補åã®ä¿¡é Œæ§ãè¡šãå質çšèªã«FITã»MTBFã»MTTFã»MTTRããããŸãã
åçšèªã®æå³ã¯äžèšãšãªã£ãŠããŸã(åŸã»ã©åçšèªã«ã€ããŠè©³ãã説æããŸã)ã
- FIT(Failure In Time)
- MTBF(Mean Time Between Failure)
- MTTF(Mean Time To Failure)
- MTTR(Mean Time To Repair)
補åã®æ éçãè¡šãåäœã®ããšã
補åã®å¹³åæ éééã®ããšããã補åã皌åããŠãã(ãŸãã¯æ éãã埩æ§ããŠãã)ãæ éãããŸã§ã®æéã瀺ããŠããã
補åã®å¹³åæ éæéã®ããšããã補åã皌åããŠãããæ éãããŸã§ã®æéã瀺ããŠããã
補åã®å¹³åä¿®çæéã®ããšããã補åãæ éããŠããã埩æ§ãããŸã§ã®æéã瀺ããŠããã
ãã®èšäºã§ã¯äžèšã«ç€ºããŠããFITã»MTBFã»MTTFã»MTTRã«ã€ããŠå³ãçšããŠè©³ãã説æããŸãã
FITãšã¯
FITãšã¯è£œåã®æ éçãè¡šãåäœã§ãã10åæé(109æé,çŽ11äž4155幎)ãããã®å¹³åæ éåæ°ãè¡šããŠããŸãã10[FIT]ã®è£œåã¯10åæéãããå¹³å10åæ éãããšããããšã«ãªããŸãããFailure In Timeãã®é æåãåã£ãŠFITãšåŒã°ããŠããŸãã
åäœã§ãã[FIT]ã[å/109æé]ã«çœ®ãæãããšèšç®ãç解ãããããªããŸãã
äŸãã°ã10[FIT](=10[å/109æé])ã®è£œåã¯ã1åæé(108[æé])皌åãããšå¹³å1åæ éãããšããããšãªããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
æ
éæ°&=&10{\mathrm{[FIT]}}Ã10^8{\mathrm{[æé]}}\\
\\
&=&10{\mathrm{[å/10^9æé]}}Ã10^8{\mathrm{[æé]}}\\
\\
&=&10^{-8}{\mathrm{[å/æé]}}Ã10^8{\mathrm{[æé]}}\\
\\
&=&1{\mathrm{[å]}}
\end{eqnarray}
ãŸãã1[FIT]ã¯æç®ãããšä»¥äžã«ç€ºãããã«[%/1000h]ã[ppm/1000h]ã®åäœã§è¡šãããšãã§ããŸãã
\begin{eqnarray}
1{\mathrm{[FIT]}}&=&1{\mathrm{[å/10^9æé]}}\\
\\
&=&10^{-9}{\mathrm{[å/æé]}}\\
\\
&=&10^{-4}{\mathrm{[{\%}/1000h]}}\\
\\
&=&1{\mathrm{[ppm/1000h]}}
\end{eqnarray}
è£è¶³
- [FIT]ã®åäœã¯åå°äœè£œåãªã©ã®å€§éã«çç£ãããæ éçã極ããŠäœã補åã«ããçšããããŠããŸãããŸãã[FIT]ã®åäœä»¥å€ã«ã[%/1000h]ã[ppm/1000h]çãçšããããããšããããŸãã
- 補å1ã€ã10åæé皌åãããŠæ éãç£èŠããããšã¯çŸå®çã«ã¯ã§ããªãã®ã§ãå®éã«ã¯è€æ°ã®åäžè£œåãäžå®æéåæã«çšŒåããããã®éã«æ éãã補åã®æ°ããFITãæ±ããŠããŸãã
- æ éçã10FITã§ãããšããããšã¯ãæ éãã確çã1åæé(108æé)ã§1åãšããããšã§ããã補åã®å¯¿åœã1åæé(108æé)ã§ã¯ãªãããšã«æ³šæããŠãã ããã
- æ éçã®èšå·ã«ã¯Î»(ã©ã ã)ãçšããã®ãäžè¬çã§ãã
ã§ã¯æ¬¡ã«FITã«é¢ããèšç®äŸã説æããŸãã
FITã«é¢ããèšç®(ãã®1)
åžå Žã§10,000å°ã®è£œåã100æé皌åããŠããããã®éã«æ éãã補åæ°ã10åã ã£ãå Žåã®æ éçλ[FIT]ãæ±ããŠã¿ãŸãããã
ãã®è£œåã®ç·çšŒåæéã¯ä»¥äžã®å€ãšãªããŸãã
\begin{eqnarray}
ç·çšŒåæé&=&10,000Ã100{\mathrm{[æé]}}\\
\\
&=&10^6{\mathrm{[æé]}}
\end{eqnarray}
ãããã£ãŠãæ éçλ[FIT]ã¯äžèšã®å€ãšãªããŸãã
\begin{eqnarray}
æ
éç{\lambda}&=&\frac{補åã®æ
éæ°{\mathrm{[å]}}}{補åã®ç·çšŒåæé{\mathrm{[æé]}}}\\
\\
&=&\frac{10{\mathrm{[å]}}}{10^6{\mathrm{[æé]}}}\\
\\
&=&10^{-5}{\mathrm{[å/æé]}}\\
\\
&=&10^{-5}Ã10^9{\mathrm{[å/10^9æé]}}\\
\\
&=&10^4{\mathrm{[å/10^9æé]}}\\
\\
&=&10^4{\mathrm{[FIT]}}
\end{eqnarray}
FITã«é¢ããèšç®(ãã®2)
10[FIT]ã®éšåã1,000åæèŒããã補åã®æ éçλ[FIT]ãæ±ããŠã¿ãŸãããã
åéšåã®æ éçã®åèšã補åå šäœã®æ éçã«ãªããŸãããããã£ãŠãéšåæ°ãå€ããªãã»ã©è£œåã®æ éçãäžæããŸããåŒã§è¡šããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
æ
éç{\lambda}&=&10{\mathrm{[FIT]}}Ã1,000\\
\\
&=&10{\mathrm{[å/10^9æé]}}Ã1,000\\
\\
&=&10^4{\mathrm{[å/10^9æé]}}\\
\\
&=&1{\mathrm{[å/10^5æé]}}
\end{eqnarray}
ãããã£ãŠã10[FIT]ã®éšåã1,000åæèŒããã補åã®å Žåã100,000(105æé)ãããã«å¹³å1åæ éãããšããããšã«ãªããŸãã
FITã»MTBFã»MTTF ã®é¢ä¿ãšæç®æ¹æ³
補åã®ä¿¡é Œæ§ãè¡šãå質çšèªã«ã¯ãFIT以å€ã«ããã®åŸã«èª¬æããMTBF(ä¿®çå¯èœãªãã®)ãMTTF(ä¿®çäžå¯èœãªãã®)ããããŸãã
FITã¯MTBFãMTTFã®éæ°ã«10å(109)ãæãããã®ã«çãããªããŸããåŒã§è¡šããšä»¥äžã®ããã«ãªããŸãã
FITã»MTBFã»MTTF ã®é¢ä¿
\begin{eqnarray}
æ
éç{\lambda}&=&\frac{1}{MTBF}Ã10^9{\mathrm{[FIT]}}\\
\\
&=&\frac{1}{MTTF}Ã10^9{\mathrm{[FIT]}}
\end{eqnarray}
â
MTBFãšã¯
MTBFãšã¯è£œåã®å¹³åæ éééã®ããšã§ãããMean Time Between Failureãã®é æåãåã£ãŠMTBFãšåŒã°ããŠããŸãã
MTBFã¯è£œåã®ç·çšŒåæéãæ éæ°ã§å²ãããšã§æ±ããããšãã§ããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
MTBF=\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}
\end{eqnarray}
äŸãã°ãäžå³ã«ç€ºã補åAãäžèšã«ç€ºããããªçšŒåãšä¿®çãè¡ã£ãŠãããšããŸãã
- 1,100æé皌åããŠæ éãã10æéä¿®ç
- ä¿®çåŸ1,000æé皌åããŠæ éãã8æéä¿®ç
- ä¿®çåŸ900æé皌åããŠæ éãã12æéä¿®ç
補åAã®MTBFãèšç®ãããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
MTBF&=&\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}\\
\\
&=&\frac{1,100+1,000+900}{3}\\
\\
&=&\frac{3,000}{3}\\
\\
&=&1,000
\end{eqnarray}
ãããã£ãŠãMTBFã1,000æéã§ãã補åAã¯ã1,000æé皌åãããšå¹³å1åæ éããããšããããšãªããŸããããã«ãMTBFãé·ããã°é·ãã»ã©è£œåã®ä¿¡é Œæ§ãé«ããšããããšã«ãªããŸãã
ãã®MTBFã¯åäœã[æé/å]ãšèãããšèšç®ãç解ãããããªããŸãã
äŸãã°ãMTBFã10,000æé(104æé)ã®è£œåã100,000æé(105æé)皌åãããšãå¹³å10åæ éãããšããããšã«ãªããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
æ
éæ°&=&\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{MTBF{\mathrm{[æé/å]}}}\\
\\
&=&\frac{10^5{\mathrm{[æé]}}}{10^4{\mathrm{[æé/å]}}}\\
\\
&=&10{\mathrm{[å]}}
\end{eqnarray}
ã§ã¯æ¬¡ã«MTBFã«é¢ããèšç®äŸã説æããŸãã
MTBFã«é¢ããèšç®
MTBFã500,000æéã®è£œåãåžå Žã§10,000å°çšŒåããŠããæã100æéãããã«æºåããªããã°ãªããªã補åã®æ°ãæ±ããŠã¿ãŸãããã
ãã®è£œåã®ç·çšŒåæéã¯ä»¥äžã®å€ãšãªããŸãã
\begin{eqnarray}
ç·çšŒåæé&=&10,000Ã100{\mathrm{[æé]}}\\
\\
&=&10^6{\mathrm{[æé]}}
\end{eqnarray}
ãã®ãããåžå Žã§æ éããæšå®åæ°ã¯ä»¥äžã®å€ãšãªããŸãã
\begin{eqnarray}
æ
éæ°&=&\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{MTBF{\mathrm{[æé/å]}}}\\
\\
&=&\frac{10^6{\mathrm{[æé]}}}{5Ã10^5{\mathrm{[æé/å]}}}\\
\\
&=&2{\mathrm{[å]}}
\end{eqnarray}
ãããã£ãŠãMTBFã500,000æéã®è£œåãåžå Žã§10,000å°çšŒåããŠããæã100æéãããã«æäœ2å°ã®ä»£æ¿åãçšæããŠããå¿ èŠããããŸãã
ãã®ããã«ãMTBFã¯åžå Žã§çšŒåããŠãã補åã®æºåæ°ã決å®ããããã«ãçšããããŠããŸãã
MTBFããFITã«æç®ããæ¹æ³
MTBFã®åäœã[æé/å]ãšèãããšãMTBFãšFITã®é¢ä¿ãåããããããªããŸãã
ç¹°ãè¿ãã«ãªããŸãããMTBFã¯æ¬¡åŒã§è¡šãããšãã§ããŸãã
\begin{eqnarray}
MTBF=\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}
\end{eqnarray}
ãããã£ãŠãMTBFã®éæ°ã¯æ¬¡åŒãšãªããŸãã
\begin{eqnarray}
\frac{1}{MTBF}=\frac{æ
éæ°{\mathrm{[å]}}}{補åã®ç·çšŒåæé{\mathrm{[æé]}}}
\end{eqnarray}
1/MTBF[å/æé]ã¯1æéãããã®å¹³åæ éåæ°ã瀺ããŠããŸããäžæ¹ãFITã¯10åæé(109æé)ãããã®å¹³åæ éåæ°ã瀺ããŠããŸãã
ãã®ããã1/MTBFã«10å(109)ãæããããšã§FITã«æç®ããããšãã§ããŸããåŒã§è¡šããšä»¥äžã®ããã«ãªããŸãã
\begin{eqnarray}
æ
éç{\lambda}&=&\frac{1}{MTBF}Ã10^9{\mathrm{[FIT]}}
\end{eqnarray}
MTTFãšã¯
MTTFãšã¯è£œåã®å¹³åæ éæéã®ããšã§ãããMean Time To Failureãã®é æåãåã£ãŠMTTFãšåŒã°ããŠããŸãã
å ã»ã©èª¬æããMTBFãšåæ§ã«MTTFã補åã®ç·çšŒåæéãæ éæ°ã§å²ãããšã§æ±ããããšãã§ããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
MTTF=\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}
\end{eqnarray}
äŸãã°ããã補å3ã€(補åAïœC)ãäžèšã«ç€ºããããªæ éæéã ã£ããšããŸãã
- 補åAïŒ1,100æé
- 補åBïŒ1,000æé
- 補åCïŒ900æé
ãã®è£œåã®MTTFãèšç®ãããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
MTTF&=&\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}\\
\\
&=&\frac{1,100+1,000+900}{3}\\
\\
&=&\frac{3,000}{3}\\
\\
&=&1,000
\end{eqnarray}
ãããã£ãŠãMTTFã1,000æéã§ãã補åã¯ã1,000æé皌åãããšå¹³å1åæ éããããšããããšãªããŸããããã«ãMTTFãé·ããã°é·ãã»ã©è£œåã®ä¿¡é Œæ§ãé«ããšããããšã«ãªããŸãã
MTTFãšMTBFã®éã
MTTFãšMTBFã¯äŒŒãŠããŸããããããã®éãã¯ãåç¥ã§ããããã
MTTFã¯ä¿®çã§ããªã補å(é»çãªã©)ã«å¯ŸããŠäœ¿ãããŸããäžæ¹ãMTBFã¯ä¿®çã§ãã補å(家é»è£œåãªã©)ã«å¯ŸããŠäœ¿ãããŸãããŸãšãããšäžèšã®ããã«ãªããŸãã
- MTTFïŒå¹³åæ éæé
- MTBFïŒå¹³åæ ééé
ãã補åã皌åããŠãããæ éãããŸã§ã®æéã®ããšã
ãã補åã皌åããŠãã(ãŸãã¯æ éãã埩æ§ããŠãã)ã次ã«æ éãããŸã§ã®æéã®ããšã
ãã®ããã«ãä¿®çã§ããªãã(MTTF)ãorãä¿®çã§ããã(MTBF)ãã®éãã ããªã®ã§ãMTTFã¯MTBFãšåæ§ã®èšç®ã§æ±ããããšãã§ããŸãããã®ãããMTTFã®èšç®äŸã«ã€ããŠã¯å²æããŸãã
MTTFããFITã«æç®ããæ¹æ³
MTTFã®åäœã[æé/å]ãšèãããšãMTBFãšFITã®é¢ä¿ãåããããããªããŸãã
ç¹°ãè¿ãã«ãªããŸãããMTTFã¯æ¬¡åŒã§è¡šãããšãã§ããŸãã
\begin{eqnarray}
MTTF=\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}
\end{eqnarray}
ãããã£ãŠãMTTFã®éæ°ã¯æ¬¡åŒãšãªããŸãã
\begin{eqnarray}
\frac{1}{MTTF}=\frac{æ
éæ°{\mathrm{[å]}}}{補åã®ç·çšŒåæé{\mathrm{[æé]}}}
\end{eqnarray}
1/MTTF[å/æé]ã¯1æéãããã®å¹³åæ éåæ°ã瀺ããŠããŸããäžæ¹ãFITã¯10åæé(109æé)ãããã®å¹³åæ éåæ°ã瀺ããŠããŸãã
ãã®ããã1/MTTFã«10å(109)ãæããããšã§FITã«æç®ããããšãã§ããŸããåŒã§è¡šããšä»¥äžã®ããã«ãªããŸãã
\begin{eqnarray}
æ
éç{\lambda}&=&\frac{1}{MTBF}Ã10^9{\mathrm{[FIT]}}
\end{eqnarray}
MTTRãšã¯
MTTRãšã¯è£œåã®å¹³åä¿®çæéã®ããšã§ãããMean Time To Repairãã®é æåãåã£ãŠMTTRãšåŒã°ããŠããŸãã
MTTRã¯è£œåã®ç·ä¿®çæéãæ éæ°ã§å²ãããšã§æ±ããããšãã§ããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
MTTR=\frac{補åã®ç·ä¿®çæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}
\end{eqnarray}
äŸãã°ãäžå³ã«ç€ºã補åAãäžèšã«ç€ºããããªçšŒåãšä¿®çãè¡ã£ãŠãããšããŸãã
- 1,100æé皌åããŠæ éãã10æéä¿®ç
- ä¿®çåŸ1,000æé皌åããŠæ éãã8æéä¿®ç
- ä¿®çåŸ900æé皌åããŠæ éãã12æéä¿®ç
ãã®ããã補åAã®MTTRãèšç®ãããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
MTTR&=&\frac{補åã®ç·ä¿®çæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}\\
\\
&=&\frac{10+8+12}{3}\\
\\
&=&\frac{30}{3}\\
\\
&=&10
\end{eqnarray}
ãããã£ãŠãMTTRã10æéã§ãã補åAã¯ã1åä¿®çããã®ã«å¹³å10æéèŠããããšããããšã«ãªããŸããããã«ãMTTRãçããã°çãã»ã©è£œåã®çšŒåçãé·ãããããšãã§ããŸãã
皌åç(ã¢ãã€ã©ããªãã£)ãšã¯
皌åç(ã¢ãã€ã©ããªãã£,Availability)ãšã¯ãã®åã®éãã補åã®ç·æé(ç·çšŒåæé+ç·ä¿®çæé)ã«ãããŠã補åãã©ãããã皌åããŠããããè¡šãããã®ã§ãã
皌åçã¯ç·çšŒåæéãç·æé(ç·çšŒåæé+ç·ä¿®çæé)ã§å²ãããšã§æ±ããããšãã§ããŸãããŸããå ã»ã©èª¬æããMTBFãšMTTRãçšããŠã皌åçãèšç®ããããšãã§ããŸããåŒã§è¡šããšæ¬¡åŒã®ããã«ãªããŸãã
\begin{eqnarray}
皌åç&=&\frac{ç·çšŒåæé}{ç·çšŒåæé+ç·ä¿®çæé}\\
\\
&=&\frac{MTBF}{MTBF+MTTR}\\
\end{eqnarray}
ãã®ãããå¹³åä¿®çæé(MTTR)ããŒãã«è¿ãã»ã©ã皌åçãåäžããŸãã
äŸãã°ãäžå³ã«ç€ºã補åAãäžèšã«ç€ºããããªçšŒåãšä¿®çãè¡ã£ãŠãããšããŸãã
- 1,100æé皌åããŠæ éãã10æéä¿®ç
- ä¿®çåŸ1,000æé皌åããŠæ éãã8æéä¿®ç
- ä¿®çåŸ900æé皌åããŠæ éãã12æéä¿®ç
äžèšã®å Žåã補åAã®MTBFãšMTTRã¯ä»¥äžã®å€ãšãªããŸãã
\begin{eqnarray}
MTBF&=&\frac{補åã®ç·çšŒåæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}=\frac{1,100+1,000+900}{3}=1,000\\
\\
MTTR&=&\frac{補åã®ç·ä¿®çæé{\mathrm{[æé]}}}{æ
éæ°{\mathrm{[å]}}}=\frac{10+8+12}{3}=10
\end{eqnarray}
ãã®ããã補åAã®çšŒåçãèšç®ãããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
皌åç&=&\frac{MTBF}{MTBF+MTTR}\\
\\
&=&\frac{1,000}{1,000+10}\\
\\
&=&0.99
\end{eqnarray}
ãªãã補åã®ç·æé(ç·çšŒåæé+ç·ä¿®çæé)ãçšããŠãåãå€ãšãªããŸããèšç®ãããšä»¥äžã®å€ã«ãªããŸãã
\begin{eqnarray}
皌åç&=&\frac{ç·çšŒåæé}{ç·çšŒåæé+ç·ä¿®çæé}\\
\\
&=&\frac{3,000}{3,000+30}\\
\\
&=&0.99
\end{eqnarray}
ãŸãšã
ãã®èšäºã§ã¯ã補åã®ä¿¡é Œæ§ãè¡šãå質çšèªã§ããFITã»MTBFã»MTTFã»MTTRã«ã€ããŠèª¬æããŸããã
ãèªã¿é ãããããšãããããŸããã
åœãµã€ãã§ã¯é»æ°ã«é¢ããæ§ã
ãªæ
å ±ãèšèŒããŠããŸããåœãµã€ãã®å
šèšäºäžèŠ§ã«ã¯ä»¥äžã®ãã¿ã³ãã移åããããšãã§ããŸãã