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INTERVAL ESTIMATION PROCESS CAPABILITY INDEX

P. Bahmani
S.M.T. Fatemi Ghomi M. Nikoukar Zanjani

M.Sc.Degree Department of Mathematics and Computer Science Amirkabir
University of Technology, [email protected] Professor Department of Industrial
Amirkabir University of
Technology,Tehran,Iran [email protected] Assistant Professor Department of
Mathematics and Computer Science
Amirkabir University of
Technology,Tehran,Iran

Abstract: Several sampling distribution properties of the estimator for Cpk are presented under the assumption that the data are normal, independent and identically distributed. In this paper using these assumptions, the expectation, variance and skewness are calculated by statistical methods, since the sampling distribution is weakly skewed, it is concluded that a symmetric interval estimator for Cpk might be reasonable. Also a symmetric interval estimator has been developed.

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!” #$!% : Cpk : 3 4 .’%&0 %1 2 Cpk +,) – +/ ( )$ * .’%”&
1268732040128

Downloaded from ijiepm.iust.ac.ir at 16:24 IRST on Saturday November 4th 2017

Downloaded from ijiepm.iust.ac.ir at 16:24 IRST on Saturday November 4th 2017

> ?( .’% +$= Cpk $! 789 ; ‘9 <(! + +5(6/ +,) .’% &0 [email protected] $! 789
+,) -7 @ 9 +; B/ +6 @ :
+9 GHMN @ ; +5(; HMN > ‘L *
GH ‘% (LSL ) *(Q (USL) O E PE
:0 + %1

C p =PCR =USL LSL

− (S)

(6 U1 P Vσ.’% 9 (6 U1 !) .0 + &5!% ‘% W76 9 0 &5!% (X! !; ” 9 +; G6)= : = Y% 9 (6 U1 + &,

Cˆp =PCRˆ =USL LSL

− (Z)
6σˆ
110454015473

.
> GH 9 +; ; 0 + & C(D E B7F
. I ‘(;
9 +; K7 ( + ; +J0 +K
.’% (ProcessCapabilityRatio) 9 +; ‘L ; &5!%

/ / :
// :
[email protected]
! “#
[email protected]
!”#”$ %& ‘” ()
[email protected]
758611-54259

⇒ Cˆ pk = USL − LSL − USL + LSL − 2X
6S6S

Cˆpk a) .0 l m? Cpk Cˆ pk ‘% l”! n l!E V
I [_^] LD ? V ],! Y% [9 \6 +; %1 ?( , B/ * .’%&0
:[`]’% &0 .’% Cpk % >
\6 GH Cpk B/ J *( ; &0 I 9
σ(6 U1 μ *(,( ” Xi ; n9 * ‘1
GH (k) = Cˆpk !L” 6D P$!L o7=E $ K% ; (X! > bK6 P/5 :?;(F !Q ?;(F t (X! >
⎛μ ⎛ USL LSL−⎞ ⎞ n ⎜ − ⎜⎟ ⎟
1524843-106731

(n−1) D ⎝⎝2⎠ ⎠ σ
n9 789 %1 a) .[r fq] ” V ‘% !J .’% PKN Cˆ pk >;
%1 – +/ ( , G .h(I &5!% 789
Cˆ pk .
\7!M J0 Cˆ pk – +/( [u] t )$ * J ; P$!L . %1 [email protected] G8 2 Cˆ pk – +/( :V 0 [email protected]# (k) = .h(I + %1

489215-58927

Cˆ pk = USL LSL−− USL LSL+− 2X
6S6S

:h a= −USL LSL b USL L, = + SL ]”(X! ((X

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