ejercicios de aseguramiento de la calidad.xlsx

= desviació est = muestra = = LCS LCI

= =

14 OZ 0.1 36 0.01666667 14 + 14 -

3 3

A)

n

= = desviació est = Z =

B)

5 50 1.7 3

LCS LCI

= =

5.30! 47.6"

Z

=



LCS LCI

= =

51.53! 4!.46

L#s $%mites de c#ntr#$ s#n m&s estrictas' (er# e$ nive$ de c#n)an*a se a reduci

,at#s

 = ,4 ,3 L#s $%mites de c#ntr#$ s#n

0.41" 1."4 0.076

A) LCS LCI

/r&)ca  = =

57.75 + 57.75 -

0.41"  0.41" 

B) LCS LCI

/r&)ca 2 = =

1."4  0.076 

1.7! = 1.7! =

= Z = ,esviación e = n = A) LCI =

40 4 5 5 -

Z Z

LCS

=

+

B) LCI

=

-

3

LCS

=

+

3

 = ,4 ,3 L#s $%mites de c#ntr#$ s#n

0.41" 1."4 0.076

A) LCS LCI

/r&)ca  = =

57.75 + 57.75 -

0.41"  0.41" 

B) LCS LCI

/r&)ca 2 = =

1."4  0.076 

1.7! = 1.7! =

= Z = ,esviación e = n = A) LCI =

40 4 5 5 -

Z Z

LCS

=

+

B) LCI

=

-

3

LCS

=

+

3

2. (r#me

= = ,at#s de $a ta$a  = ,4 = ,3 = A)

B)

X LCS LCI

= =

R LCS LCI

= =

6 705 0.30! 1.777 0.3

+ -

,4 ,3

 

 

 

= =

#ra 1  3 4 5 6 7 ! " 10 11 1 13 14 15 16 17 1! 1" 0 1  3 4

edia

#ra 1  3 4 5 6 7 ! " 10 11 1 13 14 15 16

edia

2

3.5 3.1 3. 3.3" 3.07 .!6 3.05 .65 3.0 .!5 .!3 ."7 3.11 .!3 3.1 .!4 .!6 .74 3.41 .!" .65 3.! ."4 .64 ."!0!333

0.71 1.1! 1.43 1.6 1.17 0.3 0.53 1.13 0.71 1.33 1.17 0.4 0.!5 1.31 1.06 0.5 1.43 1." 1.61 1.0" 1.0! 0.46 1.5! 0."7 1.0375

. de $as meLCS 3.5 ."!0!333 3.1 ."!0!333 3. ."!0!333 3.3" ."!0!333 3.07 ."!0!333 .!6 ."!0!333 3.05 ."!0!333 .65 ."!0!333 3.0 ."!0!333 .!5 ."!0!333 .!3 ."!0!333 ."7 ."!0!333 3.11 ."!0!333 .!3 ."!0!333 3.1 ."!0!333 .!4 ."!0!333

2 n a$a  ,4 ,3

= = = = =

X LCS LCI R LCS LCI

= = = =

La media de $a muestra m de c#ntr#$. ,e$ mism# m# 1.61' tami Las muestras 3 : 5 est&n @uera de $#s $%mites de medias. Las causas asi;na$es deen determinarse : e$iminarse. a$ ve* a: un nuev# a:udante de (anader# 8ue carece de uen Auici# s#re e$ (es# de $#s (anes. edias LCS LCI 2an;# LCS LCI

6.56 5.!4 1.141 0

Muestra

Pieza1

1  3 4 5

6.3 6 6.3 6. 6. 6.5

= =

#.

14.050 OZ 13."50 OZ

1.7! = 1.7! =

5!.4"6 57.004

3.45 0.135

=

440

=

440

=

405

=

435

706.!4! 703.15

10.66 1.33!

."! 1.04 4 0.7" .! 0

+ ,4 ,3

 

 

 

3.7! .36 .336 0

s (e8ue9a es '64' $a ma:#r 3'41. m#s s#n ien dentr# de $#s $%mites #' e$ ran;# de $a muestra m&s ;rande es de $#s $%mites de c#ntr#$. #dem#s c#nc$uir 8ue e$ (r#ces# se r#$. Sin emar;#' $#s (rimer#s cinc# va$#res (ara $a media est&n (#r da> est# (uede ser e$ indici# de un (r#$ema en $as (rimeras eta(as

/r&)c#  4 3.5 3 6edia .5  1.5 1 0.5

6. de $as medi as LCS LCI

0

0

5

10

15

0

5

30

/r&)c# de 2an;#s .5  1.5 1 0.5 0

0

5

10 2a n;#

15 6.de ra n;#

0 LCS

5 LCI

30

mm mm

,B

r#medi#$D 1 16.3  15." 3 15.! 4 15.5 5 16.3 6 16. 7 16 ! 16.1 " 15." 10 16. 11 15." 1 15." 13 16.3 14 15." 15 16.3 16 16. 17 16.1 1! 15." 1" 16. 0 15." 1 15."  16 3 15.5 4 15.! 16

A)

Z n

= = = =

16  0.1 " 0.0!

16 + 16 B)

C#n

LCS LCI

= =

0.0! = 0.0! Z

= 16.1 15.!!

Pieza 2

Pieza 3

6 6 4.! 6 6.6

Pieza 4

5." 6.3 5.6 6. 6.5

Media

5." 5." 5. 5." 6."

Rango

6.05 6.05 5.475 6.075 6.65

0.4 0.4 1.5 0.3 0.4

16.0! LCS 15." LCI 3

aD ECu&$ es $a desviación est&ndar F de$ (r#ces#G EHu< va$#r ene G D Si * = 3' Ecu&$es s#n $#s $%mites de c#ntr#$ (ara $a ;r&)ca de $a mediaG cD ECu&$es s#n $#s $%mites de c#ntr#$ (ara $a ;r&)ca de ran;#sG dD E?st& e$ (r#ces# aA# c#ntr#$G

J ?,I 2K/O 2an;# Z

1 10 " 10 " 1 50 10 3 3.3 3

2 " " 11 11 10 50 10 

3 13 " 10 10 " 51 10. 4

4 10 10 11 10 10 51 10. 1

5 1 10 " 11 10 5 10.4 3

 10 10 ! 1 " 4" ".! 4

aD ECu&$ es $a desviación est&ndar F de$ (r#ces#G EHu< va$#r ene G  F = 0.61 .3606! D Si * = 3' Ecu&$es s#n $#s $%mites de c#ntr#$ (ara $a ;r&)ca de $a media CL 10 3 0.61 11.!3 LCS 11.!46315 LCI !.17536!53 SK,O = 0'577 LCS 11."041 LCI !.0"5" cD ECu&$es s#n $#s $%mites de c#ntr#$ (ara $a ;r&)ca de ran;#sG 2K/O S?2O2 .115 2K/O IKM?2IO2 0 LCS2 6."7"5 LCI2 0

! 10 11 10 ! " 4! ".6 3

" 13 10 ! 10 ! 4" ".! 5

# ! ! 1 1 " 4" ".! 4

dD E?st& e$ (r#ces# aA# c#ntr#$G S%' tant# $a media : $#s ;r&)c#s de distriución indican (r#ces# es en c#ntr#$

1$ 10 1 " ! 1 51 10. 4

,etermine $#s $%mites de c#ntr#$ su(eri#r e in@eri#r : $as medias ;$#a$es (ara $as ;r&)cas de  : 2. ,iuAe $a ;r&)ca re(resentand# $#s va$#res de $as medias : de $#s ran;#s muestra$es. EL#s dat#s indican 8ue e$ (r#ces# est& aA# c#ntr#$G E#r 8u< s% # (#r 8u< n#G ?S2

?,I ? 2K/O 1 10.00 0.011  10.00 0.014 3 ".""1 0.007 4 10.006 0.0 5 ".""7 0.013 6 ".""" 0.01 7 10.001 0.00! ! 10.005 0.013 " ".""5 0.004 10 10.001 0.011 11 10.001 0.014 1 10.006 0.00" sumat#ria 10.006 0.13! edia 10.0005 0.0115 ?S2

?,I ? edia de  LCS LCI 1 10.00 10.0005 10.0071 ".""3!65  10.00 10.0005 10.0071 ".""3!65 3 ".""1 10.0005 10.0071 ".""3!65 4 10.006 10.0005 10.0071 ".""3!65 5 ".""7 10.0005 10.0071 ".""3!65 6 ".""" 10.0005 10.0071 ".""3!65 7 10.001 10.0005 10.0071 ".""3!65 ! 10.005 10.0005 10.0071 ".""3!65 " ".""5 10.0005 10.0071 ".""3!65 10 10.001 10.0005 10.0071 ".""3!65 11 10.001 10.0005 10.0071 ".""3!65

aD  = ,4= ,3= edia 2an;#  LCSmedia LCImedia 2 LCS2 LCL2

0.577 .115 0 10.0005 0.0115 10.0071 ".""3!65 0.0435 0

10.01 10.005 10 ".""5 "."" "."!5 "."!

1

1 ?S2

10.006

10.0005

10.0071

2K/O edia de 2 LCS LCI 1 0.011 0.0115 0.0435  0.014 0.0115 0.0435 3 0.007 0.0115 0.0435 4 0.0 0.0115 0.0435 5 0.013 0.0115 0.0435 6 0.01 0.0115 0.0435 7 0.00! 0.0115 0.0435 ! 0.013 0.0115 0.0435 " 0.004 0.0115 0.0435 10 0.011 0.0115 0.0435 11 0.014 0.0115 0.0435 1 0.00" 0.0115 0.0435

".""3!65

0 0 0 0 0 0 0 0 0 0 0 0

#d#s $#s (unt#s de dat#s de$ ;r&)c# estan dentr# de sus $%mites de c#ntr#$.

0.03 0.05 0.0 0.015 0.01 0.005 0

1

Z= 1  F = 0.!!67513 3.4641016

/2-MICO ,? 6?,I-S

3

4

?,I ?

5

6

7

edi a de e

!

" LCS

10

11 LCI

1

/2-MIC- ,? 2-K/OS



3

4 2K/O

5

6

7

edi a de 2

!

" LCS

10 LCI

11

1

,OS 2an;# Z n ,4 ,3

3.5 3 ! 1.!64 0.136

LCS2 LCI2

6.05! 0.44

aD n Z

100 3 0.0115

N SOKI?K,O H? LII? n 50 * 3

0.0115

LCS

LCS

0.05145

LCI

LCI

-0.0145

LCI

LCI

0

CD K= 100 Z= 

?$ LCI (uede $$e;ar tan aA# c#m# cer#' ( es sicamente (#si$e tener men#s de 0

LCS

0.03"3

LCI

-0.00"3

LCI

0

S 50 2IZ=

0.01745

0.06735

-0.03735 0

 

er# n# (uede ser ne;ava (#r8ue n# de@ectu#s#.

n=100 ?,I 1-mediaD 2IZ LCS LCI 0.0 0."! 0.014 0.06 -0.0 0.04 0."6 0.01"5"5" 0.0"!7!775 -0.01!7!7! 0.06 0."4 0.0374!6! 0.1314605 -0.011461 0.0! 0." 0.071"3 0.1613!7"6 -0.0013!! 0.1 0." 0.03 0.1" 0.01

0 0 0 0 0.01

,I ,?M?COS ,?M?COS ,IS  ?S2S K

1 7

 6

3 6

4 "

5 5

6 6

57 10 100 1000 0.057

0.03 LCS LCI LCI

0.166 -0.016 0

?$ (r#ces# est& @uera de c#ntr#$ en e$ te (róim#s 3 d%asD.

7 0

rcer d%a de $a

! !

" "

10 1

57

0.005435""

LCS LCI LCI

0.031307"7 -0.00130! 0

0.00!1!!! LCS LCI

0.05"65664 0.01034336

?n e$ de(artament# de (r#cesamient# de dat#s de$ Nanc# de /e#r;ia traaAan cinc# #(erad#res (ara e@ectuar $a entrada de dat#s. ,iariamente' durante 30 d%as' e$ nQmer# de re;istr#s de@ectu#s#s en una muestra de 50 re;istr#s intr#ducid#s (#r est#s #(erad#res se a an#tad# de $a si;uiente manera % muestra 1 2 3 4 5  ! " # 1$ 11 12 13 14 15 1 1! 1" 1# 2$ 21 22 23 24 25 2 2! 2" 2# 3$

30 50=

% de de&e'tos 7 5 1" 10 11 ! 1 " 6 13 1! 5 16 4 11 ! 1 4 6 16 17 1 6 7 13 10 14 6 1 3 300

?sta$e*ca $#s $%mites de c#ntr#$ su(eri#r e in@eri#r c#n 3F



7500

0.040

√(( (1−)) /)

0.013"0

C

0.07717

C

0.00!3

?$ LCL n# (uede ser ne;av# deid# a 8ue e$ (#centaAe de de@ect#s nunca (uede ser men#r 8ue 0. $#s estandares de $a indusra n# s#n tran estrist#s c#m# $as de ;e#r;ina de$ anc#. ;e#r;ina esta$ece su $imite de c#ntr#$ su(eri#r a$ 0'077 = 7'7P de@ectu#s#' mientras 8ue $a industria (ermit

a$can*ar e$ 10P antes de rec$amar 8ue $a muestra esta @uera de c#ntr#$

?$ #s(ita$ Centra$ de ,etr#it usca meA#rar su ima;en (r#(#rci#nand# una e(eriencia (#si (acientes : sus @ami$iares. arte de$ (r#;rama de ima;enT inc$u:e c#midas sar#sas 8ue invit (acientes a c#mer a$iment#s 8ue tami