For a production process for which there is a great deal of data since its last modification, the population mean μ and population standard deviation σ are assumed known. For such a process, we have the following values (using additional statistical analysis):

The values of A, d_2, D₂, and D₁ are found in the table of control chart factors in Example 2 (Table 22.2).

After bottling, the volume of soft drink in six sample bottles is checked each 10 min. For this process μ = 750.0mL and σ = 2.2mL. Find the central line, UCL, and LCL for the range.

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x chart: central line R chart: central line = d₂o, UCL = μ, UCL = μ + Ao, LCL = μ - Ao D₂o, LCL D₁o = =