Scenario
Product development is complete, and the client asks: "What is the MTBF of this equipment?"
You consult MIL-HDBK-217, sum up the failure rates of all components, and calculate an MTBF of 50,000 hours.
Problem: This number uses component failure rate data from 1991, assuming an operating temperature of 55°C, while your product actually operates in a 25°C indoor environment. This MTBF prediction underestimates your true reliability.
Reliability prediction requires understanding the methods, not just blindly consulting manuals.
Basic Calculations for System Reliability
Series Systems
All components must function correctly for the system to function correctly:
R_system = R1 × R2 × R3 × ... × Rn
Example: Three components with individual reliabilities of 99%, 98%, and 97%:
R_system = 0.99 × 0.98 × 0.97 = 0.941 = 94.1%
Lesson from Series Systems: The more components there are, the lower the system reliability. Each additional necessary component decreases system reliability.
Parallel Systems (Redundant)
At least one component must function correctly for the system to function correctly:
R_system = 1 - (1-R1)(1-R2)
Example: Two power supplies, each with 90% reliability, connected in parallel:
R_system = 1 - (1-0.9)(1-0.9) = 1 - 0.01 = 0.99 = 99%
A single component with 90% reliability, when paralleled, increases system reliability to 99%. The power of redundant design.
Derating Design
Components operating under conditions below their rated specifications experience a significant reduction in failure rate.
Principles:
| Derating Ratio | Reliability Improvement |
|---|---|
| Voltage Derating 50% | Failure rate can be reduced by more than 10 times |
| Temperature Reduced by 10°C | Failure rate approximately halves (Arrhenius Equation) |
| Power Derating 50% | Failure rate reduced by 5-8 times |
In practice: Allocating 30-50% derating margin during design is the cheapest way to improve reliability.
HALT: Finding Real Failure Modes
HALT (Highly Accelerated Life Testing)
Uses stresses (temperature shock, vibration, voltage, etc.) far exceeding normal operating conditions to quickly expose potential failure modes.
HALT is not used to predict MTBF, but rather to:
- Find the product's "operating limits" and "destruction limits"
- Discover design weaknesses before mass production
- Confirm whether design margins are sufficient
Failures found after HALT testing, when corrected during the engineering sample phase, cost 1/100 of a recall after mass production.
The Correct Approach to Reliability Prediction
Prediction is an estimate, not a guarantee:
- Data from manuals like MIL-HDBK-217 have timeliness and applicability limitations.
- Component quality, manufacturing process, and application environment all affect actual reliability.
- Field data (Demonstrated MTBF) is always more credible than predicted values.
Main uses of reliability prediction:
- Design comparison (Which design, A or B, is more reliable?)
- Identify the weakest link in the system (reliability bottleneck)
- Provide an estimated value to customers (must explain assumptions and uncertainties)
Golden Quote
"Reliability prediction gives you a starting point, not an end. In the real world, your design margin, process quality, and customer usage are the factors that determine actual reliability. Treating a predicted value as a guarantee is the most common integrity error engineers make."