1. An inspector wants to develop 3 sigma level process control charts to monitor the weight of bag of rocks. Data (in pounds) from Monday through Thursday are shown. Three samples (n = 3) were taken each day. Calculate the limits by using the table provided below. Draw the mean and range charts and discuss the results. Is the process under control?

Monday	Tuesday	Wednesday	Thursday
18	38	22	26
26	30	28	20
26	26	26	26

Factors for 3 Sigma level

Sample Control Limit Factor Control Limit Factor

Size for Sample Mean for Sample Range

n A2 D3 D4

2 1.880 0 3.267

3 1.023 0 2.575

4 0.729 0 2.282

5 0.577 0 2.116

10 0.308 0.223 1.777

15 0.223 0.348 1.652

20 0.180 0.414 1.586

25 0.153 0.459 1.541

2. Suppose a process has been monitored daily for the last ten days and the number of machine failures each day was noted. The results follow:

Day Number: 1 2 3 4 5 6 7 8 9 10

Number of Failures: 8 9 6 10 12 4 9 11 9 12

Compute control limits for a c-chart at 3 sigma level that monitors the average number of machine failures per day. Draw the chart and plot the data. Is the process under control?

3. A small town is concerned about public reaction to its new high voltage electric tower project that is currently in progress. In order to measure residents perception, a weekly survey is conducted. Each time, a sample of 100 residents is surveyed. The results to date are shown below. The P-chart can be used. Draw the graph and plot data. Is everything under control? Analyze data using 5% risk of Type I error (z=1.96).

4. A company bottles syrup in no-spill containers. They are evaluating four different machines with standard deviations of 0.006, 0.01, 0.022, and 0.04 ounces for Machines A, B, C, and D, respectively. The specification limit values are 11.95 and 12.05 ounces for LSL and USL respectively. Calculate process capability for each machine. Which machines are statistically capable?