Question

The following schematic diagram, slightly simplified, depicts the process used in the manufacture of aluminum cans Fill Cup Wash Print Depalletize Fill The initial input into the process consists of coiled aluminum sheets, approximately 0.25mm thick. In a process known as cupping," these sheets are uncoiled and shaped into can bodies, which are cylinders that are closed on the bottom and open on top These can bodies are then washed and sent to the printer, which prints the label on the can. In practice there are several printers on a line; the diagram presents a line with three printers The printer deposits the cans onto pallets, which are wooden structures that hold 7140 cans each. The cans next go to be filled Somel lines can accept cans directly from the pallets, but others can accept them only from cell bins, which are large containers holding approximately 100,000 cans each. To use these fill lines the cans must be transported from the pallets to cell bins, in a process called depalletizing. In practice there are several ill lines, the diagram presents a case where there are two fill lines, one of which will accept cans from the pallets, and the other of which will not. In the filling process the cans are filled, and the can top is seamed on. The cans are then packaged and shipped to distributors It is desired to estimate the probability that the process will function for one day without tailing. Assume that the cupping process has probability 0.995 of functioning successfully for one day. Since this component is denoted by "A" in the diagram, we will express this probability as P(A) - 0.995. Assume that the other process components have the following probabilities of functioning successfully during a one-day period: P(B)- 0.99, P(C)- P(D)P(E) 0.95, P(F)0.90, P(G) 0.90, P(H)0.98 Assume the components function independently. Find the probability that the process functions successfully for one day Hint: We can solve this problem by noting that the entire process can be broken down into subsystems, each of which consists of simple series or parallel component systems

Answer 1