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taha.ali@su.edu.krd
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esraa.haydier@su.edu.krd
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fatimah.hamarasool@su.edu.krd
ISSN 2709-6475
DOI: https://dx.doi.org/10.37940/BEJAR.2023.5.5.17
(BD-Chart)
(D-Chart)
Create a Bayesian panel for the number of weighted defects and
compare it with the Shewart panel
Prof.Dr. Taha Hussein Ali
Salahaddin University-Erbil
College of Administration & Economics
taha.ali@su.edu.krd
Lect. Israa Awni Haider
Salahaddin University-Erbil
College of Administration & Economics
esraa.haydier@su.edu.krd
Lect. Fatima Othman Hama Rasoul
Salahaddin University-Erbil
College of Administration & Economics
fatimah.hamarasool@su.edu.krd
Abstract
In this research, a proposal was made to create a Baez board for the number
of weighted defects (BD-Chart) and compare it with the Shewart board for the
number of weighted defects (D-Chart) through a simulation as well as using real
data and relying on a program in Mat lab designed for this purpose and was done
through the application Conclusion: The proposed panel was better than Stewart’s
panel for the weighted number of defects.
Key words: Quality control panels, weighted defects, BASE method.
(D-Chart)
wald
[5]
7
[2]
Daubechies
Minimax
(MATLAB)
D
[4]
(DD
Dodge,H.F.
Besterfield
8
100
4020
[8]
1
(0<dj<1djj
(j = 1, 2, 3)
Di
ji(i = 1, 2, …, m)
Cij
TTarget Line
2
m
j
[4]
1
t
Kt
(
ht
1
(
gt
(
ct
12
t
t13j
Dt
Ctj
t
13
jct
t
[4]
2
(The practical side)
(Experimental side)
(BD-Chart)
(D-Chart)A
30
51525354560
11050
603010D
45
3D
3
45
4BD
4
1000
1
D
BD
5
391.6006
136.7307
15
767.6814
219.8775
25
988.4277
275.1449
35
1168.9
321.7138
45
1324.1
361.5525
60
1528.9
415.4647
1
(Applied side)
30
[8]
230
1
120
7
143
13
120
19
121
25
107
2
94
8
134
14
116
20
108
26
105
3
89
9
97
15
127
21
131
27
143
4
162
10
145
16
92
22
119
28
132
5
150
11
128
17
140
23
93
29
100
6
82
12
83
18
60
24
88
30
60
2D
6030101050
B
5D
5
BD2
D
C
6BD
6
29
7BD
7
57
3
D
BD
3739
3962
6318
4454
1159
3470
5159
984
3BD984
D5159
(Conclusions)
D
BD984D5159
(Recommendations)
(References)
8. Ali, T.H, Rhhim, A.G. & Saleh, D.M. 2018. Construction of Bivariate F-control chart
with Application, Eurasian Journal of Science &Engineering ISSN2414-5629(Print),
ISSN 2414-5602 (Online).
9. Basterfield, 2009. Quality control, prentice Hall Englewood Cliffs, New York.
10. Grant, E.L. & Leavenworth, R.S., Statistical. 1980. Quality Control, McGraw-Hill,
International Book Company, London.
(D
% Poisson distribution m = 30; Lambda = 45; for i =1: m w = exp(-Lambda); u = rand; x(i) = 0; while u > w u = u-w ; x(i) = x(i)+1; w = (w* Lambda) / x(i) ; end x(i); end c = x ; d = [50 10 1] ; for i=1: m D(i)=d(1)*round(.6*c(i))+d(2)*round(.3*c(i))+d(3)*round(.1*c(i)); end D T = mean(D); T = [ones(size(D))*T] ; UCL = T+3*std(D) ; LCL = T-3*std(D) ; if LCL < 0 LCL = [zeros(size(D))]; end l = 1: m ; plot(l,D,'*-',l,T,'-',l,UCL,'-',l,LCL,'-') -----------------------------------------------------------------------------------------------
BD
% Poisson distribution m = 30; Lambda = 45; for i =1: m w = exp(-Lambda); u = rand ; x(i) = 0 ; while u > w u = u-w ; x(i) = x(i)+1; w = (w* Lambda) / x(i); end x(i) ; end c=x ; d=[50 10 1] ; k(1) = c(1); m = 1 r = 30 dc(1) = k(1)/ m
D(1)=d(1)*round(0.6*dc(1))+d(2)*round(0.3*dc(1))+d(3)*round(0.1*dc(1)) for t=2:r k(t) = k(t-1) + c(t-1) ; m = m+1 dc(t) = k(t) / m D(t)=d(1)*round(0.6*dc(t))+d(2)*round(0.3*dc(t))+d(3)*round(0.1*dc(t)) end D T = mean (D) T = [ones(size(D))*T] UCL = T + 3*std(D) LCL = T - 3*std(D) if LCL < 0 LCL = [zeros(size(D))] end e=1: r ; plot (e,D,'*-',e,T,'-',e,UCL,'-',e,LCL,'-')
-----------------------------------------------------------------------------------------------
(D
m=30 d = [50 10 1] ; c = [120 94 89 162 150 82 143 134 97 145 128 83 120 116 127 92 140 60 121 108 131 119
93 88 107 105 143 132 100 60]; for i = 1: m D(i)=d(1)*round(0.6*c(i))+d(2)*round(0.3*c(i))+d(3)*round(0.1*c(i)) end D T = mean(D) T = [ones(size(D))*T] UCL = T+3*std(D) LCL = T-3*std(D) if LCL < 0 LCL=[zeros(size(D))] end i = 1 : m plot (i,D,'*-',i,T,'-',i,UCL,'-',i,LCL,'-')
-----------------------------------------------------------------------------------------------
(BD
c(1) = 120 ; k(1) = c(1) ; m = 1 r = 29 d = [50 10 1]; dc(1) = k(1)/ m D(1)=d(1)*round(0.6*dc(1))+d(2)*round(0.3*dc(1))+d(3)*round(0.1*dc(1)) C = [94 162 150 82 143 134 97 145 128 83 120 116 127 92 140 60 121 108 131 119 93 88
107 105 143 132 100 60]; for t = 2: r k(t) = k(t-1) + c(t-1) ; m = m+1 dc(t) =k(t) / m D(t)=d(1)*round(0.6*dc(t))+d(2)*round(0.3*dc(t))+d(3)*round(0.1*dc(t)) end D T = mean(D) T = [ones(size(D))*T] UCL = T+3*std(D) LCL = T-3*std(D) if LCL < 0 LCL = [zeros(size(D))] end e = 1: r ; plot(e,D,'*-',e,T,'-',e,UCL,'-',e,LCL,'-')
