Component is produced on one of 4 production lines. All production lines will pr

Question

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 1. 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?

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

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