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QUESTION 1 Ali measured the velocity of light in air using a modification of a method proposed by his company. With a sample size ($n$ equal to 6) control charts for $\bar{X}$ and $S$ are maintained for an important quality characteristic. The result exhibited statistical controls with parameters are as follows Xchart S chart Upper Control Chart 708.20 3.420 Center Line 706.00 1.738 Lower Control Chart 703.80 0.052 a) Estimate the mean and standard deviation of the process. (3 marks) b) Estimate the natural tolerance limits for the process. (3 marks) c) Assume that the process output is well modeled by a normal distribution. If specifications (are 703 and 709,) estimate the fraction nonconforming. (5 marks) d) Suppose the process means shifts to 702.00, what is the probability of an out-of-control signal occurring on the first sample following the shift? (6 marks) e) For the shift in part (c), calculate the average run length? What can you conclude about ARL₁? (3 marks)

Name: question 1 ali measured the velocity of light in air using a modification of a method proposed by his company with a sample size n equal to 6 control charts for barx and s are maintained for 11488
Uploaded: 2023-09-16T12:42:04-08:00
Duration: 2 min 28 s
Channel: Adi S
Description: question 1 ali measured the velocity of light in air using a modification of a method proposed by his company with a sample size n equal to 6 control charts for barx and s are maintained for 11488

          QUESTION 1
Ali measured the velocity of light in air using a modification of a method proposed by his
company. With a sample size ($n$ equal to 6) control charts for $\bar{X}$ and $S$ are maintained for an
important quality characteristic. The result exhibited statistical controls with parameters are as
follows

Xchart S chart
Upper Control Chart 708.20 3.420
Center Line 706.00 1.738
Lower Control Chart 703.80 0.052

a) Estimate the mean and standard deviation of the process.
(3 marks)
b) Estimate the natural tolerance limits for the process.
(3 marks)
c) Assume that the process output is well modeled by a normal distribution. If specifications
(are 703 and 709,) estimate the fraction nonconforming.
(5 marks)
d) Suppose the process means shifts to 702.00, what is the probability of an out-of-control
signal occurring on the first sample following the shift?
(6 marks)
e) For the shift in part (c), calculate the average run length? What can you conclude about
ARL₁?
(3 marks)

question 1 ali measured the velocity of light in air using a modification of a method proposed by his company with a sample size n equal to 6 control charts for barx and s are maintained for 11488

Added by Kristen T.

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