4.  Organic Grains LLC uses statistical process control to ensure that its​ health-conscious, low-fat, multigrain sandwich loaves have the proper weight.   Based on a previously stable and​ in-control process, the control limits of the x​- and​ R-charts are:   UCLx ​= 5.35​, LCLx ​= 4.93​; UCLR ​= 0.894​, LCLR ​= 0.   Over the past few​ days, they have taken five random samples of four loaves each and have found the​ following:                                                                                               Net Weight Sample Loaf​ # 1 Loaf​ # 2 Loaf​ # 3 Loaf​ # 4 1 4.9 5.2 5.1 5.0 2 5.3 5.1 5.2 5.3 3 4.9 5.2 4.9 5.2 4 5.5 5.5 5.3 5.5 5 5.3 5.2 5.3 5.0 Part 2 Based on the x​-chart, is one or more samples beyond the control​ limits? ▼   No Yes .

A shirt manufacturer buys clothes by the 100-yard roll from a supplier. For setting a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier.   Sample 1 2 3 4 5 6 7 8 9 10 Irregularities 3 5 2 6 5 4 6 3 4 5   Which type of control chart should be used? Construct a control chart with two-sigma control limits. Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control? Explain and show work

A microbrewery tracks its output in gallons over a five hour period for each of seven days. Their data is in the table below, and they went ahead and calculated the averages and ranges for the individual samples and the overall averages Their data and the factors tables can be found below. Calculate the upper (LCL) and lower (UCL) control limits for X bar, and R charts for their process. Day (X values) X̅   R 1 46 49 45 47 48 47.0   4 2 43 52 46 52 44 47.4   9 3 45 55 46 51 43 48.0   12 4 39 44 42 43 40 41.6   5 5 45 50 48 50 42 47.0   8 6 44 48 45 45 40 44.4   8 7 41 44 52 50 47 46.8   11           X̿ = 46.03 R̅ 8.14     Xbar chart - LCL = 40.48, UCL=46.25, R chart LCL=0, UCL=14.01 Xbar chart - LCL = 44.21, UCL=48.41, R chart LCL=0.49, UCL=17.18 Xbar chart - LCL = 42.61, UCL=49.45, R chart LCL=0.65, UCL=15.63 Xbar chart - LCL = 44.21, UCL=51.62, R chart LCL=0, UCL=17.18 Xbar chart - LCL = 41.31, UCL=50.75, R chart LCL=0, UCL=17.18

Hermitage DNA Labs, LLC collected temperature readings in an analysis process. The data can be found in the Problems Data Compute the mean and range of each sample and calculate control limits for x-bar and R charts using the appropriate From the charts constructed, does the process appear to be in statistical control?

54 Boxes of Honey-Nut Oatmeal are produced to contain 14.0 ounces, with a standard deviation of 0.20 ounce. For a sample size of 64, the 3-sigma X chart control limits are: Upper Control Limit (UCL) = ounces (round your response 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

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 11.404 0.044 7 11.403 0.021 2 11.400 0.051 8 11.407 0.058 3 11.389 0.042 9 11.397 0.039 4 11.406 0.037 10 11.403 0.038 5 11.395 0.048 11 11.401 0.054 6 11.397 0.053 12 11.406 0.061 Part 2 For the given​ data, the x ​= enter your response here inches ​(round your response to four decimal​ places).   The control limits for the ​3-sigma ​ R-chart are ​(round all intermediate calculations to three decimal places before…

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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

How is a process operating in statistical control distinguished from one that is not