Fleet Maintenance Predictions from Early Fail Data by Paul F. Watson (Rev A)

Introduction: New product launch leaves engineers with warranty and maintenance anxiety. Products ranging from food processing machines to bicycles to airplanes all have failure and wear-out issues. While “lead the fleet”(1) programs and simulated life testing (2) can provide insight, scientific methods of extending such information to fleet maintenance predictions are a challenge.

Management typically wants a description of how many failures can be expected at various ages, similar to the graphs below.

Figure 1 is a conceptual illustration of cumulative percent product failures with increasing age. Figure 1 indicates at 300 operational hours, 30% of “fielded units” are expected to fail.

Figure 2 is a conceptual illustration of cumulative percent of aircraft landing gear failures. Figure 2 indicates at 400 landings, about 3% of the landing gears are expected to have failed. Neither figure is intended as illustrating good design practice.

Early Failure Analysis Issues: While management typically wants predictive failure models, drawing such graphs based on early field failures (or accelerated laboratory testing) is a statistical challenge for three reasons.

1. Many experts argue that failure modes should be analyzed individually. e.g. if a printed circuit board is known to fail by two predominant failure modes (solder joint fatigue else capacitor failure), then testing followed by analysis should be conducted separately for each mode (3)(4).
2. Failure data from accelerated laboratory testing must be correlatable to equivalent “real service life” to construct graphs like Figure 1. e.g. if a circuit board is exposed to thermal cycling testing, a mathematical model relating solder joint failure count to equivalent service life is required. Math correlative equations for various failure modes can be constructed from published failure model research articles. (5)(6)(7)(8)
3. Prediction of life failure behavior from limited numbers of “early failures” restricts the statistical models that can be used. Gaussian Bell curve analysis cannot be used because average life computation requires knowing failure times for an entire test sample. Weibull Analysis does work because it relies on median percents of data-points - not on total population average.

Use of Weibull Equations for Failure Modeling: Weibull statistical analysis is a good approach for modeling failure from early data because:

• Weibull is capable of modeling a wide variety of statistical behavior.
• Weibull Analysis provides well defined techniques.
• Weibull can model data sets in which half or more of the test articles have not been taken to failure. For example, if 30 widgets are subject to life testing but test is terminated after 11 failures, Weibull can model the result provided the total number of tested samples is known.
• The Weibull Plot (see below) provides good indication of analysis success.?Note that Weibull analysis can be applied to a wide variety of phenomena - not just equipment failures!

Conclusion: Statistically justified wear-out predictions for new designs are possible based on either early field failure data, or based on accelerated laboratory testing of samples. Such analysis requires either:

• Known number of units exposed to the expected service environment and usage.
• Known number of units exposed to an accelerated test regime which can be equated to equivalent service life.

When such analysis is performed, each failure mechanism should be analyzed separately. For example, radiator failures and break surface wear-out failures should not be analyzed as a single dataset. They should be analyzed separately, and individual wear-out graphs like Figures 1 and 2 should be created.

For Further Study:

• The Weibull Bible by Paul F. Watson provides clear explanations why Weibull Analysis works & provides instruction on analysis by spreadsheet. See https://www.weibullbible.com for a list of Internet bookstores.
• Weibull Dr. software provides an easy to use Weibull Analysis capability. Weibull and similar software is especially helpful for performing 3 parameter Weibull Analysis.
• https://www.weibullbible.com provides readers with Weibull Analysis articles.

Footnotes:

1. “Lead the Fleet” programs attempt to expose a small number of delivered items to extensive use in an effort to identify “early fail” features of a new design.

2. Simulated life testing exposes test articles to accelerated wear environments. For electronics, high temperature has known effect on capacitor failures while temperature cycling accelerates solder joint failures according to known mathematical models. Accelerated corrosion models can also be developed for various product assembly constructions.

3. “The Weibull Bible” by Paul F. Watson pp 136-140 , also pp 183-186. See www.amazon.com for publication details.

4. “The Use of Weibull in Defect Data Analysis”, Warwick Manufacturing Group, Internet, 6 December 2004 discusses the need for separate analysis of each failure mode.

5. David S. Steinberg in his book “Preventing thermal Cycling and Vibration Failures in Electronic Equipment” provides a power law damage model for computing tin lead solder joint life from thermal cycles. A derived test acceleration expression for full life equivalence follows:

Σni ΔTi 2.5 environ + Σ ni ΔTi 2.5 oper = nt * ΔTt 2.5 test

n = number of thermal cycles from environment, from operation or from test

ΔT is the temperature swing (Tmax-Tmin) for environment, turn-on or test.

2.5 is the fatigue exponent for tin lead solder (see D. S. Steinberg)

6. The Archard Equation by J. F. Archard “Contact and Rubbing of Flat Surfaces”, Journal of Applied Physics Volume 24, Number 8 August 1953 p275 provides a mathematical model for the amount of wear induced under varying conditions. When equipment failure can be defined in terms of surface wear, Archard equations enables determination of equivalent life damage. Recent studies support the Archard Equation.

7. Prediction of Archard’s Wear Coefficient for Metallic Sliding Friction Assuming a Low Cycle Fatigue Wear Mechanism”, Wear (1986) pp275-288 provides an alternative theory based analysis justifying the Archard Equation and provides a basis for computing Archard Coefficients.

8. The author has reviewed numerous corrosion articles. An Italian study compared corrosion effects from various land environments and from testing. The article provides sufficient detail to develop a test acceleration factor for laboratory testing.

9. “The Weibull Bible” by Paul F. Watson, see Appendices J and F. See www.amazon.com for publication details. Appendices J and F provide insight into how the size of a test population affects statistical predictions.

10. Development of accelerated test methods requires a detailed numerical understanding of the expected service environment, number of operational cycles etc. in addition to developing accelerated test models which relate test cycles to fielded use. For aircraft electronics, this implies knowing the number of flights during a lifetime, the expected take-off temperatures and associated installation bay temperatures during flight. Additional solder joint fatigue results from temperature rise at “turn on” thus the total life number of “turn-ons” is also needed.

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