# The specifications for a plastic liner for a concrete highway project calls for thickness of 5.0...

## Question:

The specifications for a plastic liner for a concrete highway project calls for thickness of {eq}5.0 mm \pm 0.10 mm. {/eq} 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 places)

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

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

## Process Capability

A process is deemed capable if its output equivalent to the six standard deviations satisfies customer requirements to the output. The customer requirements are usually represented by the lower and upper specification (or tolerance) limits.

## Answer and Explanation:

The upper specification limit (USL) for this product = 5.0 + 0.10 = 5.1 mm

The lower specification limit (LSL) for this product = 5.0 - 0.1 = 4.9 mm

As the process is centered, its process capability index (CPk) is equal to its process capability ratio (Cp), which can be found as

Cp = Cpk = (USL - LSL)/(6*standard deviation)

= (5.1-4.9)/(6*0.02)

=1.667

The upper specification lies about (USL-Centerline)/standard deviation = (5.1-5.0)/0.02 = 5 standard deviations from the centerline (mean thickness)

#### Learn more about this topic:

Process Capability: Definition & Elements

from Business 112: Operations Management

Chapter 4 / Lesson 5
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