Data was collected from a process under statistical control for developing R-Chart. The collected data is presented in Table 1 below:Table 1: Mass of containersSubgroup Mass of containers (gm)Container 1 Container 2 Container 3 Container 41 601 599 603 6012 602 600 598 6003 599 597 601 5994 601 596 600 5995 599 600 598 602The control chart factors are given in the table below:REQUIRED:Determine the value of Upper Control Limit (UCL) (in gm) for the R-Chart.
Question
Data was collected from a process under statistical control for developing R-Chart. The collected data is presented in Table 1 below:Table 1: Mass of containersSubgroup Mass of containers (gm)Container 1 Container 2 Container 3 Container 41 601 599 603 6012 602 600 598 6003 599 597 601 5994 601 596 600 5995 599 600 598 602The control chart factors are given in the table below:REQUIRED:Determine the value of Upper Control Limit (UCL) (in gm) for the R-Chart.
Solution
To determine the Upper Control Limit (UCL) for the R-Chart, we first need to calculate the range for each subgroup and then find the average range (R-bar). The UCL is then calculated by multiplying R-bar by the appropriate control chart factor (D4).
Step 1: Calculate the range for each subgroup. The range is the difference between the maximum and minimum values in each subgroup.
Subgroup 1: 603 - 599 = 4 Subgroup 2: 602 - 598 = 4 Subgroup 3: 601 - 597 = 4 Subgroup 4: 601 - 596 = 5 Subgroup 5: 602 - 598 = 4
Step 2: Calculate R-bar, the average range. This is the sum of the ranges divided by the number of subgroups.
R-bar = (4 + 4 + 4 + 5 + 4) / 5 = 4.2
Step 3: Multiply R-bar by the control chart factor D4 to get the UCL. The value of D4 is not given in the question, so we'll assume it as a variable.
UCL = D4 * R-bar
Without the exact value of D4, we can't calculate the exact UCL. However, the formula for UCL is correct. Once you have the value for D4, you can substitute it into the formula to get the UCL.
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