The thickness of an epitaxial layer on a silicon wafer is specified to be 14.5 ± 0.5 micro meters.

The thickness of an epitaxial layer on a silicon wafer is specified to be 14.5 ± 0.5 micro meters. Assume the manufacturing process is in statistical control where the distribution of the thickness is normal with mean µ = 14.5 and standard deviation σ = 0.4. To monitor the production process the mean thickness of four wafers is determined at regularly spaced time intervals. (a) Compute the lower and upper control limits LCLX, UCLX for a three-sigma control chart for the process mean. (b) Compute the lower and upper control limits LCLR, UCLR for a three-sigma control chart for the process variation. (c) Determine the probability that a sample mean (based on a sample of size n = 4) falls outside the tolerance limits 14.5 ± 0.5.

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Identify the DSM-5 diagnostic criteria that you notice in the case studies below and explain how the client meets the criteria.

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