OC Curves for Double Sampling Plan - How are they Derived?

[magomago]

Hi all,

studying for CQE here and I have some questions about OC curves for doubling sampling plans I understand single sampling plans well and even modeled it matlab just fine.

However, shifting to a double sampling plan, I found that the book did a horrible job describing it as seen in the attachment.

so I did some googlies and found a better source that made MORE sense to me as seen bin the attachment.

but when I model it, I can't seem to get the right curve (See last attachment)

I spent a few hours and still can't crack this. I think it might be due to the double summation

Lets say I had sigma_from1_to3 (y) * sigma_from 1_to_3_(x)....the way I'm calculating this in matlab (See below) is like this

y1 *( x1 + x2 + x3) + y2 *( x1 + x2 + x3) + y3 *( x1 + x2 + x3)

Is that right? Conceptually it is: I'm assessing all different probabilities, of accepting a certain # of defectives in the second sample, relative to the first.

Any help?

clear all
close all
n1=50
ac1=0
re1=3

n2=75
ac2=3
re2=4

p=[0:.001:.2]

%% this is right for sure  Pacceptance if NCR <= ac1
PaTotal=[]
for d1 = 0:ac1
    MaxCombos = ...
    (factorial(n1) ./ (factorial(d1) .* factorial(n1-d1)))
    
    Pa1array=[]
    for ii = 1:length(p)
        Pa1_Dconstant_foraPvalue = p(ii).^d1 .* (1-p(ii)).^(n1-d1);
        Pa1array = [Pa1array; Pa1_Dconstant_foraPvalue];
    end
    
    Pa1 = MaxCombos .*Pa1array;
    PaTotal=[PaTotal Pa1];
end
Pa1Final = sum(PaTotal,2)
figure(1)
% pa1plot=plot(Pa1Final,'-xg')

%%
Pa1Pa2Total=[];
Pa2Total=[]

for d1_1 = ac1+1:re1-1
    MaxCombos = ...
    (factorial(n1) ./ (factorial(d1_1) .* factorial(n1-d1_1)))
    
    Pa1array=[]
    for ii = 1:length(p)
        Pa1_Dconstant_foraPvalue = p(ii).^d1_1 .* (1-p(ii)).^(n1-d1_1);
        Pa1array = [Pa1array; Pa1_Dconstant_foraPvalue];
    end
    Pa1_1 = MaxCombos .*Pa1array;
    
    
    for d2=0:ac2-d1_1
         MaxCombos = ...
        (factorial(n2) ./ (factorial(d2) .* factorial(n2-d2)))
        Pa2array=[];
        for jj = 1:length(p)
            Pa2_Dconstant_foraPvalue = p(jj).^d2 .* (1-p(jj)).^(n2-d2);
            Pa2array = [Pa2array; Pa2_Dconstant_foraPvalue];
        end
        Pa2 = MaxCombos .* Pa2array;
        Pa2Total=[Pa2Total Pa2];
    end
    
    Pa2Summed = sum(Pa2Total,2)
    
    Pa1Pa2 = Pa1_1.*Pa2Summed;
    
    Pa1Pa2Total =[Pa1Pa2Total Pa1Pa2];
        
    end
    Pa1Pa2Final = sum(Pa1Pa2Total,2)
   hold on, plot(p,Pa1Pa2Final) 
plot(p,Pa1Final,'r')            
        plot(p,Pa1Final+Pa1Pa2Final,'k')

got it =) if you immediately break it up into 2 quick for loops and not iterate it like we'd write it, it is much simpler and i get the right answer. the code is also a LOT more cleaner...

[Marc]

Thanks for letting us know how you solved it! We appreciate it!