US CMS EMU MTTF Analysis for Chamber Components

1. US CMS EMU MTTF Analysis for Chamber Components • Mean Time To Failure (MTTF) Analysis • Goal • Identify lifetime of components “hardwired” in the chamber assembly • Rely on Vendors Data and Military Specifications • Summary • Introduction • Chamber E&E (Electrical & Electronics) Components • Vendors Data • Analysis • HV Sector Failure • Anode Protection Board Failure • Anode Channel Failure

2. US CMS EMU Introduction • Follow CERN 74-16 “Yellow Book”: • Introduction to Reliability Theory; by B. Schorr • Reliability Theory 101: Definitions • A system is unrepairable if it cannot be repaired to perform its particular task after a failure. • Definition 1 • The probability R(t) that an unrepairable system performs without failure a given task under given conditions for a given length of time t is called the reliability of the system. • Definition 2 • If R(t) is the reliability and f(t) the failure density function of an unrepairable system S , then l(t)=f(t)/R(t) is called the failure rate function of the system. Note: f(t) and R(t) are related by a 3rd definition

3. US CMS EMU Failure Rates Introduction • Pratical Experience • From direct observation, most of the l(t) distributions follow a bath-tub curve • Vendors provide information for Region II in terms of FITS (failures in 109 operating hours) or % failures/1000 hours (1FIT=0.0001%/1000 hours) I II III l(t) Random Failures Early failures Wear-out failures t

4. US CMS EMU Failure Rates Introduction • More Definitions and Theorems: • MTTF= R(t) dt • The simplest and most applied failure distribution is the exponential failure distribution for which • MTTF = R(t) = 1/l • Series Connections • Theorem: • In system consisting of n unrepairable components C1,….Cn in series connection with independent lifetimes T1,…Tn the failure rate l(t) is given by • l(t)= S li(t) • NOTE: Parallel connections do not behave like a parallel resistive connection S1 S2

5. US CMS EMU Failure Rates Chamber E&E Components 1.2 V Out 5V in • Electrical Path: Carbon Resistor Surface Mounted Resistor HV Chamber

6. US CMS EMU Failure Rates Vendors Data Chamber • Components Lifetime (Chamber): • Carbon Resistor -Discontinued, no replay from Vendor • Assume Surface Mounted Resistor Failure Rate • 0.0019%/1000 hrs (19 FITS). • Murata HV Capacitor • Failure rate: 8 FITS at Max HV (7.5 kV) Max T (85 oC) • Company Formula: 0.2 FITS at 4.5 kV and 25 oC • (0.0008 - 0.00002%/1000 hours)

7. US CMS EMU Failure Rates Vendors Data • Components Lifetime (Anode Protection Board): • Carbon Resistor -Discontinued, no replay from Vendor • Assume Surface Mounted Resistor Failure Rate • 0.0019%/1000 hrs (19 FITS). • Murata Surface Mounted C • Failure rate: 6 FITS 1.2 V • Motorola Switching Diode • Failure rate: 4 FITS Out • Surface Mounted Resistor • 0.0019%/1000 hrs (19 FITS) • 0.018%/1000 hrs (180 FITS) for • change in resistance 5V in

8. US CMS EMU Failure Rates Analysis - HV Sector Failures • Assumptions: • If any component fails, we need to turn the HV off for a given sector • Use only ME23/2 channel counts ( i.e. ~14 resistors, 2 filtering Cs on HV side and 12 decoupling Cs on Anode readout side) • Use largest l to provide an “Upper Limit” Estimate. lSector= (14 lR + 14 lC) = 14x(0.0019+0.0008 )=0.038 %/1000 hours • HV sectors in ME23/2 • 144 chambers x 6 layers/chamber x 5 sector/layer = 4320 HV Sectors • 90000 hours in 10 LHC years 4320 x 0.038 % x 90 = 148 Failures in 10 LHC years (3.4%) • If Carbon Resistors are failure-free and the Murata formula for aging at lower HV - lower Temperature is correct: lSector= 14 lC = 14 x 0.00002 =0.0003 %/1000 hours 4320 x 0.0003 % x 9000 = 1 Failure in 10 LHC years (0.02%)

9. US CMS EMU Failure Rates Analysis - Anode Protection Board • Assumptions: • If any component fails, we need to replace the Anode P.B. • Use only ME23/2 channel counts ( i.e. ~18 Carbon Resistors, 16 Surface mounted Resistors, 18 Switching Diodes and 4 Surface Mounted Capacitors). lAnode Board= (34 lR + 14 lD + 4 lC) = (34x0.0019+18X0.0006+4X0.0004) = 0.077% / 1000 hours • Anode Protection Boards in ME23/2 • 144 chambers x 24 Boards/Chamber = 3456 Boards • 90000 hours in 10 LHC years 3456 x 0.077 % x 90 = 240 Failures in 10 LHC years (7 %) • Almost no change if Carbon Resistors are failure-free. • If a failure due to “change in resistance” is a problem, then lAnode Board= 0.62% and 3456 x 0.62 % x 90 = 1928 Failure in 10 LHC years (56 %)

10. US CMS EMU Failure Rates Analysis - Anode Channel • Assumptions: • If any component fails in the Anode chain, we loose the Anode Readout. • Use only ME23/2 for the Anode Chain readout. lAnode Chain = (2 x lR + 2 x lC + 2 x lR + lD+ 2 x lR + lD) = (6x0.0019+2x0.0006+2x0.0004) =0.013%/1000 hours • Anode Channels • 144 chambers x 6 layer/chamber x 64 channels/layer=55296 Anode Channels • 90000 hours in 10 LHC years 55296 x 0.013 % x 90 = 647 Failures in 10 LHC years (1.2 %) • Almost no change if Carbon Resistors are failure-free. • If a failure due to “change in resistance” is a problem, then lAnode Chain= 0.11% and 55296 x 0.11 % x 90 = 5474 Failures in 10 LHC years (10 %)

11. US CMS EMU Failure Rates Summary • Failure rates for components that cannot be accessed during normal maintenance at LHC appear acceptable (~ few % for “chamber mounted” Resistors and Capacitors). • Failure rates for components that can be accessed appear somewhat higher (~10-50% depending on the assumptions for “hard-wired” Anode Protection Board). • Protection Circuit Boards: • Avoid “Hard-Wiring” • “Parallelize” Critical Components (i.e. +1.2 V distribution on Anode Protection Board).

12. US CMS EMU Failure Rates Summary - All Chambers