Question

Explain why it is practically impossible to validate reliability specifications when these are expressed in terms of a very small number of failures over the total lifetime of a system.

Short answer

Validating low failure reliability specifications is impractical due to the need for extensive resources and time, requiring alternative testing methods.

Step-by-step solution

Understanding Reliability Specifications

Reliability specifications often describe the expected performance of a system over its entire lifespan. These specifications can be represented in terms of the number, or frequency, of allowable failures during the system's intended use period. For example, a specification might state that a system is expected to fail no more than twice over 10 years.

Statistical Sampling Requirements

To validate a reliability specification, we need a statistically significant number of observations or data points. This often means observing many instances of the system over time to derive meaningful conclusions about its performance. The smaller the acceptable number of failures, the more instances and time are required to ensure any observed failure rate is representative.

Issues with Low Failure Rates

When a specification allows for very few failures, such as one or two over the entire lifetime, it can be practically impossible to observe enough failures to make reliable statistical conclusions. This requires an impractically large number of systems and an extended period to assess accurately.

Resource and Time Constraints

Practical constraints such as the cost, time, and resources required to test and monitor a system limit the ability to validate such specifications. Monitoring thousands of systems over a decade purely for validation purposes is often beyond feasible limits for most projects.

Reliability Testing Alternatives

Given these challenges, reliability is often tested via accelerated life testing, mathematical modeling, or simulation rather than direct observation. These methods estimate the failure rates instead of directly observing them during normal operation over the full planned lifetime.

Key concepts

Reliability Specifications

Reliability specifications define how a system is expected to perform over its life span. They typically describe the maximum number of acceptable failures that can occur during the system's operational lifetime. These specifications are crucial for setting expectations and benchmarks for system durability and quality.
They are typically expressed in terms of failure rates or the number of allowable failures across a defined period. For example, a device that is expected to fail no more than once every five years has a defined reliability specification. Understanding these specifications helps manufacturers design products that meet market expectations and regulations. However, when a reliability specification involves very few allowable failures, it poses challenges in testing and validation.

Statistical Sampling

Statistical sampling is a method used to collect, analyze, and interpret data to make estimates or inferences about a population based on a smaller sample. In reliability testing, statistical sampling involves observing a set number of units to predict the overall reliability of the product.
The larger and more randomized the sample size, the more accurate the predictions. However, when reliability specifications allow for very low failure rates, achieving a statistically significant sample size becomes challenging. Imagine needing to monitor thousands of units for several years just to confirm that a product fails less than once in a decade. This scenario represents a potential hurdle in validating reliability specifications that involve minimal expected failures.

Accelerated Life Testing

Accelerated life testing (ALT) is a useful approach to predict a product's longevity in a shorter time frame. This method artificially speeds up the life span of a product by subjecting it to higher stress levels than it would normally experience. By doing so, failures that would typically occur over years can be observed in a much shorter period.
This testing helps in estimating a product's failure rate without waiting for the natural life cycle to pass. ALT is invaluable in reliability testing when dealing with low failure rates over extensive time periods, offering a practical alternative to waiting and direct observation. It allows companies to make educated decisions about a product's reliability before it fully enters the market.

Mathematical Modeling

Mathematical modeling involves using mathematical formulas and algorithms to simulate and predict the behavior of a system. In the context of reliability testing, models are created to represent the potential failure modes of a product under various conditions. It allows engineers to predict how often and why a system might fail.
These models can be increasingly complex, depending on the number of variables involved. They provide a way to make informed predictions about reliability without needing extensive product longevity trials. Using mathematical modeling is cost-effective and time-saving and helps address the impracticalities of validating reliability specifications through real-time observation alone.