1. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.

WeightDay Package 1 Package 2 Package 3 Package 4Monday 23 22 23 24Tuesday 23 21 19 21Wednesday 20 19 20 21Thursday 18 19 20 19Friday 18 20 22 20

(a) Calculate all sample means and the mean of all sample means. (b) Calculate upper and lower control limits that allow ±2σ for natural variations. (c) Is this process in control?

2. A small, independent amusement park collects data on the number of cars with out-of-state license plates. The sample size is fixed at n=25 each day. Data from the previous 10 days indicate the following number of out-of-state license plates:

DayOut-of-state

Plates1 62 43 54 75 86 37 48 59 310 11

(a) Calculate the overall proportion of "tourists" (cars with out-of-state plates) and the standard deviation of proportions.

(b) Using ±3σ limits, calculate the LCL and UCL for these data.(c) Is the process under control? Explain.

3. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control.

SheetNumber of

flaws1 12 13 2

4 05 16 57 08 29 010 2

4. The specification for a plastic liner for concrete highway projects calls for a thickness of 6.0 mm ± 0.1 mm. The standard deviation of the process is estimated to be 0.02 mm. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.03 mm. What is the Cp and Cpk for this process?