A company is evaluating its manufacturing system to produce steel rods for a new customer. Fif- teen samples, cach containing five steel rods, were taken from the process. The length of each rod in the samples was measured and is shown in the following table: Sample Rod 1 Rod 2 Rod 3 Rod 4 Rod 5 10.001 10.013 10.009 9.999 9.992 10.002 10.001 9.992 10.001 9.989 10,001 10.002 9.993 9.999 10.011 9.999 4 10.012 10.001 10.002 9.989 9.998 9.997 10.003 9.999 9.995 10.001 6. 9.995 10.003 10.002 9.993 10,008 7 9.999 9.998 10.002 9.999 9.997 8. 10.002 10.001 9.993 10.001 9. 10,021 10.008 9.992 9.989 9.996 10 10.001 10.010 10.002 10.003 10.006 11 10.002 10.008 9.992 9.999 10,005 10.001 12 9.992 9.996 9.999 9.989 13 10.001 10.009 10.001 9.992 10.002 14 10,003 9.991 10.002 9.999 10,003 15 9.998 10.002 9.991 10.003 10.001

Control charts for X-bar and S are maintained for the fill volume of protein shake drink. The specifications are 330 + 10 mL. After 40 samples of size n=7 are analyzed, we find that: 40 40 = 13,200 Si = 296 i=1 i=D1 Find the best estimate of the process standard deviation. 7.498 7.400 7.570 2.737 7.713 8.032

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…

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 R Hour x R Hour x R Hour x R 1 3.15​" 0.71​" 7 3.15​" 0.58​" 13 3.21​" 0.80​" 19 3.31​" 1.61​" 2 3.20 1.23 8 2.75 1.18 14 2.83 1.31 20 2.79 1.09 3 3.12 1.38 9 3.02 0.71 15 3.02 1.01 21 2.65 1.13 4 3.39 1.31 10 2.75 1.38 16 2.94 0.50 22 3.38 0.51 5 3.07 1.17 11 2.93 1.22 17 2.86 1.43 23 2.94 1.63 6 2.76 0.37 12 2.87 0.40 18 2.64 1.29 24 2.64 0.92   Based on the sampling​ done, the control limits for ​3-sigma x chart are ​(round all intermediate calculations to three decimal places…

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.)

2- Quality Control Charts A local brewery and bottling plant wants to keep track of the bottling filling equipment's accuracy, Bottles are to be filled with exactly 16 ounces of the drink. The following is data from the bottling equipment where 5 samples of bottles filled were pulled every hour and measured for actual quantity filled. 1- Calculate the UCL, LCL and mean for the X-bar and R data 2- Draw an X-Bar chart and a R chart. 3- Is this filling process in control or out of control? Hour X-bar R 1 16.05 .20 2 16.03 3 15.96 4 15.97 16.03 16.06 15.98 16.09 15.94 16.01 5 6 7 8 9 10 @n-5: A2 = 0.58, D3 =0, D4 = 2.11 .25 .62 .58 .71 .37 .46 .21 .35 .29

A control chart for fraction nonconforming is to be established using a center line of p=0.03. What sample size is required if we wish to detect a shift in the process fraction nonconforming to 0.08 with probability 0.50? 1269 475 73 316 216 2 105 150 265

Lower Range, Sample Size, n Mean Factor, Upper Range, DA A2 D3 2 1.880 3.268 3 1.023 2.574 4 0.729 2.282 5 0.577 2.115 6 0.483 2.004 7 0.419 1.924 0.076 8 0.373 1.864 0.136 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284

The results of inspection of DNA samples taken over the past 10 days are given below. Sample size is 100. LCLp Day Defectives = 1 5 2 7 3 7 4 9 5 5 6 6 a) The upper and lower 3-sigma control chart limits are: UCL = 0.127 (enter your response as a number between 0 and 1, rounded to three decimal places). (enter your response as a number between 0 and 1, rounded to three decimal places). 7 1 8 6 9 10 10 1

In a fabric manufacturing factory, the quality control process using control charts from SPC. In an hour there are a total of 5 samples are taken each having 5 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.51 . 208.24, 112.44 and 123.30 respectively. In the same sample, the corresponding ranges are: 13.1713.3815.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the R chart?