% Uppgift 9.16
% Jan Rohlén
close all hidden    % Stäng alla öppna fönster på datorn
%% Molekylvikten 
X=[2048
2025
2017
1995
1983
1943
1940
1947
1972
1983
1935
1948
1966
1954
1970
2039
2015
2021
2010
2012
2003
1979
2006
2042
2000
2002
2010
1975
1983
2021
2051
2056
2018
2030
2023
2036
2019
2000
1986
1952
1988
2016
2002
2004
2018
2002
1967
1994
2001
2013
2016
2019
2036
2015
2032
2016
2000
1988
2010
2015
2029
2019
2016
2010
2000
2009
1990
1986
1947
1958
1983
2010
2000
2015
2032];


%% Beräkna autokorrelationen
figure
r=[];
korrtid=25;
N=length(X);
for k=0:korrtid;
    KORR=corrcoef(X(1:N-k),X(1+k:N));
    r=[r;KORR(1,2) ];
end
k=0:korrtid;
stem(k,r,'Filled')
set(gca,'Ylim',[-1,1])
title('Uppgift 9.16. Autokorrelationen','fontsize',18)
ylabel('Autokorrelationen','FontSize',12)


%% Shewhart för individuella data.

XM=mean(X);

RM=mean(abs(diff(X)))
s=RM/1.128;

CL=XM;
UCL=XM+3*s
LCL=XM-3*s


figure
hold
plot(X,'o-k','MarkerFacecolor','b')
plot(X*0+UCL,'r')
plot(X*0+LCL,'r')
plot(X*0+CL,'g')


%% Armamodell

% Lös ekvationen Y=AP

Y=X(2:N);
XD=X(1:N-1)
A=[ones(N-1,1), XD]


P=A\Y

% Plotta residualen

e=[];
for k=2:N;
    
    e=[e;X(k)-P(1)-P(2)*X(k-1)];
end
figure
hold
s=std(e);

XM=mean(e);
CL=XM;
UCL=XM+3*s
LCL=XM-3*s

plot(e,'o-k','MarkerFacecolor','b')
plot(X*0+UCL,'r')
plot(X*0+LCL,'r')
plot(X*0+CL,'g')
title('Uppgift 9.16c. Residualen','fontsize',18)
ylabel('e_t','FontSize',12)