Question

In an automotive production process, the most important step is characterized by the body assembly. Even though processes such as engine and chassis assembly are crucial, putting all parts together is the step whose accuracy must be really high, as a manner to avoid rework and reduce the manufacturing costs. In this process, the insertion of brake disks is made. Going by these conditions, the premise for all acquired brake disks by this automotive industry is that 5% of them wear-out before 25,000 miles, while the other 5 percent of brakes exceed 35,000 miles. Determine the reliability of the brake disks at 24,000 miles, aware that the wear-out is normally distributed.

Answer 1

Since wear out is Normally distributated we will use Normal Distribution curve for our solution. For a Normal distribution curve where X is random variable (in miles), mu is mean, Sigma is std deviation.

Normal random variable z=(X-mu)/Sigma

Given that Prob(Z) =-5% for X= 25000 and Prob (Z) =5% for X=35000. Thus Mu= 30000

from the normal distribution charts Z=0.14

therefore sigma= (35000-30000)/.14 =35714.29

the question in particular is about x=24000 so z=(24000-30000)/35714.29 =.168

Thus reliability of brakes at 24000 miles is =100%-6.36%= 93.64% from the normal distribution charts