# Presentation: 242693

## Supplemental Material: Data on Tevatron Complex Reliability

- Elliott McCrory
- 25 February 2004

## Presentation Outline

- Main talk is elsewhere
- The data here are supplemental to that talk

## Downtime Logger, D18

- Console Application: Screen Shot

## Web Page: 4 Weeks of Downtime

- Click Here...

## Focus on one subsystem: BPS

- Entries like these are uses as the basis for the analysis

## Tevatron Complex Subsystems

- BDIAG
- BMAG
- BMISC
- BPS
- BRF
- BVAC
- BWATR
- CMISC
- CNET
- CR&LK
- CTIME
- EXPAR
- FDIAG
- FMISC
- FPS
- FWATR

- LDIAG
- LMAG
- LMISC
- LPS
- LRF
- LVAC
- LWATR
- MIDIAG
- MIMISC
- MIPS
- MIRF
- MISC
- MIVAC
- MIWATR
- MIMAG
- MIXFER

- POWER
- RADTRIP
- RRMISC
- SAFETY
- TCRYO
- TDIAG
- TMAG
- TMISC
- TPS
- TQPM
- TQUEN
- TRF
- TVAC
- TWATR
- WATER

- NTF
- PACC (L)
- PBCOOL
- PBDIAG
- PBMAG
- PBMISC
- PBPS
- PBRF
- PBTRGT
- PBVAC
- PBWATR
- PBXFER

## Definition of Terms

- MTBF
- Mean Time Between Failure
- Simple arithmetic average of the time between failures
- λ
- Used to characterize the probability of an interval in the classic random queuing problem
*E.g., the arrival interval of cars at a toll booth*
*λ** = 1/<t> = 1/**σ** *
- Actually, not σ, but R.M.S.
- Calculated here as (2/(MTBF + σ(MTBF)))
- Average Downtime Fraction
- = [Σ (time down)] / (specified interval)

## MTBF For Each Major System

- Days since 1/1/2003

*Linac*

- Running average MTBF, hours

- Running average over 120 days

- Running average over 30 days

- Fall 2003
- Shutdown

- Good

- Bad

## MTBF For Each Major System

*Booster*

- Days since 1/1/2003

- Running average MTBF, minutes

- Good

- Bad

## MTBF For Each Major System

*PBar*

- Days since 1/1/2003

- Running average MTBF, minutes

*A lot less downtime*

- Good

- Bad

## MTBF For Each Major System

*Main Injector*

- Days since 1/1/2003

- Running average MTBF, minutes

- Good

- Bad

## MTBF For Each Major System

*Tevatron*

- Days since 1/1/2003

- Running average MTBF, minutes

- Good

- Bad

## MTBF For Each Major System

*Controls*

- Days since 1/1/2003

- Running average MTBF, minutes

- Good

- Bad

## Tevatron as 2 Machines

- The machines are called “Low Beta” and “Not Low Beta”
- Is “Low Beta” if energy is bigger than 900
- Otherwise, it is called “Not Low Beta”
- Only one machine exists at a time
- Time between failures
- Only count time in which the machine “exists”
- That is, count minutes at 980 to determine time between failures at 980
- Ditto for “Not Low Beta”
- Eliminate obvious bad points
- E.g., 5000+ minutes of shutdown between failures at 150 for TeV this winter.

## Tevatron as 2 machines, MTBF

- MTBF is getting longer!

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*Linac*

- Days since 1/1/2003

- Running average MTBF, hours

- Running average over 120 days

- Running average over 30 days

- Bad

- Good

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*Booster*

- Days since 1/1/2003

- Running average MTBF, hours

- Bad

- Good

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*Main Injector*

- Days since 1/1/2003

- Running average MTBF, hours

- Bad

- Good

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*PBar*

- Days since 1/1/2003

- Running average MTBF, hours

- Bad

- Good

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*Tevatron*

- Days since 1/1/2003

- Running average MTBF, hours

- Bad

- Good

##  λ(t) For Each Major System

-  *λ**(t)* For Each Major System

*Controls*

- Days since 1/1/2003

- Running average MTBF, hours

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*Linac*

- Running average over 120 days

- Running average over 30 days

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*Booster*

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*Main Injector*

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*PBar*

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*Tevatron*

- Bad

- Good

##  Average Downtime Fraction

-  Average Downtime Fraction

- Days since 1/1/2003

- Running average Downtime
-  Duration, minutes

*Controls*

- Bad

- Good

## Radioactive Decay

*λ* *e **–**λ** t** is the frequency distribution of *
*the *_*classic random queuing problem*_

*F(t) = 2** -t/**τ*

*F(t) = 2** -t/**τ*
*       **= e **-ln(2) t/**τ*
*       ≡ **e **–**λ** t*
*λ** = 0.0346*

*<t> = **σ** = 1/ **λ*
*        **= 28.9*

## Controls Downtimes

- Data Dump of All Controls
- Downtimes since 1-1-2003

## λ For All Systems

*λ* For All Systems

- Log Scale

- Probability of failure per hour = *1 – **λ*
*E.g. Linac up for 5 hours: (1-0.183)**5** = 0.364*

## Quality of λ Fit Assumption

*Q = <t>/**σ*

## Store Duration

- Stores Duration, Hours

- dN / dT

- Failures

- Intentional: 2003

- Intentional: 2004