Exam 12: Control Charts and Process Monitoring

Use the given process data to construct a control chart for p. A candy manufacturer considers a cracked piece of candy to be a defect. Each day 100 candies are randomly selected and Checked for cracks. The numbers of defects for 20 consecutive days are given below. 14 4 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7 What is the value of the center line?

There________ between two factors if the effect of one of the factors changes for different categories of the other factor.

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identity which of the three out-of-statistical-control criteria apply. A run chart for individual values W is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

Use the data in the given table and the corresponding Minitab display to test the hypothesis. The following Minitab display results from a study in which three different teachers taught calculus classes of five different sizes. The class average was recorded for each class. Assuming no effect from the interaction between teacher and class size, test the claim that the teacher has no effect on the class average. Use a 0.05 significance level. Source DF Teacher 2 56.93 28.47 1.018 0.404 Class Size 4 672.67 168.17 6.013 0.016 Error 8 223.73 27.97 Total 14 953.33

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from populations with equal medians. SAT scores for students selected randomly from two different schools are shown below. Use a significance level of 0.05 to test the claim that the scores for the two schools are from populations with the same median. $~~ ~ ~ \text { School A }$ $\quad\quad \mid$ $\quad$ $\text { School B }$ 550 480 670 460 580 620 400 700 520 380 680 570 540 740 560 660 500 480 360 560 650 600 550

Fill in the missing entries in the following partially completed one-way ANOVA table. Source df Treatment 3 14.28 Error 13.50 0.643 Total

Explain what an efficiency rating is. You may use an example to explain this concept. Do comparable parametric or nonparametric tests have higher efficiency ratings?

Describe an R chart and give an example. What does it attempt to monitor?

The data below represent the weight losses for people on three different exercise programs. Exercise A Exercise B Exercise 2.5 5.8 4.3 8.8 4.9 6.2 7.3 1.1 5.8 9.8 7.8 8.1 5.1 1.2 7.9 If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 }$ , and $\mu _ { 1 } = \mu _ { 3 }$ ?

Examine the given run chart or control chart and determine whether the process is within statistical control.

Fill in the missing entries in the following partially completed one-way ANOVA table. Source df Treatment 3 13.89 Error 13.58 0.617 Total

Sketch a control chart that indicates that a process is not statistically stable due to the run of 8 rule.

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$$\quad$ $\boldsymbol{R}$ n 2 1.880 2.659 0.000 3.267 0.000 3.267 3 1.023 1.954 0.000 2.568 0.000 2.574 4 0.729 1.628 0.000 2.266 0.000 2.282 5 0.577 1.427 0.000 2.089 0.000 2.114 6 0.483 1.287 0.030 1.970 0.000 2.004 7 0.419 1.182 0.118 1.882 0.076 1.924 8 0.373 1.099 0.185 1.815 0.136 1.864 9 0.337 1.032 0.239 1.761 0.184 1.816 10 0.308 0.975 0.284 1.716 0.223 1.777 A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\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

When applying the runs test for randomness above and below the median for 10 scores on a final exam, the test statistic is G = 2. What does that value tell us about the data?

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from populations with equal medians. Use the Wilcoxon rank-sum approach to test the claim that the sample student grade averages at two colleges come from populations with the same median. The sample data is listed below. Use a 0.05 level of significance, and assume that the samples were randomly selected. College A 3.2 4.0 2.4 2.6 2.0 1.8 1.3 0.0 0.5 1.4 2.9 College B 2.4 1.9 0.3 0.8 2.8 3.0 3.1 3.1 3.1 3.5 3.5

Sketch a run chart that that indicates that a process is not statistically stable due to increasing variation.

A rank correlation coefficient is to be calculated for a collection of paired data. lie between -10 and 10. Which of the following could affect the value of the rank Correlation coefficient? I: Multiplying every value of one variable by 3 II: Interchanging the two variables III: Adding 2 to each value of one variable IV: Replacing every value of one variable by its absolute value