17.77 Control limits for a meat-packaging process. A meat-packaging company produces one-pound packages of ground beef by having a machine slice a long circular cylinder of ground beef as it passes through the machine.

The timing between consecutive cuts will alter the weight of each section.

17 TABLE 17.14 gives the weight of three consecutive sections of ground beef taken each hour over two 10-hour days. Past experience indicates that the process mean is 1.014 pounds, and the weight varies with

σ=0.019 pound.

a. Calculate the center line and control limits for an x¯

chart.

b. What are the center line and control limits for an s chart for this process?

c. Create the x¯

and s charts for these 20 consecutive samples.

d. Does the process appear to be in control? Explain.

TABLE 17.14 Twenty samples of size 3, with x¯

and s Sample Weight (pounds) x¯ s 1 0.999 1.071 1.019 1.030 0.0373 2 1.030 1.057 1.040 1.043 0.0137 3 1.024 1.020 1.041 1.028 0.0108 4 1.005 1.026 1.039 1.023 0.0172 5 1.031 0.995 1.005 1.010 0.0185 6 1.020 1.009 1.059 1.029 0.0263 7 1.019 1.048 1.050 1.039 0.0176 8 1.005 1.003 1.047 1.018 0.0247 9 1.019 1.034 1.051 1.035 0.0159 10 1.045 1.060 1.041 1.049 0.0098 11 1.007 1.046 1.014 1.022 0.0207 12 1.058 1.038 1.057 1.051 0.0112 13 1.006 1.056 1.056 1.039 0.0289 14 1.036 1.026 1.028 1.030 0.0056 15 1.044 0.986 1.058 1.029 0.0382 16 1.019 1.003 1.057 1.026 0.0279 17 1.023 0.998 1.054 1.025 0.0281 18 0.992 1.000 1.067 1.020 0.0414 19 1.029 1.064 0.995 1.029 0.0344 20 1.008 1.040 1.021 1.023 0.0159