Question

the specification for a plastic handle calls for a length of 6.0 inches +- .2 inches. The standard deviation of the process is estimated to be 0.05 Inches. what are the upper and lower specification limits for this product.

Answer 1

The upper specification limit for the plastic handle is 6.2 inches, and the lower specification limit is 5.8 inches, with these limits defining the acceptable range for the handle length.

Step-by-step explanation:

The specification for a plastic handle is given as a length of 6.0 inches with a tolerance of ± 0.2 inches. This means the upper specification limit (USL) and the lower specification limit (LSL) are defined by adding and subtracting the tolerance to the target length respectively. The process standard deviation is 0.05 inches, but this does not affect the USL and LSL directly; it's a measure of the process variation.

The USL and LSL are calculated as follows:

• USL = Target Length + Tolerance = 6.0 inches + 0.2 inches = 6.2 inches
• LSL = Target Length - Tolerance = 6.0 inches - 0.2 inches = 5.8 inches

These limits are the range within which the plastic handle lengths should fall according to the given specifications.

Answer 2

a)

USL = 6.2 inches

LSL = 5.8 inches

b) Cp = 1.33

Cpk = 0.67

c)

Yes it meets all specifications

Step-by-step explanation:

The specification for a plastic handle calls for a length of 6.0 inches ± .2 inches. The standard deviation of the process is estimated to be 0.05 inches. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.1 inches. What is the Cp and Cpk for this process? Is this process capable of producing the desired part?

Given that:

Mean (μ) = 6.1 inches, Standard deviation (σ) = 0.05 inches and the length of the plastic handle is 6.0 inches ± .2

a) Since the length of the plastic handle is 6.0 inches ± .2 = (6 - 0.2, 6 + 0.2)

The Upper specification limits (USL) = 6 inches + 0.2 inches = 6.2 inches

The lower specification limits (LSL) = 6 inches - 0.2 inches = 5.8 inches

b) The Cp is given by the formula:

`Cp=((USL-LSL))/(6\sigma) =((6.2-5.8))/(6*0.05) =1.33`

The Cpk is given by the formula:

c)

The upper specification limit lies about 3 standard deviations from the centerline, and the lower specification limit is further away, so practically all units will meet specifications

`Cpk=min((USL-\mu)/(3\sigma),(\mu -LSL)/(3\sigma))=min((6.2-6.1)/(3*0.05),(6.1-5.8)/(3*0.05))=min(0.67,2)=0.67`