The Quality Manager for Microelectronics,Inc.is concerned about the quality of the batch of several thousand IC's (integrated circuits)which his company is about to ship.If the indifference point between complete inspection and shipment without inspection is 9% defectives,and he decides to sample 40 IC's (n = 40),what is the maximum number of sample defectives (c)for which this batch would be accepted for shipment without inspection?
A)0 defectives
B)1 defective
C)2 defectives
D)3 defectives
E)4 defectives

Question

Quizplus · Accepted Answer

To find the maximum number of sample defectives acceptable for shipment without inspection, we need to use the single-sampling plan for normal inspection at the indifference point, assuming a 10% risk of accepting a batch with more than 9% defectives. 
Using a binomial distribution with n=40 and p=0.09, we can calculate the probabilities of accepting a batch with different numbers of defectives:

- P(0 or 1 defectives) = 0.039
- P(0, 1 or 2 defectives) = 0.164
- P(0, 1, 2 or 3 defectives) = 0.467

From this, we can see that accepting up to 2 defectives gives us a probability of accepting a batch with more than 9% defectives of 16.4%, which is below the 10% risk we are willing to take. Therefore, the maximum number of sample defectives for which the batch would be accepted for shipment without inspection is 2.