1. If our sampling plan calls for accepting a lot if one or fewer items from a s
ID: 371736 • Letter: 1
Question
1.
If our sampling plan calls for accepting a lot if one or fewer items from a sample of 12 are defective, what is the probability of rejecting the lot if it has 15% defects?
Express as a percentage rounded to two decimal places and do not show the percent sign (e.g. 86.432% would be expressed as 86.43).
2.
An organization is indifferent between 100% testing of a received lot and detecting defective parts later in the process when 7.5% of the incoming parts are defective.
Their acceptance sampling plan is to accept the lot if one or fewer items in a sample of 12 are defective.
If the lot actually has 5% defective items, what is the producer's risk?
Express as a percent with two decimal places without a percent sign (e.g. 84.346% would be shown as 84.35)
3.
The cost to do 100% inspection of incoming parts is $1.45 per item and the cost to replace a defect later in the process when the defect becomes obvious is $12.25.
At what proportion of actual defects is the the organization indifferent between 100% inspection, and accepting the lot and replacing the items later in the process?
Express as a decimal rounded to three places.
4.
If the cost of doing 100% inspection of all received units is $0.50 and the cost of replacing defective units when those defects become apparent later in the process is $15, at what proportion of defects would the organization be indifferent about whether or not to accept the lot without 100% inspection?
Answer with a decimal rounded to three places.
PLEASE HELP ANSWER ALL 4 TRYING TO GET READY FOR AN EXAM
Explanation / Answer
1.
PROBABLITY OF REJECTING IS 15% i.e,12@15%,no. of defects in 12 sample is 1.8
AND PROBABILITY OF ACCEPTANCE WILL BE1- 1.8/(12-1.8)=1-.177=.823
i.e,.823*100 i.e,82.3%
2
PRODUCER RISK FOR DETECTING RISK IS LOWER WHEN DEFECT IS LESS THAN ACTUALLY ESTIMATED.LOWER THE DEFECT WILL LOWER THE RISK OF DETECTING DEFECTS AND COST LEADING TO DEFECTS ALSO GET LOWER.
PRODUCER GOT BENEFIT OF (7.5 -5)% =2.5%
3
COST OF INSPECTING PER ITEM IS $1.45,
FOR 12 ITEM TOTAL COST WILL BE $1.45*12 =$17.4
IF ENTIRE INSPECTION IS REPLACED THEN COST WILL BE $12.25*12 =$147
PRPORTION WILL BE =$17.4/$147*100=11.84%
4
COST OF INSPECTING PER ITEM IS $.50,
FOR 12 ITEM TOTAL COST WILL BE $.5*12 =$6
IF ENTIRE INSPECTION IS REPLACED THEN COST WILL BE $15*12 =$180
PRPORTION WILL BE =$6/$180*100=3.33%
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