OC curve for the single sampling plan N = 3000, n=89, c= 2
1
Slide 2
Probabilities of Acceptance for the Single Sampling Plan n =
89, c = 2 Assumed Process QualitySample size, n np 0 Probability of
acceptance, P a Percent of Lots Accepted 100P a P0P0 100P 0
0.011.0890.90.93893.8 0.022.0891.80.73173.1 0.033.0892.70.49449.4
0.044.0893.60.30230.2 0.055.0894.50.17417.4 0.066.0895.30.10610.6
0.077.0896.20.0555.5 2
Slide 3
Double Sampling Plan Inspect a sample of 150 from lot of 2400
If 1 or less Nonconforming units accept lots and stop If 4 or more
Nonconforming units the lot is not accepted and stop If 2 or 3
nonconforming units, inspect a second sample of 200 If 5 or less
Nonconforming units On both samples, Accept the lot If 6 or more
Nonconforming units On both samples The lot is not accepted
Graphical description of the double sampling plan: N=2400,n 1 =150,
c 1 =1, r 1 =4, n 2 =200, c 2 =5, and r 2 =6 3
Slide 4
OCC for Double Sampling Plan 4
Slide 5
OCC for a Multiple Sampling Plan 5
Slide 6
Type-A and Type-B OC curves: 6
Slide 7
Effect of n and c on OC curves: 7
Slide 8
Other Aspects of OC Curve Behavior 8
Slide 9
Average Outgoing Quality (AOQ). A common procedure, when
sampling and testing is non-destructive, is to 100% inspect
rejected lots and replace all defectives with good units. In this
case, all rejected lots are made perfect and the only defects left
are those in lots that were accepted. 9
Slide 10
) The Average Outgoing Quality (AOQ) is the average of rejected
lots (100% inspection) and accepted lots ( a sample of items
inspected ) Average Outgoing Quality Note that as the lot size N
becomes large relative to the sample size n, AOQ P ac p 10
Slide 11
Typically the term (N-n)/N is very close to 1; therefore, the
equation most often used is: Average Quality of Inspected Lots
11
Slide 12
Example If N = 10,000, n = 89, and c = 2, and that the incoming
lots are of quality p = 0.01. What is AOQ? AOQ = P ac p(N-n)/N = ?
12
Slide 13
Average Outgoing Quality (AOQ) for the Single Sampling Plan n =
89, c = 2 Assumed Process QualitySample size, n np 0 Probability of
acceptance, P a AOQ 100P ac p P0P0 100P 0 0.011.0890.90.93893.8
0.022.0891.8? 0.033.0892.70.4941.482 0.044.0893.6? 0.055.0894.5?
0.066.0895.30.1060.636 0.077.0896.20.0550.385 13
Slide 14
AOQ and Acceptance Sampling ProducerN=3000n=89c=2 Consumer 15
lots 2% nonconforming 11 lots 2% nonconforming 4 lots 2%
nonconforming 4 lots 0% nonconforming Figure 9-15 How acceptance
Sampling works 14
Slide 15
AOQ and Acceptance Sampling Total Number Number Nonconforming
11 lots- 2% Nonconforming 11(3000)=33,00033,000(0.02)=660 4 lots-
0% Nonconforming 4(3000)(0.98)=11,7 60 0 44,760660 Percent
Nonconforming (AOQ) = 660/44,760 X 100 =1.47% Figure 9-15
contd.
Slide 16
Average Outgoing Quality curve for the sampling plan N = 3000,
n = 89, and c = 2
Slide 17
A plot of the AOQ (Y-axis) versus the incoming lot p (X-axis)
will start at 0 for p = 0, and return to 0 for p = 1 (where every
lot is 100% inspected and rectified). In between, it will rise to a
maximum. This maximum, which is the worst possible long term AOQ,
is called the Average Outgoing Quality Level AOQL. Average Outgoing
Quality Level 17
Slide 18
Average Total Inspection (ATI) When rejected lots are 100%
inspected, it is easy to calculate the ATI if lots come
consistently with a defect level of p. For a LASP (n,c) with a
probability pa of accepting a lot with defect level p, we have: ATI
= n + (1 - pa) (N - n) where N is the lot size. 18
Slide 19
Example If a lot size N = 10,000, and sample size n = 89,
number of acceptance c = 2, find ATI at p = 0.01 19
Slide 20
20
Slide 21
Average Sample Number (ASN) For a single sampling (n,c) we know
each and every lot has a sample of size n taken and inspected or
tested. For double, multiple and sequential plans, the amount of
sampling varies depending on the number of defects observed.
21
Slide 22
Average Sample Number (ASN) For any given double, multiple or
sequential plan, a long term ASN can be calculated assuming all
lots come in with a defect level of p. A plot of the ASN, versus
the incoming defect level p, describes the sampling efficiency of a
given plan scheme. ASN = n1 + n2 (1 P1) for a double sampling plan.
22
Slide 23
Sampling Plan Design Suppose is known and the AQL is also known
then : Sampling plan with stipulated producers risk Sampling plan
with stipulated consumers risk Sampling plan with stipulated
producers and consumers risk can be designed. 23
Slide 24
Sampling Plan Design Stipulated Producers Risk = 0.05 AQL =
1.2% Pa=0.95 P0.95= 0.012 Assume values for C, find np0.95 for this
c value, calculate n 24
Slide 25
Sampling Plan Design Stipulated Consumers Risk = 0.10 LQ = 6.0%
Pa=0.10 P0.10= 0.060 Assume values for C, find np0.95 for this c
value, calculate n 25
Slide 26
Sampling Plan Design Stipulated Producers and Consumers risk =
0.10 = 0.10 AQL=0.9 LQ= 7.8 Find the ratio of P0.10/P0.95. From
table 9-4 C is between 1 and 2. Find n for c =1 and n for c =2.
26
Slide 27
Sampling Plan Design Have 4 plans. Select plan based on: Lowest
sampling size Greatest sampling size Plan exactly meets consumers
stipulation and is as close as possible to producers stipulation
Plan exactly meets producers stipulation and is as close as
possible to consumers stipulation 27