# Presentation: 175978

## 5A AOE-0588 SSQ 21654 Fiber Optic Cable

**5A AOE-0588 SSQ 21654 Fiber Optic Cable**
**Anomaly - Risk Assessment Model**

**Boeing - Avionics Design & Analysis**
**P. H. Mueggler**
**(714) 896-4977**
**February 2000**

## PROBLEM:

**PROBLEM****:**
**SSQ 21654 Fiber Optic Cable has been found to contain anomalies not previously identified.  No test other than ‘normal’ ISS acceptance testing has been performed on many installed ISS cables.**

**OBJECTIVE:**
**Quantify the risk for the ISS application.**

## Command and Data Handling System

**Command and Data Handling System**

## ANALYSIS

**ANALYSIS**

- Assumptions
- Requirements
- Probability Model
- Probability Analysis Method
- Hardware Tested
- Defects
-    Data
-    Defect rates analysis
- Detection
-    Strength data
-    Strength distribution / percentiles
- Transmission loss
-    Transmission loss data
-    Transmission loss distribution / percentiles
- Correlation of Strength to Transmission Loss
- Results

## ASSUMPTIONS / GROUNDRULES

**ASSUMPTIONS / ****GROUNDRULES**

**DEFECTS**
** ****Defects are randomly distributed along cable length**
** ****Defect rate is constant for each lot**
**INSTALLATION & CHECKOUT**
** ****At least 0.5 lbs of tension is applied during installation of each cable**
** ****Defects with strength < 0.5 lbs are detected**
**OPTICAL PERFORMANCE**
** ****Transmission loss of < 1.5 dB per defect is acceptable performance**

## CANDIDATE REQUIREMENTS

**CANDIDATE REQUIREMENTS**

- Probability of inadequate transmission of optical signal:
- Critical functions (each)                         TBD       ( < 10**-3**)
- System (all functions) )                          TBD       ( < 10**-1**)
- Personnel hazards )                               TBD       ( < 10**-6**)

## PROBABILITY MODEL

**PROBABILITY MODEL**

## Prd (L)  =  Probability of a defect in a cable of length L

**PROBABILITY ANALYSIS METHOD**

- Pr*d *(L)  =  Probability of a defect in a cable of length L
-   For  *d*  = constant, follows Exponential probability density function
-   Pr*d *(L)  =  1  -  exp [ - *d* * L ]

*d*  =  defect rate = constant
-   calculated from defect data based on the Chi-Square Pdf

*d*  =    { χ**2**  α; 2(r+1)  }  /  2L

- L  =  total cable length tested
- r   =  number of defects found
- α  =  level of significance  ( = 1 - confidence level)

## HARDWARE TESTED

**HARDWARE TESTED**

## DEFECT RATE ANALYSIS

**DEFECT RATE ANALYSIS**

## DEFECT DETECTION:  STRENGTH DATA

**DEFECT DETECTION:  STRENGTH DATA**

** ****Lot E used to estimate population distribution.**
** ****Lots A and F results are consistent with population.**

## DEFECT DETECTION:  STRENGTH DISTRIBUTION

**DEFECT DETECTION:  STRENGTH DISTRIBUTION**

-  Distribution is linear in strength region of interest
-  30% of defects have strength < 0.5 lbs

## TRANSMISSION LOSS DATA

**TRANSMISSION LOSS DATA**

** ****Lot E used to estimate population distribution.**
** ****Lots A, C and F results are consistent with population.**

## TRANSMISSION LOSS DISTRIBUTION

**TRANSMISSION LOSS DISTRIBUTION**

** ****Distribution is linear in optical loss region of interest**
** ****38% of defects have transmission loss < 1.5 dB**

## CORRELATION OF STRENGTH AND TRANSMISSION LOSS

**CORRELATION OF STRENGTH AND TRANSMISSION LOSS**

**No statistical correlation between strength and transmission loss**

## RESULTS

**RESULTS**

**For Lot A  (Fall / winter ‘96 vintage cables)**

## CONCLUSIONS

**CONCLUSIONS**

**Lower Transmission Rate**

- HRDL
- (Fiber Optic)

- Ethernet
- (Wire)

**Pr{success} < 0.5**

**Pr{success} ~ 1.0**

- Pr {‘system’ success} ~ 1.0
- @ lower transmission rate