Question

The inspection department in an automobile final assembly plant checks cars coming off the line against 85 features that are considered critical-to-quality characteristics for customer satisfaction. During a one-month period, a total of 16,578 cars were produced. For those cars, a total of 1,989 defects of various types were found, and the total number of cars that had one or more defects was 512.

Determine:
(a) The number of defects per million opportunities and corresponding sigma level.
(b) The number of defects per million and corresponding sigma level.
(c) The number of defective units per million and corresponding sigma level.

Answer 1

a) DPMO = 1412 defects/million opportunities

Sigma level = 4.5

b) DPM = 119978 defects per million

Sigma Level = 2.7

c) DUPM = 30884 defective units per million.

Sigma Level = 3.3

Step-by-step explanation:

If we summarize the data given, we have:

Let's Assume A = Product Units = 16,578 units.

Let's Assume B = Defects = 1989 defects

Let's Assume C = Number defect opportunities per product = 85 defect opportunities.

Let's Assume D = Total defective units = 512

Solution:

a) Number of defects per million opportunities and corresponding six sigma level:

So, we have

DPMO = Defects per Million Opportunities = 1 million x
`(B)/(AxC)`

DPMO = 1,000,000 x
`(1989)/(16,578 x 85)` = 1412 defects/million opportunities

and this corresponds to the 4.5 six sigma level after interpolating between 4.4 and 4.6 six sigma level. Please refer to the table attached in the attachment.

b) Number of defects per million and corresponding sigma level.

DPM = Defects Per Million = 1 million x
`(B)/(A)`

DPM = 1,000,000 x
`(1,989)/(16,578)`

DPM = 119978 defects per million

This value correspond to 2.7 sigma level after interpolating between 2.8 and 2.6 sigma level. Please refer to the table in the attachment.

c) Number of defective units per million and corresponding sigma level.

DUPM = Defective Units Per Million = 1 million x
`(D)/(A)`

DUPM = 1,000,000 x
`(512)/(16,578)`

DUPM = 30884 defective units per million.

This correspond to 3.3 sigma level after interpolating between 3.4 and 3.2 sigma level. Please refer to the table shown in the attachment.

Answer 2

a) DPMO = 1411.51 defects per million opportunities with sigma level 4.5

b) DPM = 119,978.8 defects per million opportunities with sigma level 2.7

c) DUPM = 30,884.3 defective units per million with sigma level 3.3

Step-by-step explanation:

Total number of defects = 1,989

Number of defective cars = 512

Number of units = 16,578

Critical-to-quality characteristics = 85

(a) The number of defects per million opportunities and corresponding sigma level.

DPMO = 1,989/(16,578*85)

DPMO = 1,000,000*0.001411509

DPMO = 1411.51 defects per million opportunities

From the Sigma level table (with 1.5 sigma shift), the sigma level corresponding to 1411.51 is 4.5.

(b) The number of defects per million and corresponding sigma level.

DPM = 1,989/16,578

DPM = 1,000,000*0.11997828

DPM = 119,978.8 defects per million opportunities

From the Sigma level table (with 1.5 sigma shift), the sigma level corresponding to 119,978.8 is 2.7.

(c) The number of defective units per million and corresponding sigma level.

DUPM = 512/16,578

DUPM = 1,000,000*0.0308843045

DUPM = 30,884.3 defective units per million

From the Sigma level table (with 1.5 sigma shift), the sigma level corresponding to 34,865 is 3.3.