Final answer:
To calculate the control limits for the Bama Bean Coffee Company's R chart, the average range (R-bar) was first determined to be 0.6 ounces. The upper control limit (UCL) was calculated using the factor for a sample size of 7, which led to UCL = 1.2684 ounces (rounded to 1.27 ounces). The lower control limit (LCL) is 0 ounces as negative variability is not possible.
Step-by-step explanation:
The question asks to calculate the upper and lower control limits for an R chart for the Bama Bean Coffee Company, which produces high quality ground coffee and sells it in 12 ounce packages. The sample ranges provided are 0.7, 0.4, 0.6, 0.4, and 0.9 ounces.
To determine the control limits for the range (R) chart, we must first calculate the average range (R-bar). R-bar is calculated as the average of the sample ranges:
R-bar = (0.7 + 0.4 + 0.6 + 0.4 + 0.9) / 5 = 3.0 / 5 = 0.6 ounces
Now, we use the value of R-bar in conjunction with the appropriate control chart factors, which are available in statistical quality control tables and are dependent on the sample size. For a sample size of 7, the factors for the upper and lower control limits (UCL and LCL) commonly used are D4 = 2.114 and D3 = 0, respectively.
UCL = D4 * R-bar = 2.114 * 0.6 = 1.2684 ounces
LCL = D3 * R-bar = 0 * 0.6 = 0 ounces
Arounding the upper control limit to two decimal places, the UCL is 1.27. Since there is no variability that is negative, the LCL remains as 0. Thus, from the options given, the correct control limits for the R chart are:
LCL = 0 ounces
UCL = 1.27 ounces
None of the provided options matches these calculated values exactly, which suggests there may be an error in the options or a misunderstanding in the calculation process.