After sampling a process, the Quality Manager found out that the cutting process for a certain item has an average (X) of 100 cm and

After sampling a process, the Quality Manager found out that the cutting process for a certain item has an average (X) of 100 cm² and a standard deviation (S) of 1 cm².

Design a control chart system x and S abiding by the following conditions:

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Symmetrical control limits;

False alarm probability = 0.1% on x chart and 0.4% on S chart;

In case of a shift of the standard deviation of +0.58 cm, ARL = 10 (on S chart)