1-0.5)2 =0.75 S32={(0.54,85),(0.648,100)}
Rliability of three D3 devices = 1-(1-0.5)3 =0.875 S33={(0.63,105)}
The tuple (0.63,105) is dominated by (0.648,100) and the tuple (0.4464,95) is dominated by (0.54,85)
S3={(0.36,65), (0.432,80),( 0.54,85),(0.648,100)}}
Tracing back through Si’s, we can determine that 1 D1 device, 2 D2 devices, and 2 D3 devices give the highest reliability.
