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P-chart , X-bar control chart , R-chart

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4). A manufacturer has been sampling output from a process to help measure the number of defective items the process is producing. The quality manager has taken 20 samples of 20 items each, and has found a total of 10 defective items. Given this data, what would be the lower and upper control limits for a p-chart of this process if the limits are based on 2 standard deviations?
Answer: ________________________

5). A manufacturer of cylinder valves for GM has been sampling output from their process. So far, they have collected 30 samples of 10 valves each, and measured the length of each valve in the sample. The mean length of all 300 valves so far is 45.2 mm, and the mean range of measurements within each sample has been .52 mm. What would be the 3-sigma upper control limit for an X-bar control chart based on this sample data?
Answer: ________________________

6). A manufacturer of piston rings for Toyota has been sampling from their process. They have collected 15 samples of 20 rings each, and have been measuring the outside diameter of the ring. The overall mean diameter of the rings samples is 105.1 mm, and the mean range of measurements within the samples is .28 mm. What would the correct upper limit for an R-chart?

please see the attached file, please provide me with detailed and clear answer, if you can please do not use excel.

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4). A manufacturer has been sampling output from a process to help measure the number of defective items the process is producing. The quality manager has taken 20 samples of 20 items each, and has found a total of 10 defective items. Given this data, what would be the lower and upper control limits for a p-chart of this process if the limits are based on 2 standard deviations?
<br>Answer:
<br>Upper Control Limit=p + z *?Ð = 0.04062;
<br>Lower Control Limit=p - z *?Ð= 0.00938
<br>
<br>
<br>No of samples= 20
<br>No of items in each sample= 20
<br>Total no of items=n= 400 =20*20
<br>No of defectives= 10
<br>Therefore Proportion of ...

Solution Summary

Answers to questions on p-chart , X-bar control chart , R-chart. It calculates 3-sigma upper control limit an X-bar control chart , upper limit for an R-chart and lower and upper control limits for a p-chart

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4) The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 45 grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of 10 packets and weighs each packet. When the process is in control, the range in the weight of each sample has averaged 6 grams.

a. Design an R- and x-chart for this process.
b. The results from the last 5 samples of 10 packets are below. Is the process in control? Explain.

5) Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inches) from the last six samples are : (see attachment)

a. Assume that only these six samples are sufficient, and use the data to determine control limits for an R and an X chart

11) Jim's Outfitters, Inc. makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results: (see attachment)

a. Assuming that 10 observations are adequate for these purposes, determine the three-sigma control limits for defects per shirt.
b. Suppose that the next shirt has 13 flaws. What can you say about the process now?

11) Management at Webster, in Problem 16, is now concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected, and the following numbers of leaking tubes are found: (see attachment). Calculate p-chart three sigma control limits to assess whether the capping process is in statistical control.

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