Question

A production facility produces aluminum tubes through several steps that include machining, washing, removing dirt and oils and bushing pressing. These tubes are then sold to an assembly facility to be used in axle production. Several types of defects are present while producing these tubes. The following table shows some defect types and their numbers. Data is also available

Defect Type	Number of Defects
Mis-location	63
Miscellaneous	30
Bushing depth	19
Two bearings in a tube	9
Machine adjustment	7
Bearing bore	6
Bushing machine	6
Dropped part	4
Seal bore	1
Bushing bore	1

1. Use Pareto analysis to identify the “vital few” defect types that contributed to defective tubes during production.

2. If the total number of samples tested is 3000, what is value for the defects per million opportunities (DPMO)? What is the sigma level associated with this DPMO?

Answer 1

Answer 1

Following is the table used for preparing Pareto chart:

Pareto Chart is as follows:

From the Pareto chart given above, it can be seen that 4 defect types account for around 80% of defects. These 4 defect types ("vital few") are  Mis-location, Miscellaneous, Bushing depth, and Two bearings in a tube.

Answer 2

Here, Sample size = 3000

Number of defect opportunities = 10

Total number of defects = 146

DPMO = (146*1000000)/(3000*10)

DPMO = 4866.67

Sigma Level = 4.09 (Obtained using online Sigma level calculator screenshot attached)