A component is produced on one of 4 production lines. All production lines will

Question

A component is produced on one of 4 production lines. All production lines will produce the parts at the same rate, i.e. probability of a single part coming from any one production line is 25%. Historically, each production line has a history of producing parts at a 2.5% defect rate. Production Line 1 produced parts for a short period of time with a 5% defect rate. Unfortunately, the manufacturer shipped the parts before learning of the issue on Production Line i. The customer tested 3 of the fuses and found 1 defect What is the probability that the lot of parts came from Production Line 1? (Hint: You will also need to use the Binomial distribution to determine the conditional probability of the defective part:s coming off the different production lines, e.g:

Explanation / Answer

Ans:

First use Binomial distribution for conditional probabilites of 1 defective from respective lines:

P(1 defect/line1)=3C1*0.051*0.952=0.1354

P(1 defect/line 2)=3C1*0.0251*0.952=0.0677

P(1 defect/line 3)=3C1*0.0251*0.952=0.0677

P(1 defect/line 4)=3C1*0.0251*0.952=0.0677

P(line 1)=P(line 2)=P(line 3)=P(line 4)=0.25

Now use Bayes Therom to calculate:

P(line 1/1 defect)=(0.1354*0.25)/[0.25*0.1354+0.25*0.0677+0.25*0.0677+0.25*0.0677]

=0.1354/[0.1354+0.0677+0.0677+0.0677]

=0.1354/0.3385

=0.4

So,the probabilty that lot of parts came from line 1=0.4

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.