27. Magnaplex, Inc. has a complex manufacturing process, with three operations t

Question

27. Magnaplex, Inc. has a complex manufacturing process, with three operations that are performed in series. Because of the nature of the process machines frequently fall out of adjustment and must be repaired. To keep the system going, t identical machines are used at each stage; thus, if one fails, the other can be used while the first repaired (see accompanying figure) Production System The reliabilities of the machines are as follows: Reliability 0.85 0.92 0.90 Machine a. Analyze the system reliability, assuming only one machine at each stage (all the backup machines are out of operation) b. How much is the relíability improved by having two machines at each stage?

Explanation / Answer

System relibaility = 0.85*0.92*0.90 = 0.7038

b)When backup is there, Combined reliabilty for stage A = 1- P( Both fail) = 1- (1-0.85)^2 = 0.9775

Stage B = 1- (1-0.92)^2 =0.9936

Stage C =  1- (1-0.90)^2 = 0.99

System reliabilty = 0.9775*0.9936*0.99 =0.96153

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