Baseball circumferences. Baseballs used in the major leagues in the United States must adhere to strict standards.

One such standard is that the circumference must be between 9 and 9.25 inch. One could look at this standard as a target circumference of 9.125 inches with a tolerance of + > -0.125 inch. These data (shown at the bottom of the page) were taken from a random sample of 50 baseballs from a large production batch. The actual circumference and deviation from the target circumference are listed.

Using the specification limits as the control limits,

a) Create a run chart for the baseballs’ circumferences.

b) Is the process for making baseballs in terms of their circumference in control?

c) How many baseballs produced were out of spec?

d) When should the quality team have investigated the production process?

Sample Circumference Deviation Sample Circumference Deviation 1 8.998 -0.127 26 9.121 -0.004 2 9.181 0.056 27 9.111 -0.014 3 9.147 0.022 28 9.130 0.005 4 9.182 0.057 29 9.116 -0.009 5 9.087 -0.038 30 9.035 -0.090 6 9.154 0.029 31 9.188 0.063 7 9.108 -0.017 32 9.092 -0.033 8 9.109 -0.016 33 9.078 -0.047 9 9.141 0.016 34 9.101 -0.024 10 9.093 -0.032 35 9.113 -0.012 11 9.142 0.017 36 9.087 -0.038 12 9.140 0.015 37 9.054 -0.071 13 9.125 0.000 38 9.177 0.052 14 9.175 0.050 39 9.058 -0.067 15 8.985 -0.140 40 9.179 0.054 16 9.119 -0.006 41 9.147 0.022 17 9.140 0.015 42 9.123 -0.002 18 9.109 -0.016 43 9.097 -0.028 19 9.190 0.065 44 9.108 -0.017 20 9.087 -0.038 45 9.214 0.089 21 9.046 -0.079 46 9.140 0.015 22 9.108 -0.017 47 9.151 0.026 23 9.188 0.063 48 9.041 -0.084 24 9.125 0.000 49 9.061 -0.064 25 9.114 -0.011 50 9.162 0.037