??a?e???s? ????? ?????f??????

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??a?e???s? ????? ?????f??????

• ????e?? 6?
• ???t?a PERT

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?ßeßa??t?ta

• ?? ?????µe ?ta? ? e?t?µ?s? t?? d????e?a? t??
  d?ast????t?t?? e??? ????? e???e? aßeßa??t?ta
• ???ß??µa st?? efa?µ??? t?? µe??d?? ???s?µ??
  d?ad??µ?? (CPM)

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????d?? PERT

• ??apt?????e ap? t? ???eµ??? ?a?t??? t?? ??? µe
  st??? t? d?a?e???s? t?? ???a???? e?t??es?? t??
  ?????.
• ?a d??t?a PERT ap?te????ta? ap? t??a ?a? ??µß???
  (t???t?). ? ?µfas? d??eta? sta ?e????ta.
• ?at?????? ??a pe??pt?se?? a??pt???? ????
  s?st?µ?t?? (p?????t??) p?? e?????? te???????????
  ???d????? ? p?????? ast??µ?t??? pa?????te?.

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???t?a PERT

• ? d????e?a ???e d?ast????t?ta? e??a? st??ast???
  µetaß??t?
• ?p????µe ?a ?p?????s??µe t?? p??a??t?ta P(x) ?a
  ?????????e? t? ???? se x ???????? µ???de?
• ?p????µe ?a ?p?????s??µe t? d????e?a t ??a t??
  ?p??a e?p????µe, µe ??p??a p??a??t?ta, ?t? ?a
  ???p????e? t? ????.

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• ????p???se?? ??a t?? efa?µ??? µe??d?? PERT
• ?? d????e?e? t?? d?ast????t?t?? e??a? st??ast???
  a?e???t?te?
• ?p??e? ?a efa?µ?ste? t? ?e?t???? ???a?? Te???µa,
  d??. ? ???s?µ? ??ad??µ? pe???aµß??e? epa????
  p????? d?ast????t?t??

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?e????? PERT

• G?a ?a efa?µ?s??µe t? µ???d? PERT ??e?a??µaste
  t?e?? e?t?µ?se?? ??a t? d????e?a ???e
  d?ast????t?ta?.
• H e?t?µ?s? ta a?t?st???e? st?? p?? a?s??d???
  ????? ???p???s??
• H e?t?µ?s? tb a?t?st???e? st?? p?? apa?s??d???
  ????? ???p???s??
• H e?t?µ?s? tm a?t?st???e? st?? p?? p??a?? ?????
  ???p???s?? t?? ?????
• ?? t?e?? e?t?µ?se?? p??pe? ?a ?????ta? µe t??
  ?d?e? p???p???se??/s?????e? (p.?. p?????,
  a????p??? d??aµ???)
• ?? t?e?? e?t?µ?se?? ??a t? ??????? d????e?a ???e
  d?ast????t?ta? (a?s??d??? ta, apa?s??d??? tb,
  pe??ss?te?? p??a?? tm) a????????? t?? ?ata??µ? ß.

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?ata??µ? ß

• ??? ?e???s??µe t? d????e?a t?? d?ast????t?ta?
  (i,j) dij ?? t??a?a µetaß??t?, ap?de????eta? st??
  p???? ?t? a????????ta? t?? ?ata??µ? ß ????µe ta
  ?a??te?a ap?te??sµata.
• S??e??? ?ata??µ?, d?af??et??? ap? t?? ?a??????
• ??e??e?t?µata
• ??t?st???e? µ???? p??a??t?ta st? e?de??µe?? ?a
  ?????????e? ? d?ast????t?ta st?? p?? a?s??d???
  ????? (ta) ?a? ep?s?? µ???? p??a??t?ta st?
  e?de??µe?? ?a ?????????e? ? d?ast????t?ta st??
  p?? apa?s??d??? ????? (tb)
• ??t?st???e? µ?a µ??? p??a??t?ta (tm) st?
  e?de??µe?? ?a ?????????e? ? d?ast????t?ta µeta??
  t?? p?? a?s??d???? (ta) ?a? t?? p?? apa?s??d????
  ?????? (tb)

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?e????? PERT

• ??aµe??µe?? t?µ? ?(di,j)te1/6 (ta 4tm tb )
• ??a??µa?s? s2((tb - ta ) / 6) 2
• ??p??? ap????s? 1/6 (tb - ta )

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?a??de??µa

• S?µf??a µe t?? e??????? ??µ??es?a, ??a ?a ???e?
  p??µ??e?a ?????? ? ????sµ???? ap? ??a d?µ?s??
  ???a??sµ?, apa?te?ta? ? e???af? t?? p?????????
  t?? p??µ??e?a? st? ???a?? ?????aµµa ???µ??e???.
• G?????ete ?t? s?????? ? d?ad??as?a e???af?? t??
  p????????? st? ??? ?????????eta? se 15 eßd?µ?de?.
  ??? ?µ?? ? p??tas? e??a? ?a?? te?µ????µ??? ?a? ??
  ?µe??µ???e? s??ed??as?? t?? a?µ?d?a? ?p?t??p??
  e??a? e???????, ? e???af? µp??e? ?a ?????????e?
  se 5 eßd?µ?de? µ???. Ost?s?, ??e? s?µße? st?
  pa?e???? ?a ??e?aste? ?a pe??s??? 60 eßd?µ?de?
  ??a t?? ????????s? t?? e???af??!
• ???a ? a?aµe??µe?? d????e?a t?? d?ad??as?a? a?t??
  ?a? p??a ? d?a??µa?s? t??
• E?? ?atas?e???ate t? d??t?? t?? s?et???? ?????
  p??a t?µ? ?a d??ate st? d????e?a t??
  d?ast????t?ta?

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?p??t?s?

• te (541560)/6 20,833, d??. 21 eßd?µ?de?
  pe??p??
• s2((60-5)/6)284,02

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??????? ep???s? d??t??? PERT

• ??? ?p????????µe t? d????e?a e??? ?????
• ??? ?p???e? µ??? µ?a d?ad??µ? ap? t? (e?a??t????)
  ?e????? k st? ?e????? (p??at??) m, t?te
• ? d????e?a e??a? ?km?dij ??a ??e? t??
  d?ast????t?te? (i,j) p?? µes??aß???
• ? a?aµe??µe?? t?µ? t?? d????e?a? e??a? ?(?km)
  ??(dij) ?a?
• ? d?a??µa?s? t?? d????e?a? e??a?
  Var(?km)?Var(dij)
• ??? ?p?????? pe??ss?te?e? d?ad??µ?? t?te
• ?p????????µe t?? a?aµe??µe?? d????e?a ???e µ?a?
• ??? ?p?????? d?ad??µ?? µe t?? ?d?a a?aµe??µe??
  t?µ? ?(?km) t?te ? d?ad??µ? µe t? µe?a??te??
  d?asp??? a?t?p??s?pe?e? t?? aßeßa??t?ta t?? ?????.

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??????? ep???s? d??t??? PERT

• ?atas?e?????µe t? d??t?? ?a? e?t?µ??µe ??a ???e
  d?ast????t?ta (i,j) t??? ??????? ta(i,j) ,
  tb(i,j) ?a? tm(i,j)
• ?p????????µe t?? a?aµe??µe?? d????e?a ???e
  d?ast????t?ta? ?(di,j)te(i,j)1/6 (ta 4tm tb
  )
• ?e ß?s? t?? t?µ?? te(i,j) ?p????????µe ta EXj ?a?
  ?Xj

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??????? ep???s? d??t??? PERT

• ?p????????µe t? S??????? ?e??????? ???e
  d?ast????t?ta?, t?? ???s?µe? ??ast????t?te? ?a?
  t?? ???s?µ? ??ad??µ?.
• G?a t?? ???s?µ? ??ad??µ? ?p????????µe µ ?
  te(i,j) ?a? Var ?Var(dij)
• ??? ?p?????? pe??ss?te?e? d?ad??µ?? µe t?? ?d?a
  a?aµe??µe?? d????e?a, ?? ??????? µe?a??te??
  ?e????µe e?e??? µe t? µe?a??te?? d?asp???.

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??????? ep???s? d??t??? PERT

• ?p????????µe t?? t?µ? t?? t?p?p???µ???? ?a???????
  µetaß??t??
• z (?????aµ. ?????. ??aµe?. ?????.) / ??p???
  ?p????s?
• z (?-µ) / vVar
• H z a??????e? t?? ?ata??µ? ?(m, Var) ? ?(1,0)

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??????? ep???s? d??t??? PERT

• ? ?p?????sµ?? t?? p??a??t?ta? P(x) ?a ?????????e?
  t? ???? se ????? µ????te?? ? ?s? t?? x ????????
  µ???d?? e??a? P(EXn m x) F (z) ?a?
  ß??s?eta? ap? t??? p??a?e? t?? t?p?p???µ????
  ?a??????? ?ata??µ?? ?? t? eµßad?? ap? -8 ??? t??
  t?µ? z

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• ???a?a? ??µ?? t?? ???a??t?t?? t?? ??p?p???µ????
  ?a??????? ?ata??µ?? ?(0,1) ??a z0

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?s??s? 7

• ?a ?atas?e??sete t? d??t?? PERT.
• ?a ?p?????sete t?? a?aµe??µe?? µ?s? t?µ? (µi,j)
  ?a? t? d?asp??? var (di,j) ??a ???e d?ast????t?ta
• ???e? e??a? ?? ???s?µe? d?ast????t?te? ?a? p??a ?
  ???s?µ? ??ad??µ?
• ???a ? p??a??t?ta ?a ?????????e? t? ???? µ?sa se
  25 ???????? µ???de? P(x25)
• ??s?? ?????? apa?te?ta? ?ste ?a e?µaste ß?ßa???
  ?at? 95 ?t? ?a ??e? ?????????e? t? ????

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??s?
Var1.7772.7770.4442.7777.775
Z (25-22)/v7.775 1.08. ?p? t?? ???a?a ??µ??
t?? p??a??t?t?? t?? t?p?p???µ???? ?a???????
?ata??µ?? p????pte? ?t? P(x25)0.85993. P((z-22)/
v7.775)0.95 ? (z-22)/v7.7751.65 ? x27 ?µ??e?