Question

The specifications for a plastic liner for a concrete highway project calls for thickness of 5.0 mmplus or minus±0.10 mm. The standard deviation of the process is estimated to be 0.02 mm.  

The upper specification limit for this product​ = ? mm ​(round your response to three decimal​places).

The lower specification limit for this product = ? mm (round to three decimal palces)

The process capability index (CPk) = ? (round to three decimal places)

The upper specification lies about ? standard deviations from the centerline (mean thickness)

Answer 1

Answer and Explanation:

The computation is shown below:

Upper specification limit is

= 5 + 0.1

= 5.1 mm

Lower specification limit is

= 5- 0.1

= 4.9 mm

The process cabability index is

= min(USL - mean ÷ 3 × standard deviation , mean - LSL ÷ 3 × standard deviation)

= min((0.1 ÷ 3 ×0.02) , (0.1 ÷ 3 × 0.02))

= min(1.67,1.67)

= 1.67

Since Upper specification is 5.1 mm

And, the Mean line is 5 mm

So, the upper specification lies at a distance for

= 5.1 - 5

= 0.1 mm

Standard deviation is 0.02 mm

Hence, upper specification lies at

= 0.1 ÷ 0.02

= 5

This standard deviation from the means