# The specifciations for a plastic linear for a concrete highway project calls for thickness of...

## Question:

The specifciations for a plastic linear for a concrete highway project calls for thickness of 4.00mm {eq}\pm {/eq}. 0.10mm. The standard deviation of the process is estimated to be 0.22 mm

1) The process is known to operate at a mean thickness of 4.0 mmThe process capability index {eq}(C_pk) {/eq} = _____round your response to three decimal places

2) The upper specification limit lies about ?

## Process Capability

The process is considered capable if a sufficient amount of its output, usually six standard deviations, satisfies customer requirements. For centered process, the process capability ratio is calculated and compared to 1 to determine if a process is capable.

The upper specification limit is 4.00+0.10=4.10mm

The lower specification limit is 4.00-0.10=3.90mm

1) Finding the process capability index

As the process is centered, i.e., its average output is equal to the average requirement of exactly 4.00mm, its process capability index will be equal to its process capability ratio:

{eq}C_{pk}=C_p=\frac{\text{Upper Specification Limit}-\text{Lower Specification Limit}}{6\times \text{Standard Deviation}}\\ =\frac{4.10-3.90}{6\times 0.22}\approx 0.152 {/eq}

2) Finding the location of the upper specification interval

The upper specification limit lies about {eq}\frac{\text{Upper Specification Interval}-\text{Process Mean}}{\text{Standard Deviation}}=\frac{4.10-4.00}{0.22}\approx 0.455 {/eq} standard deviations above the process mean.