Exam 12: Control Charts and Process Monitoring

Construct an R chart and determine whether the process variation is within statistical control. $\text { Control Chart Constants }$ $\quad$$\quad$$\quad$$\quad$$\quad$$\bar{x}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ $\boldsymbol{s}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ $\boldsymbol{R}$ n 2 1.880 2.659 0.000 3.267 0.000 3.267 3 1.023 1.954 0.000 2.568 0.000 2.574 4 0.729 1.628 0.000 2.266 0.000 2.282 5 0.577 1.427 0.000 2.089 0.000 2.114 6 0.483 1.287 0.030 1.970 0.000 2.004 7 0.419 1.182 0.118 1.882 0.076 1.924 8 0.373 1.099 0.185 1.815 0.136 1.864 9 0.337 1.032 0.239 1.761 0.184 1.816 10 0.308 0.975 0.284 1.716 0.223 1.777 A machine is supposed to fill cans that contain 12 ounces. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. $\text { Sample }\mid$ $\quad \text { ~~~Can Volume (oz) } \quad\mid$$\quad\overline{\boldsymbol{~~x}} \quad\mid$$\text { Range }$ 1 11.2 11.7 11.8 11.7 11.600 0.6 2 11.8 11.3 11.6 11.6 11.575 0.5 3 11.3 12.0 11.8 11.7 11.700 0.7 4 12.1 11.6 12.1 12.0 11.950 0.5 5 11.8 11.8 11.9 11.9 11.850 0.1 6 12.0 11.9 11.8 11.7 11.850 0.3 7 11.6 12.0 11.9 11.8 11.825 0.4 8 11.5 12.1 11.9 12.0 11.875 0.6 9 12.1 12.1 11.7 11.9 11.950 0.4 10 11.7 12.0 11.6 11.9 11.800 0.4 11 12.1 12.4 11.9 12.2 12.150 0.5 12 12.5 12.0 12.4 12.3 12.300 0.5 13 12.5 12.0 12.1 12.1 12.175 0.5 14 12.4 12.0 12.0 12.4 12.200 0.4 15 12.4 12.4 12.6 12.1 12.375 0.5

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour. What would be the centerline for a control chart for $\bar { x }$ ? $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Bottle Volume (mL) }$ Sample Range 1 19.9 20.1 20.2 20.3 20.125 0.4 2 20.4 20.0 20.3 20.3 20.250 0.4 3 20.0 20.7 20.4 20.3 20.350 0.7 4 20.4 20.1 20.1 19.9 20.125 0.5 5 19.9 19.8 19.6 19.5 19.700 0.4 6 19.4 19.4 19.6 19.7 19.525 0.3 7 19.8 19.4 19.6 19.7 19.625 0.4 8 19.9 19.8 20.0 20.0 19.925 0.2 9 20.2 20.3 20.1 20.3 20.225 0.2 10 20.0 20.3 20.0 20.2 20.125 0.3 11 20.3 20.5 20.1 20.2 20.275 0.4 12 20.1 19.9 19.8 19.7 19.875 0.4 13 19.5 19.8 19.7 19.6 19.650 0.3 14 19.4 19.8 19.8 19.4 19.400 0.4 15 19.5 19.6 19.6 19.9 19.650 0.4

Use the rank correlation coefficient to test for a correlation between the two variables. Use the sample data below to find the rank correlation coefficient and test the claim of correlation between math and verbal scores. Use a significance level of 0.05. Mathematics 347 440 327 456 427 349 377 398 425 Verbal 285 378 243 371 340 271 294 322 385

Provide an appropriate response. Describe what process data are. Why are process data important to businesses? What is a common goal of businesses using quality control?

If the critical values for a run test (found from table A-10)are 8 and 19 and the G value is 17, what should your conclusion about randomness be?

A control chart for $R$ is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

Find the critical value. Assume that the test is two-tailed and that $\mathrm { n }$ denotes the number of pairs of data. $n = 30 , \alpha = 0.05$

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come From populations with the same mean. Identify the p-value. Source Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come From populations with the same mean. Identify the P-value. Source Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

Match the parametric test with its related nonparametric test. Analysis of variance ( $F$ test)

Use the given process data to construct a control chart for p. A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below. 4 7 5 6 8 3 12 4 4 5 6 2

Select an appropriate null hypothesis for a one way analysis of variance test.

Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-statistical-control criteria apply. x is shown below. Determine whether the process mean is within statistical

A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come From populations with the same mean. What can you conclude about the equality of the Population means? Source Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

Find the ranks corresponding to the ages of five statistics professors when they were hired? 47, 51, 47, 47, 48

Given below are the analysis of variance results from a Minitab display. to use a 0.05 significance level in testing the null hypothesis that the different samples come From populations with the same mean. Identify the P-value. Source DF SS MS F Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80

At the same time each day, a researcher records the temperature in each of three greenhouses? The table shows the temperatures in degrees Fahrenheit recorded for one week. Greenhouse \#1 Greenhouse \#2 Greenhouse \#3 73 71 67 72 69 63 73 72 62 66 72 61 68 65 60 71 73 62 72 71 59 i)Use a 0.05 significance level to test the claim that the average temperature is the same in each greenhouse. ii)How are the analysis of variance results affected if the same constant is added to every one of the original sample values?

Which type of chart does not have control limits?