The Farley Manufacturing Company prides itself on the quality of its products. The company is engaged in competition for a very important project. A key element is a part that ultimately goes into precision testing equipment. The specifications are 8.000 ± 3.000 millimeters. Management is concerned about the capability of the process to produce that part. The following data (shown below) were randomly collected during test runs of the process:   Observation (Millimeters) Sample 1 2 3 4 5 6 7 8 1 9.100 8.900 8.800 9.200 8.100 6.900 9.300 9.100 2 7.600 8.000 9.000 10.100 7.900 9.000 8.000 8.800 3 8.200 9.100 8.200 8.700 9.000 7.000 8.800 10.800 4 8.200 8.300 7.900 7.500 8.900 7.800 10.100 7.700 5 10.000 8.100 8.900 9.000 9.300 9.000 8.700 10.000 Assume that the process is in statistical control. Is the process capable of producing the part at the three-sigma level? Explain.

Twenty samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 20 samples, a total of 140 items were found to be defective. (a) What is an estimate of the proportion defective when the process is in control? (b) What is the standard error of the proportion if samples of size 100 will be used for statistical process control? (Round your answer to four decimal places.) (c) Compute the upper and lower control limits for the control chart. (Round your answers to four decimal places.) UCL = LCL =

Twelve​ samples, each containing five​ parts, were taken from a process that produces steel rods at Emmanual​ Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results​ were:                                                                                                                              Sample Sample Mean​ (in.) Range​ (in.) Sample Sample Mean​ (in.) Range​ (in.) 1 9.602 0.033 7 9.603 0.041 2 9.602 0.041 8 9.605 0.034 3 9.593 0.034 9 9.597 0.027 4 9.606 0.051 10 9.601 0.029 5 9.599 0.031 11 9.603 0.039 6 9.599 0.036 12 9.606 0.047 Part 2 For the given​ data, the x double overbarx ​= 9.6013 inches ​(round your response to four decimal​ places). Part 3 Based on the sampling​ done, the control limits for ​3-sigma x overbarx chart​ are:   Upper Control Limit ​(UCL Subscript x…

Aspen Plastics produces 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 whe the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 4 1 0.602 0.601 0.604 0.594 2 0.588 0.581 0.612 0.573 0.588 0.571 0.578 0.574 4 0.582 0.612 0.603 0.582 5 0.596 0.602 0.597 0.609 6 0.583 0.602 0.615 0.579 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Suppose that the specification for the bottle neck diameter is 0.600 ± 0.050 in. and the population standard deviation i 0.012 in. a. What is the process capability index? The Cok is 1.19. (Enter your response rounded to two decimal places.) b. The process capability ratio? The Cp is (Enter your response rounded to two decimal places.)