Question

A manufacturing process produces piston rings, with ID (inner diameter) dimension as shown above.
Process variation causes the ID to be normally distributed, with a mean of 10.021 cm and a standard
deviation of 0.040 cm.
a. What percentage of piston rings will have ID exceeding 10.075 cm? What percentage of piston rings
will have ID exceeding 10.080 cm? (4)

b. What is the probability that a piston ring will have ID between 9.970 cm and 10.030 cm? (This is the
customer’s specification that the supplier tries to provide .)
(ie.) If the specification is “9.970cm < ID < 10.030cm”, what %’age of piston rings are “out of spec”? (4)

c. Half (50%) of all piston rings have ID below 10.021 cm. What is the dimension corresponding to
the smallest 10%, and what is the dimension corresponding to the largest 10%? What is the
dimension corresponding to the smallest 20%, and what is the dimension corresponding to the
largest 20%

d. Piston rings with ID too small or too large have different problems that the assembly operation
(customer) would like to know about in advance.
From your results in b., how many parts in a production run of 5000 pieces would be above
specification? How many parts would be below specification?

Parts with large ID out-of-specification are charged back to the vendor at $2.00 each. Parts with
small ID out of specification are charged back at $1.25 each. What is the total expected penalty
cost (for the vendor) for the 5000 pieces?

Answer 1