Question

(b) In a conventional production, operations of turning, splines cutting and grinding are followed in sequence to produce splined shaft for gear boxes and lathe, milling and grinding machines are used for the operations. The reliability of the lathe, milling machine and grinder are 0.89, 0.87 and 0.93 respectively. It has been suggested that to improve reliability two identical machines could be used at each stage. If one fails the other can be used while the first one is being repaired. Another suggestion has been put forward to buy a CNC machining center with a reliability of 0.90 which will do the functions of the lathe and the milling machine.

i) Calculate the system reliability for each of the 3 layouts and decide which is the most reliable. [4 Mark ]

Figure Q5(b): Splined shaft

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Answer 1

Symbols RL ( Reliability of lathe) = oi 89 RM ( Reliability of milling) = 0.87 Rac Reliability of griding) = 0.93 Case I lay out RL Rimf RG mru RC system reliability ) = RL Rm R, = 0.72 Case I Re RM Ru layo at RL Rm Ru

Ru Rm' Red Ri= 1-[(1-R() (1-Red symilarly Rń Ron and Rá R O, 9 879 = 0.98 31 Rá = 0,9951 R2= ^ R'm Ri Ra=0.9665 Case in lay out CNC Ru Renc-oigo Ran 0,93 R₂ = 0,837 R3 = 0,93x0,9 so system lay out of since R2 > R3>R, case II is best.