Question

# In an electrical circuit, the capacitance of a component should be between 25 and 40 picofarads...

In an electrical circuit, the capacitance of a component should be between 25 and 40 picofarads (pF). A sample of 25 components yields a mean of 30 pF and a standard deviation of 3 pF. Calculate the process capability index Cpk, and comment on the process performance. If the process is not capable, what proportion of the product is nonconforming, assuming a normal distribution of the characteristic?

Here USL = 40 and LSL = 25

and standard deviation = 3

mean = 30

Cpk = minimum value of ((USL - MEAN)/3*STANDARD DEVIATION), (MEAN - LSL)/3*STANDARD DEVIATION))

(USL - MEAN)/3*STANDARD DEVIATION) = (40-30)/3*3

= 10/9

1.1

(MEAN - LSL)/3*STANDARD DEVIATION) = (30-25)/3*3

= 5/9

= 0.56

minimum of (1.1, 0.56) = 0.56

therefore, Cpk = 0.56

Here the process is not capable as the value of Cpk is less than 1.

Now to calculate the proportion of product non conforming

we need to multiply Cpk with 3

3*0.56 = 1.7 (approx)

now we need to see the z value in -z table corresponding to 1.7

which is 0.1423

so the proportion of product which is non conforming is 0.1423

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