A product is made up of two subsystems in series. The first subsystem consists of 20 components in series. The second subsystem consists of 3 components in parallel. The components in subsystem 1 are all of the same design and each has a 1/10,000 chance of failure. The parallel components each has a 3/10,000 chance for failure. What is the overall reliability of the system?

Solution Number of samples 5 Sample size 5 Data Results Mean Range Xbar Sample 1 5.906 0.8 x-bar value 5.9904 Sample 2 6.074 0.65 Sample 3 6.03 0.35 R bar Sample 4 5.942 0.47 Sample 5 6 0.65 Upper control limit 6.327368 Average 5.9904 0.584 Center line 5.9904 Lower control limit 5.653432 Table Sample size, n 2 1.88 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 A quality control engineer monitors the quality of a cylinder production line. He regselects a sample of 5 units and measures the diameters. The specification requires thediameter to be 6 inches plus/minus 0.1 inch. The following is a record of his measuremthe production process in control?