A supplier is producing a machined part for the transmission of your vehicle. the upper specification limit is 0.125 cm and the lower specification limit is 0.085. the process standard deviation for the process that makes this part is 0.008 and the process average is 0.105. what conclusion can be drawn from these process capability data?

Given

μ =0.105

σ =0.008

Specs: [0.085≤ x≤ 0.125]

Need to know probabilities of exceeding specs.

First lower limit:

P[x<0.085]

=Z ((0.085-μ ) / σ )

=Z ((0.085-0.105) / 0.008)

=Z (-2.5)

=0.0062

=0.62%

Next, probability of exceeding upper limit.

P (x<=0.125)

=Z ((0.125-0.105) / 0.008)

=0.9937903

=>

P (x>0.125)

=1-0.9937903

=0.0062

=0.62%

Therefore probability of parts not conforming to specs is (0.62+0.62) = 1.24%, or

98.76% of parts conform to specs.