6-9. A process that produces computer chips has a mean of .04 defective chip and a standard deviation of .003 chip. The allowable variation is from .03 to .05 defective. (a) Compute the capability index for the process (b) Is the process capable?
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- 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?Each of the processes listed is noncentered with respect to the specifications for that process.Compute the appropriate capability index for each, and decide if the process is capable.Process Mean Standard Deviation Lower Spec Upper SpecH 15.0 0.32 14.1 16.0K 33.0 1.00 30.0 36.5T 18.5 0.40 16.5 20.1Using 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?
- The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control. Day Sample Size Defects 1 100 8 2 120 4 3 190 10 4 190 7 5 240 20 6 245 8 7 105 4 8 165 6 9 245 27 10 255 37 Find the UCL. Find the LCL. Is the process in control? Why/why not?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?In a sausage factory, quality managers are studying the compliance of the sausages with the requirements. Any sausage having pin holes, air pockets, deformation or breakage in its casings is counted as defective and total number of such defective sausages alone is noted in each shift. The following data represents the number of defective sausages in samples of 200 sausages taken from 10 shifts. Sample Defectives Percent Defective 1 40 20% 2 28 14% 3 15 8% 4 23 (a) 5 20 10% 6 21 11% 7 19 10% 8 15 8% 9 16 8% 10 17 9% Calculate the value for (a) in the table above. Calculate p-bar based on the samples above. What is the UCL and LCL for a p chart based on the data provided and a desired control level of 99.74%? Use your control limits from part b along with the data provided to draw a p-chart. Is the process in control? Why or why not? If not in control, suggest some potential reasons.
- 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 excel1. From a perspective of Statistical Process Control (SPC), a six-sigma process will have which of the following attributes? a) The USL and LSL will be separated by a distance of six sigma b) The process center will be aligned with the LSL c) The number of defects produced by the process will be 0.0018 parts per million d) All of the aboveThe overall average on a process you are attemptingto monitor is 50 units. The process population standard deviationis 1.72. Determine the upper and lower control limits for a meanchart, if you choose to use a sample size of 5. PXa) Set z = 3.b) Now set z = 2. How do the control limits change?
- 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. 5Taguchi Loss Function Panguitch Company manufactures a component for tablet computers. Weight and durability of the component are the two most important quality characteristics for the tablet manufacturers. With respect to the weight dimension, the component has a target value of 100 grams. Specification limits are 100 grams, plus or minus five grams. Products produced at the lower specification limit of 95 grams lose $20. A sample of five units produced the following weight measures: Unit No. Measured Weight 1 100 2 105 3 110 4 90 5 85 During the first quarter, 100,000 units were produced. Required: 1. Calculate the loss for each unit. If required, round your answers to the nearest cent.$_______ Per Unit Calculate the average loss for the sample of five.$______ 2. Using the average loss, calculate the hidden quality costs for the first quarter.$_________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. 0.75