w4, Zarządzanie i Inzynieria Produkcji, Prognozowanie i symulacje

AYMaCF6@%
1PCNKZCTMaCFPKMCNQTQXGIQ%
1Wprowadzenie
<QFEZCTCPCNKZYTCUCELQPCSPGIQTZGSGIVEZCTQXGIQ)D
(
*
#"("%
Ia`XPGZCFCPKGDCFCEZC
RQNGICPCXYZPCEZGPKVQSCZQTZCEQXCPKVHVPMELKPKGNQTQXYEJ!USGPFV;
('
!B"#TG$
ZQPQX_C)!B"#EYMNKEZP_C'!B""%
D
(
/!
$
B
('
!B"#!
%
)!B"#!
&
'!B"#(
(
FNCB/$+%+&+****+1 !'"
<QQFICFPK_GEKVRQTUCEKHVPMELKPKGNQTQXGLTZGSGIV)D
(
*
(#%$$%$###$%&
!'"OVTKOYFQMQPC]E
FQMaCFPGLCPCNKZYTMaCFPKMCNQTQXGIQ
(
(
/D
(
!
$
B
('
!B"!
%
)!B"!
&
'!B" !("
COKCPQXKEKG0
'%TUXKGSFZK]EEZYMQNGLPQ]T]EXYTU_CRKG]PXCSUQ]TEKZOKGPPGL(
(
OCEJCSCMUGSNQTQXY
(%ZPCNG
]
Z]ESQZMaCFTZGSGIV)(
(
*
#"("%
)%ZDCFC]EMQSGNCELGRQOK_GFZYGNGOGPUCOKTZGSGIV)(
(
*
#"("%
AUYOEGNVRQTaV
^
ZYOYTK_GPCTU_GRVL_CEYOKPCSZ_GFZKCOK0UGTUTGSKK#XGSY[MCELCJKRQUGZY
QPQSOCNPQ
]
TEKTMaCFPKMCNQTQXGIQ%A!'"ZCDVSZGPKGXYTU_GRVLGXRQTUCEKLGFPGL
ZOKGPPGLNQTQXGL#PCUQOKCTUXPKGMU`SYEJOQFGNCEJZDVSZGPKGLGTURQTUCEKMQO$
DKPCELKNKPKQXGLZOKGPPYEJNQTQXYEJ!PR%1=!?"#1=91!?+@""%3QQFICFPK_GEKC
RQTUCEKZCDVSZG]PXGSY[MVLGOYJKRQUGZ_GQTMQSGNQXCPQ]TEKTMaCFPKMCNQTQXGIQ!VFZKGNC
QFRQXKGFZKPCRYUCPKGEZYTMaCFPKMKNQTQXGXSQZMaCFZKG!'"T_CZGTQD_CTMQSGNQXCPG"%
Uwaga:
<QPK
^
ZGLSQ
^
ZXC
^
ZCOYTZGSGISGTZU)(
(
*
#"("%
QTEYNVL_CEYFQQMQaC ZGSC #COKCPQXKEKG
LG
^
ZGNKZCVXC
^
ZYOY
^
ZGXCSUQ]T]E]TSGFPKCTZGSGIVSGTZULGTUS`
^
ZPCQFZGSC#UQRQXY
^
ZTZY
TZGSGITUCPFCSYZVLGOY#UZP%OQFY[MVLGOYPR%HVPMEL_GUSGPFV;
('
! "XTRQT`D
;
('
!B"/;
('
!B" "
"
!)"
FNCB%)%+&+***+1*%IFZKG
)
%
"
"
/
%
(
(
1
('$
KXYZPCEZCOYPCPQXQTZGSGISGTZU)(
(
*
#"("%
ZGXZQSV!("%
2Badanielosowo·sci
?GTUTGSKK>UGWGPTCTUQTVLGOYIFYEJEGOYVRGXPK]ETK_G
^
ZGGNGOGPUYTZGSGIV)(
(
*
#"("%
TRGaPKCL_CRQTUVNCUNQTQXQ]TEKRS`DY%?YOTCOYOXGSY[MCELCJKRQUGZYQNQTQXQ]TEK
(
1PCNKZCTMaCFPKMCNQTQXGIQ%AYMaCF6@%
TMaCFPKMC(
(
OCPCEGNVTUXKGSFZGPKGDSCMVPKGNQTQXGLTMaCFQXGLXSQZMaCFZKG!("%
AUYOEGNVMQPTUSVLGOYJKRQUGZ_GSQDQEZ_C
0
#
.DSCMXCPCNKZQXCPYOTZGSGIVPKGNQTQXGLTMaCFQXGL!XCSUQ]TEKTZGSGIV
GXCNVVL_CXTRQT`DNQTQXYFQQMCaCRQZKQOVZGSQXGIQ"
XQDGEJKRQUGZYCNUGSPCUYXPGL
0
$
.KTUPKGLGXCPCNKZQXCPYOTZGSGIVPKGNQTQXCTMaCFQXC%
3NCVRQSZ_CFMQXCPGIQEK_CIV)(
(
*
#"("%
QDNKEZCOYNKEZD_GTGSKK4SGTZUOQFGNV%
>GSK_CLGTUMC
^
ZFYRQFEK_CISGTZUZaQ
^
ZQPYXYa_CEZPKGZGNGOGPU`XFQFCUPKEJNVDVLGO$
PYEJQSCZNKEZD_GSGTZUFQFCUPKEJ>
$
KNKEZD_GSGTZUVLGOPYEJ>
%
#GNGOGPUYZGSQXG
RQOKLCOY%
1.je•zeli>
$
"&$i>
%
"&$
:CRQZKQOKGKTUQUPQ]TEK QFEZYUVLGOYFXKGMSYUYEZPGNKEZDYTGSKK4
!
K4
!
*UZPQF$
EZYUVLGOYXCSUQ]TEKMSYUYEZPGFNC
%
KFNC%
%
#ZUYO
^
ZG
&
'
&
'
4
!
/4
&
+>
$
+>
%
/4
&
+>
%
+>
$
&
'
&
'
%
%
!
4
/4
&
+>
$
+>
%
/4
&
+>
%
+>
$
!
UQPCRQZKQOKGKTUQUPQ]TEK PKGOCRQFTUCXFQQFSZVEGPKC
JKRQUGZYSQDQEZGL0
#
%;ZPCEZCUQ
^
ZGXCPCNKZQXCPYOTZGSGIVEZCTQXYOPKGOC
HVPMELKPKGNQTQXGLQSCZZCDVSZGPKC(
(
OCL_CEJCSCMUGSNQTQXY%:CUQOKCTULG
^
ZGNK4"4
!
NVD4
7G
^
ZGNK4
!
, 4 , 4
!
"4UQJKRQUGZ_G0
#
PCNG
^
ZYQFSZVEK]EXQDGEJKRQUGZYCNUGSPCUYXPGL0
$
ZCUGO
KTUPKGLGXCPCNKZQXCPYOTZGSGIV)(
(
*
#"("%
PKGNQTQXCTMaCFQXC%
2.je
•
zeli>
$
-&$lub>
%
-&$
BOKGPPCNQTQXC4F_C
^
ZYCTYORUQUYEZPKGFQSQZMaCFVPQSOCNPGIQ1!=+$"#IFZKG
GTUYOCUQSYXCSUQ]TEK]TSGFPKGLKXCSKCPELKZOKGPPGLNQTQXGL4XYZPCEZCOYZGXZQS`X
2=/
&>
$
>
%
1
#%
2$
%
/
&>
$
>
%
!&>
$
>
%
1"
!1%"1
%
AUGFYTUCUYTUYMC
7/
4
2=
2$
OCSQZMaCFPQSOCNPY1!$+%"%:CRQZKQOKGKTUQUPQ]TEK QFEZYUVLGOYXCSUQ]T]E
TUCUYTUYMKMSYUYEZPGLE
!
%
%
%
%
LGTUMXCPUYNGOSZ_GFV%
%
/C
IFZKGC
SQZMaCFVPQSOCNPGIQ1!$+%"%
ARSZYRCFMVIFYE
PKGOCRQFTUCXFQQFSZVEGPKCJKRQUGZY
SQDQEZGL0
#
PCRQZKQOKGKTUQUPQ]TEK QZPCEZCUQ#
^
ZGZCDVSZGPKC(
(
OCL_CEJCSCM$
UGSNQTQXY%ARSZYRCFMVIFY7#E
!
, 7 , E
!
UQPCRQZKQOKGKTUQUPQ
]
TEK
QFSZVECOYJKRQUGZ_GSQDQEZ_C0
#
XQDGEJKRQUGZYCNUGSPCUYXPGL0
$
#QZPCEZCUQ
^
ZG
KTUPKGLGXCPCNKZQXCPYOTZGSGIV)(
(
*
!
NVD7"E
!
#"("%
PKGNQTQXCTMaCFQXC%
 )
4%8QZaQXTMK
3Badanierozkaduskadnikalosowego
3.1Badanienormalno·scirozkaduskadnikalosowego
AGSY[MCELCJKRQUGZYQPQSOCNPQ]TEKZCDVSZG
]
PNQTQXYEJVFZKGNCQFRQXKGFZKPCRY$
UCPKG#EZYZCDVSZGPKGNQTQXGTZGSGIV!'"OQ
^
ZGOYOQFGNQXC]EZCRQOQE_CZOKGPPYEJ
NQTQXYEJQSQZMaCFZKGPQSOCNPYO%BCUGOOVTKOYZDCFC]EEZYTZGSGISGTZU)(
(
*
#"("%
RQTUCEK!("OCSQZMaCF5CVTTC%AUYOEGNVRQTaV
^
ZYOYTK_GUGTUGO8QaOQIQSQXC%
2VFVLGOYJKRQUGZ_GSQDQEZ_C
0
#
.(
(
OCSQZMaCF1!$+$"
XQDGEJKRQUGZYCNUGSPCUYXPGL
0
$
.(
(
PKGOCSQZMaCFV1!$+$"
QSCZPCRQZKQOKGKTUQUPQ]TEK XGSY[MVLGOYUGJKRQUGZY%
Wprzypadkuliczebno·scipopulacji$"1"%$$
'%RQSZ_CFMVLGOYXYPKMKSGTZU
(
$!
"(
%!
"***"(
%!
(%;DNKEZCOYS`
^
ZPKEG
B
1
/
(
(!
#FNCB/%+&+***+1
IFZKG/! "LGTUFYTUSYDVCPU_CSQZMaCFVPQSOCNPGIQ1!$+$"#GTUYOCUQSQF$
EJYNGPKCTUCPFCSFQXGIQTZCEVLGOYLCMQ
.
-
-
,
)
%
%
1
2$/
:
%
(
('$
QSCZQZPCEZCOY
%
%
%
%
%
%
%
%
B
1
9
"
/435
(#%$$%$###$%&
/
(
(!
)%;DNKEZCOYS`
^
ZPKEG
B
%
/
(
(!
1
#FNCB/%+&+***+1
QSCZQZPCEZCOY
%
%
%
%
%
%
%
%
B
%
1
9
/435
(#%$$%$###$%&
/
(
(!
*%AYDKGSCOY
#
$
+9
"
9
%
/435
9
 *
1PCNKZCTMaCFPKMCNQTQXGIQ%AYMaCF6@%
!
+%;FEZYUVLGOYXCSUQ]T]EMSYUYEZP_CTUCUYTUYMK8QaOQIQSQXC.
/9
$
%7G
^
ZGNK
!
9
%
, .
UQPCRQZKQOKGKTUQUPQ]TEK PKGOCRQFTUCXFQQFSZVEKGPKCJKRQUGZY
0
#
#XRSZGEKXPYOSCZKGQFSZVECOY0
#
XQDGE0
$
%
Wprzypadkugdyliczebno·s·c1 -%$$
RVPMUY!'"$!*"XYMQPVLGOYLCMRQXY
^
ZGL#PCUQOKCTUFNCRVPMUV!+"RQTaVIVLGOY
TK_GSQZMaCFGOICSPKEZPYO8QaOQIQSQXC
&
'
+
2
19
%
#9
$
/
IFZKGXCSUQ]TEKMSYUEZPGQFEZYUVLGOYZUCDNKE
%
$*- $*-)$*-+)
9
$
%*&&(%*')(%**&,
AUGFYRVPMU!+"ZCTU_GRVLGOY
!
!
+
;
FE
ZYUVLGOYXCSUQ]T]EMSYUYEZP_CSQZMaCFVISCPKEZPGIQ.
/9
$
%7G
^
ZGNK
+
UQPC
R
QZKQOKGKTUQUPQ
]
TEK PKGOCRQFTUCXFQQFSZVEKGPKC
JKRQUGZY0
#
#LG
^
ZGNK
19
%
, .
!
+
!
19
%
#.
QFSZVECOY0
#
XQDGE0
$
%
3.2Werykacjahipotezyozerowejwarto·scioczekiwanejskad-
nikalosowego
7G
^
ZGNKTUXKGSFZKNK]TOY
^
ZGTZGSGISGTZU)(
(
*
#"("%
OCSQZMaCF5CVTTC#UQFQFCUMQXQ
OVTKOYZXGSY[MQXC]EJKRQUGZ_GQZGSQXGLXCSUQ]TEKQEZGMKXCPGLTMaCFPKMCNQTQXGIQ%
2VFVLGOYJKRQUGZ_GSQDQEZ_C
0
#
."
"
/$
XQDGEJKRQUGZYCNUGSPCUYXPGL
0
$
."
"
&/$
3QXGSY[MCELKJKRQUGZTUQTVLGOYUGTUQRCSUYPCTUCUYTUYEG
+
5/
"
"
4
"
1%
!*"
MU`SCOCSQZMaCFU\>UVFGPUCQ!1%"TUQRPKCEJTXQDQFY#IFZKG "
"
)
%
"
"
/
%
(
(
!+"
1
('$
PCUQOKCTU
.
-
-
,
)
%
%
1%
!(
(
"
"
"
%
4
"
/
!,"
('$
:CRQZKQOKGKTUQUPQ]TEK QFEZYUVLGOYXCSUQ]T]ETUCUYTUYMKMSYUYEZPGL
 +
4%8QZaQXTMK
!
%
%
+1%
%
%
+1%
LGTUMXCPUYNGOSZ_GFV%
%
SQZMaCFV
5
/5
IFZKG5
U\>UVFGPUCRSZY1%TUQRPKCEJTXQDQFY%
ARSZYRCFMVIFY5
!
!
PKGOCRQFTUCXFQQFSZVEGPKCJKRQUGZY
SQDQEZGL0
#
PCRQZKQOKGKTUQUPQ
]
TEK #ZCUGOTZGSGISGTZU)(
(
*
, 5 , 5
#"("%
OCSQZMaCF
PQSOCaPY1!$+$"!RSZYLOVLGOY$/4
"
"%ARSZYRCFMVIFY5%!$+5
!
1'
05
+$"UQPCRQZKQOKGKTUQUPQ]TEK QFSZVECOYJKRQUGZ_GSQDQEZ_C0
#
XQDGEJKRQUGZY
CNUGSPCUYXPGL0
$
#QZPCEZCUQ
^
ZGGNGOGPUYXDCFCPYOTZGSGIVSGTZU)(
(
*
!
#"("%
PKG
OCL_CSQZMaCFV5CVTTC1!$+$"!DY]EOQ
^
ZG
]
ZNGZQTUCaCFQDSCPCHVPMELCPKGNQTQXCX
SQZMaCFZKG!'""
4Badaniekorelacjiskadnikalosowego
<SZYOQFGNQXCPKVTZGSGIV)D
(
*
#"("%
RQTUCEK!'"XC
^
ZPGLGTUPKGUYNMQFQDSZGFQDSC]E
HVPMEL_GPKGNQTQX_C#CNGS`XPKG
^
ZFQDSZGTMQPTUSVQXC]EZCDVSZGPKCNQTQXGUGIQTZGSGIV%
AUYOEGNVOVTKOYQFRQXKGFZKG]EPCRYUCPKG#EZYGNGOGPUYTZGSGIV)(
(
*
#"("%
T_C
RQTUCEKZOKGPPGLNQTQXGLEZYMQODKPCELKNKPKQXGLZOKGPPYEJNQTQXYEJ!KPPYOKTaQXY
EZYGNGOGPUYTZGSGIV)(
(
*
#"("%
T_CTMQSGNQXCPGEZYPKG"%AXK_GMTZQ
]
TEKRSZYRCFM`X
CDYTUXKGSFZK]EKTUPKGPKGMQSGNCELKXTZGSGIVSGTZU)(
(
*
#"("%
XYTUCSEZYXYMQPC]EUGTU
FNC%/%+&+'
BTZGSGIVEZCTQXGIQ)D
(
*
#"("%
XYDKGSCOYTMaCFPKMNQTQXY#EZYNKMQPTUSVLGOY
TZGSGISGTZU)(
(
*
#"("%
RQTUCEK!("%AEGNVXGSY[MCELKJKRQUGZYPCKTUPKGPKGMQSGNCELK
XDCFCPYOTZGSGIV)(
(
*
#"("%
UXQSZYOYJKRQUGZ_GSQDQEZ_C!DSCMMQSGNCELK"
0
#
.3
!
/$!DSCMMQSGNCELKRSZYRSZGTVPK_GEKV%"
XQDGEJKRQUGZYCNUGSPCUYXPGL
0
$
.3
!
&/$!KTUPKGLGMQSGNCELCRSZYRSZGTVPK_GEKV%"
7CMQGTUYOCUQSXTR`aEZYPPKMCMQSGNCELK3
!
TZGSGIVSGTZU)(
(
*
#"("%
XYDKGSCOY
(
(
%!
%!
$
%!
(
(
(
("!
1
(
(
(
("!
('$
('$
2A
"
!%"/
/
!-"
(
(
%
%
$
%
(
%
(
(
%
(
!1%"
('$
('$
FNC%/%+&+'+***+<
1.Liczebno·s·cpopulacji1#'#%
>UCUYTUYMC
+
#
!
/
2A
"
!%"
+
1&%
!."
%2A
%
"
!%"
OCSQZMaCFU$>UVFGPUCZ!1&%"TUQRPKCOKTXQDQFY%
:CRQZKQOKGKTUQUPQ
]
TEK QFEZYUVLGOYXCSUQ
]
T
]
ETUCUYTUYMKMSYUYEZPGL
LGTUMXCPUYNGOSZ_GFV%
%
SQZMaCFVU\>UVFGPUCRSZY1&%TUQRPKCEJTXQDQFY%
!
%
%
+1&%
%
%
+1&%
#
!
/5
IFZKG5
 

zanotowane.pl

doc.pisz.pl

pdf.pisz.pl

alter.htw.pl