The following schematic diagram describes and depicts the process of a production method used in the manufacture of aluminum cans. Fill F A В D Cup Wash G Н E Depalletize Fill Print In a process known as “cupping" coiled aluminum sheets are uncoiled and shaped into can podies. These can bodies are then washed and sent to the printer, which prints the label on he 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. Some fill lines can accept cans directly from he 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 fill lines; the diagram presents a case where there are two fill lines, one of which requires depalletization. In he filling process the cans are filled, and the can top is sealed 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 failing. 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, and P[H] = 0.98. Assume the components function independently Find the probability that the process functions successfully for one dav

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The following schematic diagram describes and depicts the process of a production method
used in the manufacture of aluminum cans.
Fill
C
F
A
B
D
Cup
Wash
G
Н
E
Depalletize
Fill
Print
In a process known as "cupping" coiled aluminum sheets are uncoiled and shaped into can
bodies. 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. Some fill 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 fill lines; the
diagram presents a case where there are two fill lines, one of which requires depalletization. In
the filling process the cans are filled, and the can top is sealed 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
failing. 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]
independently. Find the probability that the process functions successfully for one day.
0.90, P G = 0.90, and P |H = 0.98. Assume the components function
Transcribed Image Text:The following schematic diagram describes and depicts the process of a production method used in the manufacture of aluminum cans. Fill C F A B D Cup Wash G Н E Depalletize Fill Print In a process known as "cupping" coiled aluminum sheets are uncoiled and shaped into can bodies. 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. Some fill 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 fill lines; the diagram presents a case where there are two fill lines, one of which requires depalletization. In the filling process the cans are filled, and the can top is sealed 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 failing. 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] independently. Find the probability that the process functions successfully for one day. 0.90, P G = 0.90, and P |H = 0.98. Assume the components function
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