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.  

A) The upper specification limit for this product​ = ? mm ​(round your response to three decimal​places).
B) The lower specification limit for this product = ? mm (round to three decimal palces)
C) The process capability index (CPk) = ? (round to three decimal places)
D) The upper specification lies about ? standard deviations from the centerline (mean thickness)

Answer 1

a) 5.10 mm

b) 4.90 mm

c) 1.67

d) upper specification lies at 5 standard deviations from mean.

Step-by-step explanation:

Given:

Mean = 5.0mm

Standard deviation = 0.02 mm

a) The upper specification limit:

5.0 + 0.10

= 5.10 mm

b) The lower specification limit:

5.0 - 0.10

= 4.90 mm

c) The process capability index (CPk):

Use the formula below to find the process capability index

`C_p_k = min ((USL - mean)/(3\sigma), (mean - LSL)/(3\sigma))`

Substitute figures:

`C_p_k = min ((5.1 - 5.0)/(3*0.02), (5.0 - 4.9)/(3*0.02))`

`C_p_k = min ((0.1)/(0.06), (0.1)/(0.06))`

`C_p_k = min( 1.67, 1.67)`

`C_p_k = 1.67`

d) The upper specification lies at a distance of (5.1-5) = 0.1 mm

Standard deviation = 0.02 mm

upper specification lies at:

`(0.1)/(0.02) = 5`

Therefore, upper specification lies at 5 standard deviations from mean.