Motorola used the normal distribution to determine the probability of defects an

Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 15 ounces. The process standard deviation is 0.2, and the process control is set at plus or minus 0.75 standard deviation. Units with weights less than 14.85 or greater than 15.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (to 0 decimals)? Through process design improvements, the process standard deviation can be reduced to 0.07. Assume the process control remains the same, with weights less than 14.85 or greater than 15.15 ounces being classified as defects. What is the probability of a defect (rounded to 4 decimals; getting the exact answer, although not necessary, will require Excel)? In a production run of 1000 parts, how many defects would be found (to 0 decimals)? What is the advantage of reducing process variation?

Explanation / Answer

1)with std deviation =0.2

probability of a a part to be ok=

therefore probability of defect =1-0.5467 =0.4533

hence number of defects to be found =np =1000*0.4533 =~453

2)

with std deviation =0.07

probability of a a part to be ok=

therefore probability of defect =1-0.9679  =0.0321

hence number of defects to be found =np =1000*0.0321 =~32

as we reduce process variation more number of parts will be produced with in tolerance and as a result less number of defects will be there.

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