- Zack Salloum

# Reliability Calculations for an Array of Electronic Components

**I. Introduction**

“The reliability is the ability of a system or component to perform its required function under stated conditions for a specified time.” (*Wikipedia*)

Historically, the bathtub failure rate curve has been used to discuss electronic equipment (product) reliability. Observations and studies have shown that failures for a given part or piece of equipment consist of a composite of the following:

The bathtub curve (the blue curve) is the sum of infant mortality, random failure, and wear out curves.

The calculation of Mean Time Between Failure (MTBF) is often required as an aid in predicting the reliability of electronic equipment under different operating conditions.

The value of MTBF for a component is based upon failure-rate models which have been developed in conjunction with MIL-HDBK-217E. The MTBF is not a guarantee of useable product lifetime, but is a guide for planning the operational use of the equipment.

**A. Region I – Infant Mortality / Early Life Failures**

This region of the curve is depicted by a high failure rate and subsequent flattening (for some product types). Failures in this region are due to quality problems and are typically related to gross variations in processing and assembly. Stress screening has been shown to be very effective in reducing the failure (hazard) rate in this region.

**B. Region II—Useful Life or Random Failures**

Useful life failures are those that occur during the prolonged operating period of the product (equipment). For electronic products it can be much greater than 10 years but depends on the product and the stress level. Failures in this region are related to minor processing or assembly variations. The defects track with the defects found in Region I, but with less severity. Most products have acceptable failure rates in this region. Field problems are due to “freak” or maverick lots. Stress screening cannot reduce this inherent failure rate, but a reduction in operating stresses and/or increase in design robustness (design margins) can reduce the inherent failure rate.

**C. Region III—Aging and Wear out Failures**

Failures in this region are due to aging (longevity exhausted) or wear out. All products will eventually fail. The failure mechanisms are different than those in regions I and II. It has been stated that electronic components typically wear out after 40 years. With the move to deep submicron ICs, this is dramatically reduced. Electronic equipment/products enter wear out in 20 years or so, mechanical parts reach wear out during their operating life. Screening cannot improve reliability in this region, but may cause wear out to occur during the expected operating.

**II. Part Failure-rate Model**

In the case of electronic systems, an area of primary concern is the MTBF values for discrete components. The determination of the predicted MTBF of every component is a calculation using the part failure-rate model for electronic devices as found in MIL-HDBK-217E.

Based on the model, we can get the adjusted MTBF based on operating junction temperature. The junction temperature is function of operating current. By applying statistical distributions we can predict operational failures based on the calculated MTBF.

**III. Statistical Distributions for electronic components**

For components reliability prediction we use the “Exponential distribution”. The exponential distribution is one of the most important distributions in reliability work. It is used almost exclusively for reliability prediction of electronic equipment. The exponential model is useful and simple to understand and use; it is good for introductory concepts and calculations.

When the same component is used in large numbers as the case of LED signs, or resistors arrays or LCD displays, applying the “Exponential distribution” will predict large number of fails.

Example :

Consider LED matrix of 10K unit. The individual LED MTBF is 100K. If we consider all the LED are in “series” for the reliability calculations (any fail on any LED is equal a fail on the matrix) then LED array MTBF=10. This implies a failure every 10 hours!!!

The “Poisson Distribution” is used to predict the array failure when large number of components is used.

Applying the “Poisson Distribution” for the same example gives an MTBF ~ 20K which is more likely to happen then 10!