Average Outgoing Quality
Outline
• Average Outgoing Quality (AOQ)
• Average Outgoing Quality Limit (AOQL)
• Average Total Inspection (ATI)
• Average Fraction Inspected (AFI)
1
Average Outgoing Quality
• If a lot is accepted, it may contain some defective
items. Many of the items (N-n items in a single
sampling plan) not inspected may be defective.
• The items which are inspected and found defective,
may be
– Case 1: returned to the producer or
– Case 2: repaired or replaced by the producer.
• We assume Case (2).
2
Average Outgoing Quality
• If a lot is rejected, it may be subjected to a 100%
inspection. Such action is referred to as screening
inspection, or detailing. This is sometimes described
as an acceptance/rectification scheme.
• Again, There may be two assumptions regarding the
defective items. The defective items may be
– Case 1: returned to the producer or
– Case 2: repaired or replaced by the producer.
• We assume Case 2. So, if a lot is rejected, it will
contain no defective item at all. The consumer will get
N good items.
3
Average Outgoing Quality
• Thus, if there is an average of 2% defective items,
the accepted lots will contain little less than 2%
defective items and rejected lots will not contain any
defective item at all. On average, the consumer will
receive less than 2% defective items.
• Given a proportion of defective, p the Average
Outgoing Quality (AOQ) is the proportion of
defectives items in the outgoing lots. More precise
definition is given in the next slide.
4
Average Outgoing Quality
E{Outgoing number of defectives }
AOQ 
E{Outgoing number of items}
Let
Pa  P{lot is accepted | proportion of defectives  p}
N  Number of items in the lot
n  Number of items in the sample
5
Average Outgoing Quality
Case 1 is not discussed in class
Case 1 : Defective items are not replaced
Pa ( N  n ) p
AOQ 
N  np  p(1  Pa )( N  n)
If N is much larger than n,
Pa p
AOQ 
1  p(1  Pa )
6
Average Outgoing Quality
Case 2 : Defective items are replaced
Pa ( N  n ) p
AOQ 
N
If N is much larger than n,
AOQ  Pa p
7
Average Outgoing Quality
• Given a proportion of defective, we can compute the
Average Outgoing Quality (AOQ)
• As p increases from 0.0, the AOQ values increases
up to a limit called Average Outgoing Quality Limit
(AOQL), after which the AOQ values descend
continuously to 0.0. This is shown in the next slide.
8
AOQ Curve and AOQL
0.015
AOQL
Average
Outgoing
Quality
0.010
0.005
0.01 0.02
AQL
0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
LTPD
(Incoming) Percent Defective
9
Example: Suppose that Noise King is using rectified
inspection for its single sampling plan. Calculate the
average outgoing quality limit for a plan with n=110, c=3,
and N=1000. (Assume that the defective items are
replaced)
10
n
c
N
Proportion
Defective
(p)
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
110
3
1000
np
0.55
1.1
1.65
2.2
2.75
3.3
3.85
4.4
AOQL
0.01564264
Probability
of c or less
Defects
(Pa)
0.997534202
0.974258183
0.914145562
0.819352422
0.703039994
0.580338197
0.463309958
0.359447773
AOQ
0.004439
0.008671
0.012204
0.014584
0.015643
0.015495
0.014432
0.012796
11
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0.
00
5
0.
01
5
0.
02
5
0.
03
5
0.
04
5
0.
05
5
0.
06
5
0.
07
5
0.
08
5
0.
09
5
Average Outgoing Quality
Average Outgoing Quality
Proportion of Defectives
12
ATI and AFI
• Average Total Inspection (ATI)
ATI  nPa  N (1  Pa )  n  ( N  n)(1  Pa )
• Average Fraction Inspected (AFI)
ATI
AFI 
N
• Relationship between AOQ and AFI
AOQ  p(1  AFI)
13
Reading and Exercises
• Chapter 11
– Reading: all
– Problems: 11.3, 11.4, 11.7, 11.9, 11.11, 11.17
Notes:
• Disregard the reference to hypergeometric
distribution in 11.17
• Use Excel for repetitive calculations in 11.3, 11.4,
11.11 and 11.17
14