# The specifications for a plastic liner for a concrete highway project calls for thickness...

## Question:

The specifications for a plastic liner for a concrete highway project calls for thickness of 4.0mm plus or minus 0.10mm. The standard deviation of the process is estimated to be 0.02mm.

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

The lower specification limit for this product = ?

The process capability index is Cpk = ?

## Process Capability

The process capability ratio and index are used in quality management to determine whether the range of the process is less than the tolerance interval, i.e., whether the process is capable.

The Upper Specification Limit for the product = USL = 4 + 0.10 = 4.1mm

The Lower specification Limit for the Product = LSL = 4 - 0.10 = 3.9mm

Assuming the process is centered, i.e., the average thickness of the plastic liners is exactly 0.4mm, the process capability index is equal to the process capability ratio, i.e., {eq}C_{pk}=C_p=\frac{\text{USL}-\text{LSL}}{6*\text{Standard Deviation}}=\frac{4.1-3.9}{6*0.02} = 1.67 {/eq} 