The specifications for a plastic liner for a concrete highway project calls for

Question

The specifications for a plastic liner for a concrete highway project calls for thickness of 3.0 mm ±0.10 mm. The standard deviation of the process is estimated to be 0.02 mm The upper specification limit for this product = 3.100 mm (round your response to three decimal places) The lower specification limit for this product = 2.9 mm (round your response to three decimal places). The process is known to operate at a mean thickness of 3.0 mm. The process capability index (Cpk)-L (round your response to three decimal places)

Explanation / Answer

Standard deviation (SD )= 0.02 mm

Upper specification limit (USL) = 3.0 + 0.10 = 3.100 mm

Lower specification limit (LSL) = 3.0 - 0.10 = 2.900 mm

Mean = 3.0 mm

Cpu = (USL - Mean) / (3 x SD)

= (3.100-3.0)/(3x0.02)

= 0.100/0.06

= 1.667

Cpl = (Mean - LSL) /(3 x SD)

= (3.0-2.900)/(3 x 0.02)

= 0.100/0.06

= 1.667

Cpk = Minimum of (Cpu, Cpl)

= Minimum of (1.667,1.667)

= 1.667

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