KALI, Inc., manufactures home appliances that are marketed under
a variety of trade names. However, KALI does not manufacture every
component used in its products. Several components are purchased
directly from suppliers. For example, one of the components that
KALI purchases for use in home air conditioners is an overload
protector, a device that turns off the compressor if it overheats.
The compressor can be seriously damaged if the overload protector
does not function properly, and therefore KALI is concerned about
the quality of the overload protectors. One way to ensure quality
would be to test every component received through an approach known
as 100% inspection. However, to determine proper functioning of an
overload protector, the device must be subjected to time-consuming
and expensive tests, and KALI cannot justify testing every overload
protector it receives.
Instead, KALI uses an acceptance sampling plan to monitor the
quality of the overload protectors. The acceptance sampling plan
requires that KALI's quality control inspectors select and test a
sample of overload protectors from each shipment. If very few
defective units are found in the sample, the lot is probably of
good quality and should be accepted. However, if a large number of
defective units are found in the sample, the lot is probably of
poor quality and should be rejected.
The quality control manager requested a producer's risk of 0.10
when
p0 was 0.04 and a
consumer's risk of 0.20 when
p1 was 0.25. Consider the
acceptance sampling plan based on a sample size of 20 and
an acceptance number of 1. Answer the following questions.
(a)
What is the producer's risk for the
n = 20, c =
1
sampling plan? (Round your answer to four decimal places.)
__________
(b)
What is the consumer's risk for the
n = 20, c =
1
sampling plan? (Round your answer to four decimal places.)
________
(c)
Does the
n = 20, c =
1
sampling plan satisfy the risks requested by the quality
control manager? Discuss. (Select all that apply.)
The producer's risk is acceptable since it is less than
0.10.
The producer's risk is not acceptable since it is greater than
0.10.
The consumer's risk is acceptable since it is less than
0.20.
The consumer's risk is not acceptable since it is greater than
0.20.