Question 1: A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm. What is the process capability index (Cpk) for the process?
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- 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)Do control charts assist in monitoring quality as conformance or quality as improvement?3.6. One of the stages in the process of making denim cloth at the Southern Mills Company is to spin cotton yarn onto spindles for subse- quent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some num- ber of breaks is considered normal; however, too many breaks might mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours: Number of Number of Sample Breaks Sample Breaks 1 3 11 3 2 12 4 3 4 13 4 1 14 7 5 15 8. 16 7 17 4 18 7. 8 19 8 9. 20 6. 10 Construct a c-chart using 3ơ limits for this process and indicate if the process was out of control at any time. ohoin when orders come into 3. 6
- 4. Problem 8.29 The number of imperfections in bond paper produced by a paper mill is observed over a period of several days. Table 8-28 shows the area inspected and the number of imperfections for 25 samples. Construct a control chart for the number of imperfections per square meter. Revise the limits, if necessary, assuming special causes for the out-of-control points. TABLE 8-28 Area Area Sample Inspected (m?) Imperfections Sample Inspected (m²) Imperfections 1 150 6 14 300 8 2 100 8 15 300 12 3 200 5 16 200 6 4 150 4 17 150 4 250 10 18 200 7 6. 100 11 19 150 14 7 150 20 100 4 8 200 5 21 100 8 9 300 10 22 200 10 250 10 23 300 12 11 100 24 250 7 12 200 4 25 200 5 13 250 12Quality Engineering question Why is decreasing variability so important during data collection and sampling? Please answer in your own words. Thank youAuto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? x= 156.76 mm (round your response to two decimal places). b) What is the value of R? Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 R = 4.40 mm (round your response to two decimal places). c) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCL) = mm (round your response to two decimal places). Range R (mm) 4.2 4.4 4.3 4.8 4.3 Ç
- 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?Quality Engineering question Why is decreasing variability so important during data collection and sampling? Please answer in your own words and please don't use handwriting. Thank youAt 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?
- Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes were taken, each tube was weighed, and the weights in Table were obtained. Ounces of Caulking Per Tube Tube Number Sample 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7.98 8.33 7.89 8.24 7.87 8.13 8.34 8.22 7.77 8.18 8.13 8.14 8.02 8.08 7.91 7.83 7.92 8.11 7.94 8.51 8.04 8.05 7.99 8.13 8.44 8.41 8.00 7.90 8.10 8.14 7.68 8.28 7.89 8.16 7.81 8.12 7.81 8.09 7.93 7.97 8.14 8.13 8.11 8.16 8.09 8.07 7.88 8.14 a. Assume that only six samples are sufficient and develop the control charts for the mean and the range.b. Plot the observations on the control chart and comment on your findings.Production phase After the pre-production phase, the product entered the production phase without introducing any changes in the process. Since it seemed to be stable SPC was not performed for several months, with process stability and variability being assessed by the level of nonconformities it it produced. However, after a time, an increasing number of customer complaints due to products supplied outside the specification/. The Quality Engineer decided to take 20 samples from the process with regular spacing between samples. Each sample is made up of 3 parts. The data obtained for the highlighted dimension samples are presented in Table 2 below: measurements in mm for critical sample dimension number 1 2 3 4 5 6 7 8 9 Observations 2 3 50.767 1 50.972 50.785 50.956 50.97 50.914 51.066 50.933 51.086 50.917 51.081 51.092 50.948 50.828 51.054 50.859 51.083 50.789 50.984 50.961 50.943 51.013 51.02 50.734 50.898 50.956 50.885 51.004 50.984 50.839 Table 2: Measurements in mm for critical…The Healthy Chocolate Company makes a variety of chocolate candles, including a 12-ounce chocolate bar (340 grams) and a box of six 1-ounce chocolate bars (170 grams). a.Specifications for the 12-ounce bar are 322 grams to 358 grams. What is the largest standard deviation (In grams) that the machine that fills the bar molds can have and still be considered capable if the average fill is 340 grams? (Round your intermediate calculations to 2 decimal places and final answer to 3 decimal places.) Standard deviation b.The machine that filles the bar molds for the 6-ounce bars has a standard deviation of .84 grams. The filling machine is set to deliver an average of 1.04 ounces per bar. Specifications for the six-bar box are 150 to 190 grams per box. Is the process capable? Hint: The variance for the box is equal to six times the bar variance. Convert all calculations Into grams. O Yes O No grams c.What is the lowest setting in ounces for the filling machine that will provide capability in…