The time needed for checking in at a hotel is to be investigated. Historically, the process has had astandard deviation equal to .146. The means of 39 samples of n = 14 areSample Mean Sample Mean Sample Mean Sample Mean1 3.86 11 3.88 21 3.84 31 3.882 3.90 12 3.86 22 3.82 32 3.763 3.83 13 3.88 23 3.89 33 3.834 3.81 14 3.81 24 3.86 34 3.775 3.84 15 3.83 25 3.88 35 3.866 3.83 16 3.86 26 3.90 36 3.807 3.87 17 3.82 27 3.81 37 3.848 3.88 18 3.86 28 3.86 38 3.799 3.84 19 3.84 29 3.98 39 3.8510 3.80 20 3.87 30 3.96a. Construct an x¯ -chart for this process with three-sigma limits. Is the process in control?b. Analyze the data using a median run test and an up/down run test. What can you conclude?

A wood shop produces processed wood chips with high precision. The shop wants know whether the process is still controlled using statistical process methods control. The shop owner takes measurements against the Length with 5 samples every day for 10 consecutive days with the results according to the table below. day sample 1 sample 2 sample 3 sample 4 sample 5 1 146 147 145 141 144 2 139 134 135 135 146 3 135 150 130 146 143 4 142 136 145 141 133 5 142 132 146 134 149 6 143 143 141 145 144 7 134 146 144 141 144 8 133 139 146 140 145 9 140 135 135 133 146 10 136 132 130 146 145 From the data mentioned above, the shop owner asks you as a quality expert todetermine whether the production process is still under control with regard toquality.a. Calculate the LCL-X and UCL-X from these measurements and make a sketch of the XChartb. Calculate the LCL-R and UCL-R from these measurements and draw an RChart sketchc. Analyze whether the process is still controlled or…

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?

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?