Comparison of Different Level Sampling Plans in Z1.4
The following operating characteristic curves show the effect of using different Special or
General Inspection Level sampling plans in Z1.4. The set of operating characteristic curves,
shown below, represent all normal inspection sampling plans available in Z1.4 for an AQL value
of 1%. There are 9 such plans with sample size code letters E, H, J, K, L, M, N, P, and Q.
As you can see by comparing these operating characteristic curves for various sample size code
letters, there is very little loss of statistical power for values of quality (%defective) in the
neighborhood of the AQL or better (as it should be since plans being compared all have the same
specified AQL). The only issue would be if the slight loss of statistical power for quality levels
worse than the AQL would justify staying with the larger sample size plans. When you look at
the operating characteristic curves being compare for each case, you will note that each plan will
accept good quality equally well and each plan will reject very poor quality (quality levels at the
maximum RQL for all plans) equally well. The only measurable differences exist for quality
levels between the AQL and maximum RQL.
Sample Sample Maximum
%Defective Where
Size Code Size (n)
#(c)
Probability of Acceptance
Letter
Defectives
Equals 50%
E
13
0
5.19
H
50
1
3.33
J
80
2
3.33
K
125
3
2.94
L
200
5
2.84
M
315
7
2.43
N
500
10
2.13
P
800
14
1.83
Q
1250
21
1.73
In order to compare the operating characteristic curves for several of the inspection levels
[S-3, S-4, I, and II (the current level being used)] for various lot sizes in Z1.4, the
operating characteristic curves for the appropriate sampling plans are presented below.
LOT SIZE: 1.2K - 3.2K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: E, G(converts to H), H, and K
As reflected above, the level II plan (K: n=125, c=3) has a 50% probability of accepting
quality levels around 2.94% defective, the level S-4 and I plan (H: n=50, c=1) have a
50% probability of accepting quality levels around 3.33% defective, and the level S-3
plan (E: n=13, c=0) has a 50% probability of accepting quality levels around 5.19%
defectives. There is certainly very little variation in statistical power between the level I,
II, and S-4 plans above and very little difference from the level S-3 plan.
LOT SIZE: 3.2K - 10K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: F(converts to E), G(converts to H), J, and L
As reflected above, the level II plan (L: n=200, c=5) has a 50% probability of accepting
quality levels around 2.84% defective, the level I plan (J: n=80, c=2) has a 50%
probability of accepting quality levels around 3.33% defective, the level S-4 plan (H:
n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defective and
the level S-3 plan (E: n=13, c=0) has a 50% probability of accepting quality levels around
5.19% defectives. There is certainly very little variation in statistical power between the
level I, II, and S-4 plans above and not a major difference from the level S-3 plan.
LOT SIZE: 10K - 35K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: F(converts to E), H, K, and M
As reflected above, the level II plan (M: n=315, c=7) has a 50% probability of accepting
quality levels around 2.43% defective, the level I plan (K: n=125, c=3) has a 50%
probability of accepting quality levels around 2.94% defective, the level S-4 plan (H:
n=50, c=1) has a 50% probability of accepting quality levels around 3.33% defective and
the level S-3 plan (E: n=13, c=0) has a 50% probability of accepting quality levels around
5.19% defectives. There is certainly very little variation in statistical power between the
level I, II, and S-4 plans above and not a major difference from the level S-3 plan.
LOT SIZE: 35K – 150K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: G(converts to H), J, L, and N
As reflected above, the level II plan (N: n=500, c=10) has a 50% probability of accepting
quality levels around 2.13% defective, the level I plan (L: n=200, c=5) has a 50%
probability of accepting quality levels around 2.84% defective, the level S-4 plan (J:
n=80, c=2) has a 50% probability of accepting quality levels around 3.33% defective and
the level S-3 plan (H: n=50, c=1) also has a 50% probability of accepting quality levels
around 3.33% defectives. In this case there is very little variation in statistical power
between the level I, S-3, and S-4 plans above and not a major difference from the level I
plan.
LOT SIZE: 150K – 500K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: G(converts to H), J, M, and P
As reflected above, the level II plan (P: n=800, c=14) has a 50% probability of accepting
quality levels around 1.83% defective, the level I plan (M: n=315, c=7) has a 50%
probability of accepting quality levels around 2.43% defective, the level S-4 plan (J:
n=80, c=2) has a 50% probability of accepting quality levels around 3.33% defective and
the level S-3 plan (H: n=50, c=1) has a 50% probability of accepting quality levels
around 3.33% defectives. In this case there is almost no variation in statistical power
between the S-3 and S-4 plans above and not a major difference from the level I and level
II plans.
LOT SIZE: > 500K
LEVEL S-3, S-4, I, and II
SAMPLE SIZE CODE LETTER: H, K, N, and Q
As reflected above, the level II plan (Q: n=1250, c=21) has a 50% probability of
accepting quality levels around 1.73% defective, the level I plan (N: n=500, c=10) has a
50% probability of accepting quality levels around 2.13% defective, the level S-4 plan
(K: n=125, c=3) has a 50% probability of accepting quality levels around 2.94%
defective and the level S-3 plan (H: n=50, c=1) has a 50% probability of accepting
quality levels around 3.33% defectives. In this case there is very little variation in
statistical power between the S-3 and S-4 plans , very little difference between the level I
and II plans and not a major difference between all four.
SUMMARY:
When one has a choice of inspection level, the decision should be based on a combination
of things such as (a) the sampling cost, (b) the level, power, of protection afforded by the
sampling plan, (c) the marginal increase in power associated with a larger sample size
plan, (d) the current defect rate being produced by the process, (e) the historical stability
of the process, (f) the effectiveness of process controls during production, and (g) the
seriousness of accepting lots with “marginal” quality. While all of the available sampling
plans will protect you against accepting lots with marginal quality, my recommendation
would be to allocate your quality resources to process control activities and use your
sampling plans to detect serious breakdowns in the lot quality, in the event your process
controls fail to detect this breakdown. The following table for plans with an AQL of 1%
summarizes the lot quality for inspection levels S-3, S-4, I, and II where the probability
of accepting a lot is 50%.
INSPECTION LEVEL
LOT SIZE
S-3
S-4
I
II
1.2K - 3.2k
5.19
3.33
3.33
2.94
3.2K - 10k
5.19
3.33
3.33
2.84
10K - 35K
5.19
3.33
2.94
2.43
35K - 150K
3.33
3.33
2.84
2.13
150K - 500K
3.33
3.33
2.43
1.83
>500K
3.33
2.94
2.13
1.73
LOT QUALITY - % Defective where
Probability of Acceptance Equals 50%
Based on the results presented above, it is my opinion that you gain very little additional
power by using inspection level II plans. Indeed, I would suggest that inspection level S-4
or maybe even S-3 plans, coupled with effective process controls would afford you
adequate protection and insure release of quality products.
In the event you chose to use inspection level S-4 plans, for lot sizes greater that 1.2k,
you would end up at one of three possible sampling plans (H: n=50, c=1), (J: n=80, c=2)
or (K: n=125, c=3) depending on your lot size. The operating characteristic curves for
these three plans are given below. If these plans afford you with the protection you feel
is necessary, given effective process controls, it would seem logical to select inspection
level S-4.
In the event you chose to use inspection level S-3 plans, for lot sizes greater that 1.2k,
you would end up at one of two possible sampling plans (F: n=13, c=0), or (H: n=50,
c=1) depending on your lot size. The operating characteristic curves for these two plans
are given below. If these plans afford you with the protection you feel is necessary, given
effective process controls, it would seem logical to select inspection level S-3. You will
note that the c=0 plan is far weaker than the other plan recommended, as are all c=0
sampling plans.