What is the UCL using 3-sigma?(round your response to two decimal places).
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- A quality control manager in an Omani bottling company takes 5 samples for quality control purposes. These sample mean (X- bar) are; 8.51, 8.18, 11.07, 10.03, and 10.23 respectively. Additionally, the range values for these 5 samples are; 3.33, 2.61, 3.39, 4.39, and 6.49. If the lower control limit for X- bar chart is 7.664, what should be the most appropriate sample size? O a. 3 O b. None is correct O C. 4 O d. 6 O e. 5Suppose a manufacturing process produces small metal rods. The desired length of these rods is 50 cm. Quality control personnel take samples of 5 rods every hour and measure their lengths. After 8 hours, they have the following data for the average lengths (in cm) of the 8 samples: Hour (h): 1, 2, 3, 4, 5, 6, 7, 8Average Length (X-bar): 49.8, 50.2, 50.1, 49.9, 50.3, 50.1, 49.7, 50.0 Additionally, the standard deviation (s) for each sample is provided: Hour (h): 1, 2, 3, 4, 5, 6, 7, 8Standard Deviation (s): 0.1, 0.12, 0.11, 0.1, 0.12, 0.11, 0.09, 0.1 Based on the given data, is the process under control?BlueMoon Bottlers has a bottle-filling process with a mean value of 64 ounces and a standard deviation of 8 ounces. Suppose the upper and lower specification limits are 71 and 57 ounces, respectively. What is the process capability index of this process? (Note: You MUST show every single step and detailed derivation for full credit)
- A component part for a motorcycle is manufactured by an investment casting process. The air vent opening on this casting is an important functional parameter of the part. The results for five samples are given in the table. The values given have been coded using the last two digits of the dimension Sample Air vent opening diameter (in mm 1 58 61 54 60 2 61 55 58 62 3 66 60 59 55 4 53 57 58 64 5 65 63 79 61 Determine the central line and control limits for the range and mean charts, and discuss whether or not the process is in statistical control.c) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505cm and standard deviation 0.008cm.Specifications call for the diameter to be in the interval 2.5 ‡ 0.01 cm. estimate the proportion of the ball bearings will meet the specification?Using samples of 200 credit card statements, an auditor found the following:Sample 1 2 3 4Number with errors 4 2 5 9a. Determine the fraction defective in each sample.b. If the true fraction defective for this process is unknown, what is your estimate of it?c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size?d. What control limits would give an alpha risk of .03 for this process?e. What alpha risk would control limits of .047 and .003 provide?f. Using control limits of .047 and .003, is the process in control?g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What arethe values of the mean and standard deviation of the sampling distribution?h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using twosigma control limits. Is the process in control?
- At Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its lengthis between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49inches and a standard deviation of 0.014 inches. A) Is the process capable of meeting specifications? B) Does the process meet specifications?Aspen Plastic produce 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 (in Inches) from the last six sampes are Bottle Sample 1 2 3 4 1 0.594 0.622 0.598 0.590 2 0.587 0.611 0.597 0.613 3 0.571 0.580 0.595 0.602 4 0.610 0.615 0.585 0.578 5 0.580 0.624 0.618 0.614 6 0.585 0.593 0.607 0.569 Assume only these six samples are sufficient, and use the data to determine control limits for an R- and an X-chartIn a fabric manufacturing factory, the quality control process using control charts from SPC. In an hour there are a total of 5 samples are taken each having 5 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.51 . 208.24, 112.44 and 123.30 respectively. In the same sample, the corresponding ranges are: 13.1713.3815.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the R chart?
- The Big Black Bird Company produces fiberglass camper tops. The process for producing the tops must be controlled so as to keep the number of dimples low. When the process was in control, the defects shown to the right were found in 10 randomly selected camper tops over an extended period of time. Top Dimples 1 7 2 8 3 12 4 9 5 4 6 14 7 7 8 3 9 6 10 8 a. Assuming 10 observations are adequate for this purpose, determine the three-sigma control limits for dimples per camper top. The UCLc equals nothing and theLCLc equals nothing. (Enter your responses rounded to two decimal places. If your answer for LCLc is negative, enter this value as 0.) b. Suppose that the next camper top has 16 dimples. What can you say about the process now? A. The number of defects is greater than the upper control limit, so it is assumed that the process is in…The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13. SAMPLE NUMBER OBSERVATIONS 1 2 3 4 5 1 0.486 0.499 0.493 0.511 0.481 2 0.499 0.506 0.516 0.494 0.529 3 0.496 0.500 0.515 0.488 0.521 4 0.495 0.506 0.483 0.487 0.489 5 0.472 0.502 0.526 0.469 0.481 6 0.473 0.495 0.507 0.493 0.506 7 0.495 0.512 0.490 0.471 0.504 8 0.525 0.501 0.498 0.474 0.485 9 0.497 0.501 0.517 0.506 0.516 10 0.495 0.505 0.516 0.511 0.497 11 0.495 0.482 0.468 0.492 0.492 12 0.483 0.459 0.526 0.506 0.522 13 0.521 0.512 0.493 0.525 0.510 14 0.487 0.521 0.507 0.501 0.500 15 0.493 0.516 0.499 0.511 0.513 16 0.473 0.506 0.479 0.480 0.523 17 0.477 0.485 0.513 0.484 0.496 18 0.515 0.493 0.493 0.485 0.475 19 0.511 0.536 0.486 0.497 0.491 20 0.509 0.490 0.470 0.504 0.512 Calculate the mean and range for the above samples.…At Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its length is between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49 inches and a standard deviation of 0.014 inches. a) is the process capable of meeting specifications? b) Does the process meet specifications?