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In a quality income control, lengths of screws are measured. The length is normally
distributed with µ = 60:01mm and σ = 0:003mm.
(a) What is the probability that a randomly selected screw is out of specification
if the tolerance interval is [LSL; USL] = [60:00; 60:04]mm?
(b) The process capability index is defined as cpk = min(USL - µ; µ - LSL)=(3σ).
Calculate cpk and interpret the result.
(c) For several applications, an industry standard is cpk 2. What is an economically reasonably parameter combination to reach the industry standard?