# Presentation: 266164

## Mean Time To Failure (MTTF) Analysis

**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**

## US CMS EMU

**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 (t)=f(t)/R(t) is called the failure rate function of the system. 			**Note: f(t) and R(t) are related by a 3****rd**** definition**

## US CMS EMU Failure Rates

**US CMS EMU Failure Rates**
**Introduction**

**Pratical Experience**
- From direct observation, most of the (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)

******(t)**

**t**

**I**

**II**

**III**

**Early**
**failures**

**Random Failures**

**Wear-out failures**

## US CMS EMU Failure Rates

**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/
- Series Connections
- Theorem:
- In system consisting of n unrepairable components C1,....Cn in series connection with independent lifetimes T1,...Tn the failure rate (t) is given by
- (t)= i(t)
**NOTE: Parallel connections do not behave like a parallel resistive connection**

**S1**

**S2**

## US CMS EMU Failure Rates

**US CMS EMU Failure Rates**
**Chamber E&E Components**

**Electrical Path:**

**Carbon Resistor**

**Surface Mounted Resistor**

**Chamber**

**HV**

## US CMS EMU Failure Rates

**US CMS EMU Failure Rates**
**Vendors Data**

**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)

## US CMS EMU Failure Rates

**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**

**Out**

**5V in**

**Motorola Switching Diode**
- Failure rate: 4 FITS

**Surface Mounted  Resistor **
- 0.0019%/1000 hrs (19 FITS)
- 0.018%/1000 hrs (180 FITS) for
- change in resistance

## US CMS EMU Failure Rates

**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 ******** to provide an “Upper Limit” Estimate.**
******Sector****= (14********R**** + 14 ********C****) = 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:**
******Sector****= 14 ********C**** = 14 x 0.00002 =0.0003 %/1000 hours**
**4320 x 0.0003 % x 9000 = 1 Failure in 10 LHC years (0.02%)**

## US CMS EMU Failure Rates

**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).  **
******Anode Board****= (34********R**** + 14 ********D ****+ 4 ********C****) = (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 ********Anode Board****= 0.62% and**
**3456 x 0.62 % x 90 = 1928 Failure in 10 LHC years (56 %)**

## US CMS EMU Failure Rates

**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.  **
******Anode Chain ****= (2 x ********R**** + 2 x ********C**** + ****2 x ********R**** + ********D**** ****+ ****2 x ********R**** + ********D**** ****) = (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 ********Anode Chain****= 0.11% and**
**55296 x 0.11 % x 90 = 5474 Failures in 10 LHC years (10 %)**

## US CMS EMU Failure Rates

**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).**

## US CMS EMU Failure Rates

**US CMS EMU Failure Rates**
**Summary - All Chambers**