The design of a bearing for automobile axle specifies the diameter of the bearin

ID: 3234836 • Letter: T

Question

The design of a bearing for automobile axle specifies the diameter of the bearing to be 1.250 inches ± 0.005 inch.

(i) If the mean diameter is 1.250 inches with a standard deviation of 0.003, determine the fraction of nonconforming bearings. (4 pts)

(ii) If 10,000 bearings are produced using this process, approximately how many bearings will be nonconforming? (2 pts)

(iii) Calculate the process-capability ratio of the process. (3 pts) (iv) Interpret the process-capability ratio found in part (ii). (2 pts)

(i) Fraction of non - conforming bearings can be calculated by estimating the probability of automobile axles outside the specifications.

so Pr( X > 1.250 + 0.005 and X < 1.250 - 0.005) = 1 - Pr (1.245 <= X <= 1.255)

where X is the diameter of Axle

so Pr (1.245 <= X <= 1.255) = ?

Here value of Z = (1.255 - 1.250)/ 0.003 = 1.67

so Pr( X > 1.250 + 0.005 and X < 1.250 - 0.005) = 1 - Pr (1.245 <= X <= 1.255) = 1 - [(1.67) - (-1.67)]

here is the cumulative normal probability distribution.

so non conforming fractin = 1 - [0.9522 - 0.0478] = 0.0956

(ii) If 10,000 bearings are produced using this process, approximately how many bearings will be nonconforming?

Answer = Total nonconforming bearings = 10000 * 0.0956 = 956

(iii) process-capability ratio

Cp = (USL - LSL)/ 6 sigma = (1.255 - 1.245)/ (6 * 0.003) = 0.5555

(iv) Here we can interpret that the process is only 55.55% capable to produce 6 sigma level. Pro