# How to Create a Control Chart for Average Call Length

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A control chart is a tool used in statistical process control to determine if a process, such as the time an operator spends handling a complaint or soliciting a donation, is under control. A process is under control if the measured process variable stays within a specified range of values. A control chart might be used in a call center to ensure that the average time that operators spend with a single individual is neither too long nor too short.

## Create Subgroup Samples

Divide the data into subgroups, usually by grouping the calls by the day they were made. If working with a large number of phone calls, create subgroups for each hour. For a small number of phone calls, it may be necessary to use every two days or every week. You need a minimum of 15 subgroups. If you have more than 30 subgroups, use the most recent data to limit the number of subgroups to 30.

Create a random sample from each subgroup. Take two to 10 phone calls from each subgroup as a random sample of that subgroup. Use the same sample size for each subgroup. Your sample size cannot be larger than the smallest subgroup. For instance, if your smallest subgroup only has five phone calls, use a sample size of five. Choose the sample phone calls from each subgroup randomly.

Calculate the average (X_bar) of each subgroup sample. Add the length of the calls in each subgroup sample and divide by the number of calls in the sample. For example, if the sample consists of calls five calls of 1.25, 4.87, 3,29, 1.73, and 6.25 minutes the average would be (1.25 plus 4.87 plus 3.29 plus 1.73 plus 6.25. Divided by 5, this equals 3.38 minutes.

Calculate the range (R) of each subgroup sample. Subtract the minimum call length from the maximum call length in the sample. For example, the subgroup sample given in Step 3 has a range of 6.25 minus 1.25, which equals five minutes.

## Calculate Control Limits

Calculate the grand average (X_double_bar). Add the averages of all the subgroup samples and divide by the number of subgroups. The grand average is the average of the averages.

Calculate the average range (R_bar). Add the ranges of all the subgroup samples and divide by the number of subgroups.

Calculate the upper control limit for the call length (UCL_X) using the formula UCL_X=X_double_bar+A_2*R_bar. Based on the number of calls in each subgroup sample (N), use the following list to determine the value of A_2: n=2, A_2=1.880; n=3, A_2=1.023; n=4, A_2=0.729; n=5, A_2=0.577; n=6, A_2=0.483; n=7, A_2=0.419; n=8, A_2=0.373; n=9, A_2=0.337; n=10, A_2=0.308.

Calculate the lower control limit for the call length (LCL_X) using the formula LCL_X=X_double_bar-A_2*R_bar. Based on the number of calls in each subgroup sample (N), use the following list to determine the value of A_2: n=2, A_2=1.880; n=3, A_2=1.023; n=4, A_2=0.729; n=5, A_2=0.577; n=6, A_2=0.483; n=7, A_2=0.419; n=8, A_2=0.373; n=9, A_2=0.337; n=10, A_2=0.308. The UCL adds to the grand average while the LCL subtracts from it.

Calculate the upper control limit for the range (UCL_R) using the formula UCL_R=D_4*R. Based on the number of calls in each subgroup sample (N), use the following list to determine the value of D_4: n=2, D_4=3.268; n=3, D_4=2.574; n=4, D_4=2.282; n=5, D_4=2.114; n=6, D_4=2.004; n=7, D_4=1.924; n=8, D_4=1.864; n=9, D_4=1.816; n=10, D_4=1.777.

Calculate the lower control limit for the range (LCL_R) using the formula LCL_R=D_3*R. Based on the number of calls in each subgroup sample (N), use the following list to determine the value of D_3: n=2, D_3=0.000; n=3, D_3=0.000; n=4, D_3=0.000; n=5, D_3=0.000; n=6, D_3=0.000; n=7, D_3=0.076; n=8, D_3=0.136; n=9, D_3=0.184; n=10, D_3=0.223.

## Make the Charts

Plot the lines showing the grand average (X_double_bar), the UCL of the call length (UCL_X) and the LCL of the call length (LCL_X). These will be horizontal lines on your graph.

Plot the values of the averages (X_bar) of each subgroup sample and connect the points with a line.

Repeat Steps 1 to 3 of this section using the average range (R_bar), the UCL for the range (UCL_R) and LCL for the range (LCL_R) for step 2, and the range for each subgroup sample for Step 3.

## Tips & Warnings

• The greater the number of measurements in each subgroup sample, the more sensitive the control chart will be to changes between subgroups.
• For subgroups having a large number of measurements, there is a method of creating a control chart using standard deviations rather than range.

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