Question

6) We are Manufacturing Parts and those beyond +0.68 Standard Deviations away from the Mean are beyond the Upper Spec Limit and are scrap. Additionally, those parts below -1.645 Standard Deviations from the Mean are scrap as well. What is our expected scrap rate?

Answer 1

Mean of Manufacturing Parts = m

standard deviation of Manufacturing Parts = s

Upper Spec Limit : beyond +0.68 Standard Deviations away from the Mean

Upper Spec Limit : > m + 0.68*s

Lower Spec Limit : below -1.645 Standard Deviations from the Mean

Lower Spec Limit : < m -1.645*s

Let, X be the actual size

Scrap rate = P[ X > m + 0.68*s & X < m -1.645*s ]

Scrap rate = P[ X > m + 0.68*s ] + P[ X < m -1.645*s ]

Scrap rate = P[ ( X - m )/s > ( m + 0.68*s - m )/s ] + P[ ( X - m )/s < ( m -1.645*s - m )/s ]

Scrap rate = P[ Z > 0.68 ] + P[ Z < -1.645 ]

Scrap rate = 0.2483 + 0.05

Scrap rate = 0.2983