23. A quality control engineer is considering the optimal design of an X chart. Based on his experience with the production process, there is a probability of .03 that the process shifts from an in-control to an out-of-control state in any period. When the process shifts out of control, it can be attributed to a single assignable cause; the magnitude of the shift is 2ơ. Samples of n items are made hourly, and each sampling costs $0.50 per unit. The cost of searching for the assignable cause is $25, and the cost of operating the process in an out-of-control state is $300 per hour. a. Determine the hourly cost of operating the system when n = 6 and k = 2.5. b. Estimate the optimal value of k for the case n = 6. If you are doing the calcu- lations by hand, use k = 0.5, 1, 1.5, 2, 2.5, and 3.0. If you are using a computer, use k = 0.1, 0.2, . , 2.9, 3.0. c. Determine the optimal control chart design that minimizes average annual .... costs.

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23. A quality control engineer is considering the optimal design of an X chart. Based
on his experience with the production process, there is a probability of .03 that
the process shifts from an in-control to an out-of-control state in any period.
When the process shifts out of control, it can be attributed to a single assignable
cause; the magnitude of the shift is 2ơ. Samples of n items are made hourly,
and each sampling costs $0.50 per unit. The cost of searching for the assignable
cause is $25, and the cost of operating the process in an out-of-control state is
$300 per hour.
a. Determine the hourly cost of operating the system when n = 6 and k = 2.5.
b. Estimate the optimal value of k for the case n = 6. If you are doing the calcu-
lations by hand, use k = 0.5, 1, 1.5, 2, 2.5, and 3.0. If you are using a computer,
use k = 0.1, 0.2, . , 2.9, 3.0.
c. Determine the optimal control chart design that minimizes average annual
....
costs.
Transcribed Image Text:23. A quality control engineer is considering the optimal design of an X chart. Based on his experience with the production process, there is a probability of .03 that the process shifts from an in-control to an out-of-control state in any period. When the process shifts out of control, it can be attributed to a single assignable cause; the magnitude of the shift is 2ơ. Samples of n items are made hourly, and each sampling costs $0.50 per unit. The cost of searching for the assignable cause is $25, and the cost of operating the process in an out-of-control state is $300 per hour. a. Determine the hourly cost of operating the system when n = 6 and k = 2.5. b. Estimate the optimal value of k for the case n = 6. If you are doing the calcu- lations by hand, use k = 0.5, 1, 1.5, 2, 2.5, and 3.0. If you are using a computer, use k = 0.1, 0.2, . , 2.9, 3.0. c. Determine the optimal control chart design that minimizes average annual .... costs.
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