6.18 samples of n=6 items each are taken at regular intervals. A quality characteristic is measured and x bar and r values are calculated for each sample. After 50 samples, we have sum of x bar=2000 and sum of R=200. Assume that the quality characteristic is normally distributed.
Added by Mandy S.
Step 1
To find the average of x̄, we use the formula: \[ \bar{x} = \frac{\text{Sum of } \bar{x}}{\text{Number of samples}} = \frac{2000}{50} = 40 \] Show more…
Show all steps
Close
Your feedback will help us improve your experience
Lien Le and 98 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
6.12. Samples of n=6 items each are taken from a process at regular intervals. A quality characteristic is measured, and x̄ and R values are calculated for each sample. After 50 samples, we have Σx̄ᵢ=2000 and ΣRᵢ=200. Assume that the quality characteristic is normally distributed. (a) Compute control limits for the x̄ and R control charts. (c) If the specification limits are 41 ± 5.0, what are your conclusions regarding the ability of the process to produce items within these specifications?
Lien L.
Q1): Samples of n=8 items each are taken from a manufacturing process at regular intervals. A certain quality characteristic is measured, and X and R values are calculated for each sample. After 50 samples, we have X = 2000 and R = 250 Assume that the quality characteristic is normally distributed. a) Compute control limits for the X and R control charts. b) Make suggestions as to how the process performance could be improved.
Suman K.
Samples of n = 6 items each are taken from a process at regular intervals. A quality characteristic is measured, and x̅ and R values are calculated for each sample. After 50 samples, we have ∑x̅i = 2000 and ∑Ri = 200. Assume that the quality characteristic is normally distributed. (a) Compute control limits for the x̅ and R control charts. (b) All points on both control charts fall between the control limits computed in part (a). What are the natural tolerance limits of the process? (c) If the specification limits are 41 ± 5.0, what are your conclusions regarding the ability of the process to produce items within these specifications? (d) Assuming that if an item exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit it must be scrapped, what percent scrap and rework is the process producing? (e) Make suggestions as to how the process performance could be improved.
Madhur L.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD