Question

100 bottles entered a bottle-filling process that has three main stags.

The first one has three possible failures.

The second has four possile failures.

The third has five possible failures.

The first stage produced 27 defects. The defects were found in 10 bottles.

The second stage produced 57 defects . The defects were found in 15 bottles.

The third stage produced 64 defects. The defects were found in 20 bottles.

Determine:

1. DPMO [10 points]

2. SQL(Approximately)[5points]

3. PPM [5 points]

Answer 1

DPMO= (total number of defects found in a sample/ (sample size*number of defect opportunity found per unit in the sample))*1000000

The first stage:

DPMO= (27/10*3)*1000000 = 8100000

The second stage:

DPMO= (57/15*4)*1000000 = 15200000

The third stage:

DPMO= (64/20*5)*1000000 = 16000000

PPM= (Total number of defective units found in a sample/ sample size)*1000000

The first stage:

PPM= (10/100)*100000 = 10000

The second stage:

PPM= (15/100)*100000 = 15000

The third stage:

PPM= (20/100)*100000 = 20000