A process is controlled with a fraction nonconforming control chart with three-sigma limits, n = 100, UCL = 0.161, center line =
0.080, and LCL = 0.
a. Find the equivalent control chart for the number nonconforming.
b. Use the Poisson approximation to the binomial to find the probability of a type I error.
c. Use the normal approximation to binomial to find the probability of a type II error if the process fraction nonconforming shifts to 0.2.
d. What is the probability of detecting the shift in part (c) by at most the fourth sample after the shift?
a. Find the equivalent control chart for the number nonconforming.
b. Use the Poisson approximation to the binomial to find the probability of a type I error.
c. Use the normal approximation to binomial to find the probability of a type II error if the process fraction nonconforming shifts to 0.2.
d. What is the probability of detecting the shift in part (c) by at most the fourth sample after the shift?
1 answer:
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This question is far easier to understand if we draw it out. I've included an image attachment to help show the relationships of the measurements. As we can see from the image, their positioning helps form a triangle that we can use the Pythagorean Theorem to find the connection range.
The Theorem is
where a and b are the legs and c is the hypotenuse.
So the answer to the nearest meter is 55 meters.
The Theorem is
So the answer to the nearest meter is 55 meters.