Four samples of three observations each have been taken, with actual measurements (in centimetres) shown below. Construct three sigma mean and range charts, and determine if corrective action is needed. Sample 1 12.3 12.2 12.1 2 11.9 12.2 12.2 3 12.0 12.2 11.8 4 12.1 11.8 11.8
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- Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed: Sample Mean Range Sample Mean Range 1 3.06 .42 4 3.13 .46 2 3.15 .50 5 3.06 .46 3 3.11 .41 6 3.09 .45 a. Using the factors in Table 10.3 , determine upper and lower limits for mean and range charts. b. Is the process in control?The time to replace vehicle wiper blades at a service center was monitored using a mean and a rangechart. Six samples of n = 20 observations were obtained and the sample means and ranges computed:Sample Mean Range Sample Mean Range1 3.06 .42 4 3.13 .462 3.15 .50 5 3.06 .463 3.11 .41 6 3.09 .45 a. Using the factors in Table 10.3, determine upper and lower limits for mean and range charts.b. Is the process in control?Auto 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 5 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean (mm) Range R (mm) 158 4.3 151.2 4.4 155.7 4.2 153.5 4.8 156.6 4.5 What is the UCL using 3-sigma?(round your response to two decimal places). 1. 2. 4.
- Construct a 3-sigma X-bar chart for the length in centimeters of a part from the following tabble . What is the upper controt limit? sample observation 1 observation 2 observation 3 observation 4 1 0.486 0.499 0.493 0.511 2 0.499 0.506 0.516 0.494 3 0.496 0.5 0.515 0.488 4 0.495 0.506 0.483 0.487 5 0.472 0.502 0.526 0.469 6 0.473 0.495 0.507 0.493 7 0.495 0.512 0.49 0.471 8 0.525 0.501…A garment manufacturer wants to set up a control chart for irregularities. Each week a random sample of 25 garments is collected from production and the number of irregularities is recorded. The table below gives the results for the past 20 weeks: 1 6 8 10 Sample Number Irregularities 11 2 3 4 5 7 9 8 12 4 16 5 8 17 10 11 16 20 Sample Number | Irregularities 11 12 13 14 15 17 18 19 7 12 13 8 17 11 9 10 (a) Using the data set up an appropriate control chart using a three sigma control limits. (b) Comment on the process. [8 marks] [2 marks] 9,1. The data shown in Table 1 are x and R values for 20 samples of size n= 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 5 33.8 38.4 31.6 15 35.6 7 3 16 30.8 7 4 17 33.0 5 8 36.8 10 18 31.6 3 9. 35.0 15 19 28.2 9 10 34.0 6 20 33.8 Table 1: Bearing Diameter Data
- 4: A production manager at a Contour Manufacturing plant has inspected the number of defective plastic molds in 5 random samples of 20 observations each. Following are the number of defective molds found in each sample: Sample N Number of observations Number of defections 1 1 20 2 2 20 3 2 20 4 1 20 5 0 20 a) Construct a 3-sigma control chart (P-chart) with this information.Distinguish between a sampling error and a nonsampling error.How can each be reduced?< Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Hour X 1 2 3 4 5 6 R 3.25" 0.65" 3.00 1.23 3.32 1.43 3.39 1.26 3.07 1.17 2.96 0.37 Hour X R Hour R Hour 7 2.95" 0.48" 13 X 3.11" 0.90" 2.73 1.36 19 20 8 2.55 1.18 14 9 0.71 3.12 1.11 21 3.12 2.85 15 16 10 1.38 2.74 0.50 22 11 2.83 1.22 17 2.86 1.38 23 12 3.07 0.45 18 2.64 1.29 24 X 4.51" 2.89 2.65 3.18 3.04 2.54 R 1.56" 1.14 1.13 0.51 1.58 1.02 Based on the sampling done, the control limits for 3-sigma x chart are (round all intermediate calculations to three decimal places before proceeding with further calculations): Upper Control Limit (UCL) = inches (round your response to three decimal places).
- Ngqabutho Ltd produces plastic bottles to customer’s order. The quality inspector randomly selectsfour bottles from the bottle machine and gathers the following data ( see image) 1. Assume that only these six samples are sufficient, and use the data to determine controllimits for an R (range)- and an X (mean) chart. ( 2. Suppose that the specification for the bottle neck diameter is 0.600 ± 0.050 and thepopulation standard deviation is 0.013 in. What are the process capability index and theprocess capability ratio?The Road King Tire Company in Birmingham wants to monitor the quality of the tires it manufactures. Each day the company quality-control manager takes a sample of 100 tires, tests them, and determines the number of defective tires. The results of 20 samples have been recorded as follows: Sample Number of Defectives Sample Number of Defectives 1 14 11 18 2 12 12 10 3 9 13 19 4 10 14 20 5 11 15 17 6 7 16 18 7 8 17 18 8 14 18 22 9 16 19 24 10 17 20 23 Construct a P -chart for this process using 2q limits and describe the variation in the process. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: Machine Measurements #1 17 15 15 17 #2 16 25 18 25 # 3 23 24 23 22 What is the estimate of the process mean for whenever it is under control? What is the sample average range based upon this limited sample? What are the x-bar chart upper and lower control limits?