Using the PRISM Bayesian or Telcordia Method III Technique to Incorporate Field Data

The basis for many reliability analyses begins with predictive modeling. This essentially involves breaking down a system design and analyzing the components of the system at the assembly, subassembly, and part level. Many accepted predictive models can be used to analyze system components to produce an expected MTBF (Mean Time Between Failure) or failure rate. To make predictive analyses even more accurate, it can be very helpful to factor in field data. Field data refers to actual real-world data that includes important information on failures and operational time. Using metrics accumulated through the tracking of fielded units, you can augment your predictive analyses to provide MTBF values with more confidence.

Collecting Field Data

To augment your predictive analyses with field data, the first step is to determine whether field data is available. Often, information on deployed systems is tracked in a FRACAS (Failure Reporting and Corrective Action System). If field data is not being recorded in this type of system, it may be available in a database or other recording system. However, if field data is being collected but not being recorded in an organized manner, implementing a FRACAS may be a beneficial approach. Not only will a FRACAS help in data collection, it will aid in early detection of problems, improve corrective actions, and assist in the analysis of corrective actions. As an added bonus, it can augment current and future predictive analysis for new design, providing a closed-loop life cycle that significantly improves products with each design cycle.

An effective FRACAS will track field failures and provide good reliability metrics for your fielded units. Collected information such as number of failures, operating time, number of repairs, and repair time can be used to calculate actual field MTBF. When either the fielded system is being redesigned, or a new design is being developed based on the fielded system, the "real-world" metrics obtained from the FRACAS can be fed into your reliability prediction to produce results that are more accurate.

Figure 1. Example MTBF Parameters Calculated in a FRACAS

Using Field Data

If field data is available, there are several ways this data can be factored into your predictive analyses. This article discusses two common approaches. The first approach uses Bayesian techniques and is described in the PRISM standard; the second approach is a modified Bayesian technique described in the Telcordia standard.

Bayesian Technique

The Bayesian analysis method accounts for real-life experiences by combining the predicted component failure rate with empirical data. Field data can be combined with predictive data to provide an adjusted predicted value.

When you integrate field and test data into a prediction, you do not need to rely solely on the industry average values yielded by PRISM predictive models. Using Bayesian analysis, you can obtain failure rates that are more representative of your individual applications.

The benefits of adding test and field data to determine a calculated failure rate are:

• Integration of current reliability data when the actual failure rate prediction is being performed.
• Optimization of the reliability prediction based on valid historical data.

When you use an assembly or component in multiple systems, the operating parameters between systems will likely vary. Using Bayesian techniques, you can specify different stresses and temperatures while using the "lessons learned" in the field to modify the predicted results.

Figure 2. Example of Information Needed to Use Bayesian Analysis in PRISM

To begin, Bayesian techniques require a known or "prior" distribution, which will be adjusted based on sample field data. The starting point for number of failures and operating time is obtained from the prediction analysis, and is represented by a₀ and b₀ in the equation below. The following equation is used to obtain a failure rate employing Bayesian techniques:

Where:

λ	=	The resulting "adjusted" predicted failure rate.
a0	=	The equivalent number of failures of the "prior" distribution. This corresponds to the reliability prediction failure rate. a0= 0.5 (This value is determined by RAC.)
b0	=	The equivalent number of hours associated with the reliability prediction. Because a0 = 0.5, b0 = 0.5/λp Where: λp = The calculated predicted failure rate.
a1through an	=	The number of failures experienced in the test or field data. There may be n different types of datasets available. A dataset is defined as a matched pair of ai and bi values; a1 through an.
b1through bn	=	The corresponding number of cumulative hours (in millions) experienced from the empirical data. You will need to convert these values to equivalent hours by accounting for the accelerating effects between the applied test conditions and the actual use conditions.

If test data (in total test hours) taken at accelerated conditions is to be used in the Bayesian analysis, PRISM first converts it to an equivalent number of field hours under actual field stresses. After a traditional reliability prediction for the assembly is performed at both the test and field conditions, PRISM determines the equivalent number of hours (b_i) by using the failure rate ratio between the test and use temperatures as follows:

λ_T1 is the predicted failure rate at the test temperature, λ_T2 is the predicted failure rate at the actual use temperature, and H_T is the actual number of test hours.

Example

Assume that the calculated failure rate of a device is 1 FPMH. Two datasets are available: one is from field conditions (4 failures in 10⁶ total operating hours), and the other one is from accelerated conditions (5 in 10⁵ total test hours) where the acceleration factor is 10. Therefore,

a₀ = 0.5,  a₁ = 4,  a₂ = 5,   b₀ = 0.5/1.0E-6 = 0.5E6,  b₁ = 1.0E6,  b₂ = 10 * 1.0E5 = 1.0E6

Hence, the effective hours from the test data is 10⁶. Therefore,

λ = (0.5 + 4 + 5)/ (0.5E6 + 1.0E6 + 1.0E6) = 3.8E-6

As expected, the adjusted failure rate of 3.8 FPMH differs from the calculated failure rate (1 FPMH) and better represents the device in use.

Telcordia Method III

If Telcordia is used to perform reliability predictions, it provides a method for adjusting the prediction values with either accumulated test data or real-life field data. Using Telcordia Method III (Black Box Integrated with Field Data), the predicted MTBF of a unit or device based is based on field data.

Method III MTBF values are calculated as a weighted average of the observed field failure rate and the Telcordia predicted failure rates. The weighting factor is determined by the number of total operating hours during field testing. When the number of total operating hours is large, the field data heavily influences the results. When the number of total operating hours is small, the predicted values heavily influence the results. Method III is applying Bayesian techniques in the same manner as described above.

Depending on your situation and the field data that you have collected, you can choose from Telcordia Method III (a), (b), or (c).

Method III(a) provides failure rate predictions for devices, units, or subsystems based on actual in-service performance by accounting for Operating Time and Number of Failures.

Figure 3. Telcordia Method III(a) Inputs

Method III(b) provides failure rate predictions for devices, units, or subsystems based on in-service performance as part of another system by accounting for Operating Time, Number of Failures, and Tracked Unit Temperature.

Figure 4. Telcordia Method III(b) Inputs

Method III(c) provides failure rate predictions for devices, units, or subsystems based on the in-service performance of similar equipment by accounting for Operating Time, Number of Failures, and Tracked Unit Failure Rate.

Figure 5. Telcordia Method III(c) Inputs

When there is field data, the device steady-state failure rate (λ_SS) can be obtained using the formula below. In this formula, it is assumed that the predicted black box failure rate (λ_BB) is based on data that includes at least two failures. To use this technique, the total operating hours must be sufficiently long to provide a reasonable opportunity for at least two failures to have occurred. The steady state failure rate is determined by:

λ_SS = (2+f) / (2/λ_BB + V * t * π_E * 10^-9)

Where λ_BB is the predicted failure rate of the system being analyzed, t is the total operating hours of the comparable system, π_E is the environmental factor for the subject system, f is the number of failures, and V is the factor to adjust for differences between the subject and its counterpart in the tracked systems.

The equation for V is:

V = λ_BBC * π_EC / (λ_BB * π_E)

Where λ_BBC is the predicted failure rate of the comparison system and π_EC is the environmental factor for the comparison system. If the subject system is a test unit and is operated in the same environment as the comparable system, then V = 1.

Example

Consider a device whose predicted failure rate is 26.4 FITs, and the environmental factor is 2. Assuming that there are eight failures (f = 8) from the field data of t = 1.0 E8 total operating hours:

λ_SS = (2+8) / (2/26.4 + 10⁸ * 2 * 10^-9) = 36.3 FITs

Now if we assume that the subject device is operated at 450^oC and the test unit was operated at 500^oC, then we need to calculate V using their temperature factors (1.2 and 1.5). Here V = 1.5/1.2 = 1.25.

λ_SS = (2+8) / (2/26.4 + 10⁸ * 1.25 * 2 * 10^-9) = 30.7 FITs

The predicted failure rate is lower in this case because the field units are operating at a greater degree of temperature stress.

Conclusion

Prediction analyses can be effectively augmented using field data to provide reliability metrics based on actual real-world information. Relex software tools support all the techniques mentioned in this article, and provide these capabilities across all our predictive models. To learn more about Relex prediction tools or Relex FRACAS, go to www.relex.com/products/index.asp. For additional information, please email info@relex.com or contact your Relex Application Consultant.