A company manufactures a product that has a design nominal)target width of 5 inches with tolerances of inch.The process that produces the product has a mean of 4.995 inches and a standard deviation of 0.01 inch.The process capability index for this process is
A)1.67
B)1.5
C)-1.5
D)-1.67

Question

A company manufactures a product that has a design nominal)target width of 5 inches with tolerances of  inch.The process that produces the product has a mean of 4.995 inches and a standard deviation of 0.01 inch.The process capability index for this process is
A)1.67 
B)1.5 
C)-1.5 
D)-1.67

Quizplus · Accepted Answer

The process capability index (Cpk) is calculated as the minimum of two ratios:

Cpk = min[(USL - mean)/3σ, (mean - LSL)/3σ]

where USL and LSL are the upper and lower specification limits, respectively.

In this case, the USL is 5.01 inches (5 + 0.01) and the LSL is 4.99 inches (5 - 0.01).

Substituting these values and the given mean and standard deviation into the formula, we get:

Cpk = min[(5.01 - 4.995)/(3 x 0.01), (4.995 - 4.99)/(3 x 0.01)]
    = min[0.5, 0.1667]
    = 0.1667

Since the minimum of the two ratios is less than 1, the process is not capable of meeting the specifications.

The best choice is therefore B, which is the only option that corresponds to a value less than 1.

A Company Manufactures a Product That Has a Design Nominal)target