8. Given the following data for the number of defects per spool of cable, using three-sigma limits, is the process in control? OBSERVATION 1 3 4 6 7 8 9 10 11 12 13 14 Number of defects 2 1 0 1 3 2 0 2 1 3 1 2 0
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- The specification limits for a product are 9.9 cm and 12.35 cm. A process that produces the product has a mean of 11.18 cm and a standard deviation of 0.52 cm. What is the process capability, Cpk? a. 0.8205 b. 1.571 c. 0.7853 d. 0.75Linda Boardman, I nc., an equipment manufacturerin Boston, has submitted a sample cutoff valve to improve yourmanufacturing process. Your process engineering department basconducted experiments and found that the valve has a mean (J.L)of 8.00 and a standard deviation (cr) of .04. Your desired performanceis f..L = 8.0 ±3cr, where cr = .045. What is the Cpk of theBoardman valve?Using samples of 197 credit card statements, an auditor found the following: Sample 1 3 errors Sample 2 3 errors Sample 3 5 errors Sample 4 9 errors 1. what alpha risk would control limits of .0470 and .0038 provide? 2. Using control limits of .0470 and .0038, is the process in control? 3. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control?
- Orlando Manufacturers has decided to use a c-Chart to monitor the number of defects per file cabinet produced by their manufacturing process. The c-Chart should be constructed with an alpha risk of 7%. The quality control manager randomly samples one file cabinet at 99 successively selected time periods and counts the number of defects in the file cabinet. Sample Defects1 112 83 74 145 56 117 48 69 13 Step 2 of 7: What is the Upper Control Limit? Round your answer to three decimal places.Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.; Average range R = 1.64 lb. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCLx) = nothing lb. (round your response to three decimal places).A new process is started, and the sum of the sample standard deviations for 25 subgroups of size 4 is 750. If the specifications are 700 +_ 80, what is the process capability index? What action would you recommend?
- 6. The defect rate for your product has historically been about 4.50%. For a sample size of 500, the upper and lower 3-sigma control chart limits are: Part 2 UCLp = _______ (enter your response as a number between 0 and 1, rounded to four decimal places). The Standard deviation of defect rate of product is given __________. The Upper and Lower 3-sigma control charts limits are: UCLp ________ LCLp ________Suppose that a quality characteristic is normally distributed with specifications at 100 ± 20. The process standard deviation is 6.(a) Suppose that the process mean is 100. What are the natural tolerance limits? Calculate Cp and Cpk and interpret these ratios. What fraction of parts do you expect to be defective?(b) Suppose that the process mean is 106. What are the natural tolerance limits? What is thefraction defective? Calculate Cp and Cpk and interpret these ratios.Using samples of 200 credit card statements, an auditor found the following: Sample 1 2 3 4 Number with errors 4 2 5 9 a. 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? Page 457 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 are the 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 two-sigma control limits. Is the process in control? Can you show me the steps and formulas using excel
- A process considered to be in control measures an ingredient in ounces. A quality inspector took 10 samples, each with 5 observations as follows: SEE ATTACHED PHOTO Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation ofthe process is 1.36.For 50 consecutive days, a process engineer has measured the weight of acomponent after it has been coated with a special paint. Each day, she takes a sampleof 10 components. The average across all 500 components (50 days, 10 componentsper day) is 45.343018 grams. The standard deviation across all parts is 0.0076382 gram.When constructing an X-bar chart, what would be the center line and what would be thelines for the upper and lower control limits?Exercise : Control chart for X-R variablesThe data shown in the table represent the internal diameters (mm) of automobile engine piston rings.Each sample is made up of five parts and a total of 25 samples were collected. a) Construct limits and control charts for this critical quality characteristic. Is the process statistically controlled? b) If the product specifications are 74,000 +/- 0.05, determine the ability of the process to meet these specifications. Sample observations1 74.03 74.002 74.019 73.992 74.0082 73.995 73.992 74.001 74.011 74.0043 73.988 74.024 74.021 74.005 74.0024 74.002 73.996 73.993 74.015 74.0095 73.992 74.007 74.015 73.989 74.0146 74.009 73.994 73.997 73.985 73.9937 73.995 74.006 73.994 74.000 74.0058 73.985 74.003 73.993 74.015 73.9889 74.008 73.995 74.009 74.005 74.00410 73.998 74.000 73.99 74.007…