Question

Acme Biotech requires all new employees to undergo a drug test screening.   As part of the collection process, key donor information is entered on a form referred to as the “Non-Federal Four-Part Drug Testing Custody and Control Form”. To test the effectiveness of the process, managers review randomly selected forms. It has been determined from earlier studies that six typical types of mistakes or errors are made when completing the form. Assume each Control Form represents one “unit”, and then calculate the following attribute quality measures:

1. Defects per unit (dpu)

2. Defects per opportunity (dpo)

3. Defects per million opportunities (dpmo)

4. Sigma capability (σ_cap)

Results from Sample of Drug Testing Custody Control Forms

Donor	Invalid Social Sec.	Wrong Phone number	Wrong D.O.B.	Missing Donor Signature	Missing Date of Signature	Missing Collection time	Number of Defects	Defective (Yes/No)
1	x					x
2
3	x	x	x
4
5						x
6	x
7
8				x
9
10
11			x		x
12
13
14						x
15		x	x
16
17						x
18
19
20	x
21

Answer 1

6 types of mistakes(defects) are there and we have to consider each control form as one "unit".hence there are total 21 units.

And count of all 6 types of mistakes is "15"(# of defects)

a) Defects per unit (DPU)

-- is number of defects(mistakes) divided by total number of units=(15/21)= 0.714286

b) Defects per opportunity (DPO)

-- is stated as total # of defects by total # of units = (15/21)= 0.714286

we can see that DPU and DPO both are same they are just different terminologies but have same meaning here.

c) Defects per million opportunities (DPMO)

-- is just the conversion of DPU or DPO per 1,000,000 (one million) units.

hence,DPMO=DPO*1000000= 0.714286*1000000 =0.714286*10^6 = 714286 in a million.

Hence there are 714286 defects in 1 million

d)Sigma capability (σ_cap):-

From DPMO we can calculate sigma by looking into the six sigma conversion tables.

So for here we need to look into value near to our DPMO value in table for sigma which is

see below snapshot-

the highlighted value.

here sigma cap= 0.9 and it will give 28 % yeild.