Model Form vs Level

The form of the model to be developed will depend on the level and the approach. For example, if empirical data is used directly without a model developed from it, assuming constant failure rate, the best estimate of the failure rate is simply:

time operating

Failures

= λ

If a life model is developed from life tests performed at various stress levels, the result will be a time-to-failure (TTF) distribution (described by the Weibull, lognormal or other statistical distributions) that is a function of stress levels. If a Weibull distribution is used, the general model will be:

( )

If models are to be derived from the analysis of field data, there are several possible model forms. Traditional methods of reliability prediction model development have included the statistical analysis of empirical failure rate data. When using multiple linear regression techniques with highly variable data (which is often the case with empirical field failure rate data), a requirement of the model form is that it be multiplicative (i.e. the predicted failure rate is the product of a base failure rate and several factors that account for the stresses and component variables that influence reliability). An example of a multiplicative model is as follows:

where:

λp = Predicted failure rate λb = Base failure rate πe = Environmrntal factor πq = Quality factor πs = Stress factor s q e b p

λ

π

π

π

λ

=

However, a primary disadvantage of the multiplicative model form is that the predicted failure rate value can become unrealistically large or small under extreme value

conditions (i.e., when all factors are at their lowest or highest values). This is an inherent limitation of multiplicative models, primarily due to the fact that individual failure mechanisms, or classes of failure mechanisms, are not explicitly accounted for. Another possible approach to model reliability is to segment the failure rate for each group of failure causes that are accelerated by stresses incurred during specific portions of a mission. Each of these failure rate terms are then accelerated by the appropriate stress or component characteristic. This is the model form used in the RIAC 217Plus methodology. This model form is as follows;

where:

λp = predicted failure rate

λo = failure rate from operational stresses

πo = Product of failure rate multipliers for Operational Stresses λe = failure rate from environmental stresses

πe= Product of failure rate multipliers for Environmental Stresses λc = failure rate from power or temperature cycling stresses πc = Product of failure rate multipliers for Cycling stresses

λI = failure rate from induced stresses, including electrical overstress and ESD λsj = failure rate from solder joints

πsj = Product of failure rate multipliers for solder joint stresses

The concept of this approach is that the occurrence of each group of failure causes is mutually exclusive, and their failure rates can be modeled separately and summed. By modeling the failure rate in this manner, factors that account for the application and component-specific variables that affect reliability (π factors) can be applied to the appropriate additive failure rate term. Additional advantages to this approach are that they:

o Address Operating-, Non-Operating- and Cycling-related Failure Rates in an additive model. These individual failure rates are weighted in accordance with the operational profile (duty cycle and cycling rate). The Pi factors modify only

sj sj i c c e e o o p

λ

π

λ

π

λ

π

λ

λ

π

λ

=

+

+

+

+

the applicable failure rate term, thereby eliminating many of the extreme value problems that plague multiplicative models.

o Are based on observed failure mode distributions, so that observed component root failure causes are empirically modeled

o Can be tailored with test data (if available) by applying it in a Bayesian fashion to the appropriate failure rate term. As examples, temperature cycling data can be combined with the failure rate from power or temperature cycling stresses (λc), or high temperature operating life can be combined with the failure rate from

operational stresses term (λo).

2.4. Assess Data Available

A predominant factor that will dictate the options that an analyst has in modeling the reliability of a product is the availability of data. The analyst should consider the following questions when assessing the availability of test data:

• Is field data available on the specific product or system?

• Is data on a similar product or system available? If so, is it field data or test data? • If data is available, is it:

o Relevant?

o Of sufficient quantity? o Of sufficient quality?

• If physics-based models are to be employed, is the required detailed data and information available, such as:

o Defect rates

o Material properties (e.g., functional characteristics) o Defect (flaw) distributions

o Material variation quantification (e.g., purity, yields, dimensions) o Etc.

Perhaps the most important element of a reliability program is the reliability testing of the product. Reliability test data is, in turn, a critical element for assessing reliability. In this context, a reliability test consists of two primary elements: measurement and exposure. The measurement is the means of assessing the performance of the product or system relative to its requirements. It usually consists of quantifying parameters that are specifiable attributes. It may include both continuous variables (i.e. gain, power output, etc.) or attribute data (i.e. a binomial representation of whether a product possesses an attribute or not). Exposure is the application of a stress or stresses. These stresses may consist of operational stresses or environmental stresses. Operational stresses are defined as those stresses to which the product will be exposed by the act of operating the product.

For example, a transistor is designed to have a voltage applied, and pass a given amount of current. As such, these are operational stresses. It will also be exposed to externally applied environmental stresses such as temperature, temperature cycling, vibration, etc. Reliability tests can be performed either by sequentially performing repeated cycles of a measurement, exposure, measurement, etc., or by continuously measuring performance parameters in-situ during exposure. It is usually desirable to perform in-situ

measurement so that times to failure can be accurately determined. In practical cases, however, it is not always feasible due to the complexities of setting up such measurement capabilities. If repeated cycles of a measurement, exposure, and measurement are used, the measurement intervals should be frequent enough so that sufficient resolution in the times-to-failure data is available.

Practical considerations for assessing the feasibility of testing products are: • Are samples available? If so, are they available in sufficient quantity?

• Are measurement systems available for continuous, in-situ, measurements during exposure? If not, repeated cycles of a measurement and exposure may be

required.

• Are laboratory facilities available to perform the exposure?

• Are the measurement and exposure facilities available to support a multi-cell test at various stress levels (i.e., application of various combination of stresses)? Additional considerations for testing products and systems are provided in Chapter 5.