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).

In the production of robot links and tests for their lengths, it has been found that μ = 2.725in. and σ = 0.032in. Find the central line, UCL, and LCL for the mean if the sample subgroup size is 5.

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