Three Methods for Incorporating Failures Rates for Mechanical Components into System-Level Reliability Predictions

While reliability practitioners are generally familiar with the many methods available for modeling the reliability of electronic components, many are unfamiliar with the methods available for modeling the reliability of mechanical components. This document describes three different methods that you can use to estimate the reliability of a mechanical component and then incorporate the predicted failure rate into your system-level reliability predictions:

• NPRD and EPRD databases. The Nonelectronic Parts Reliability Databook (NPRD) and Electronic Parts Reliability Databook (EPRD) are databases of failure rate data. Created by the Reliability Analysis Center, these two databases supply failure rate data for many different mechanical and electronic components.
• The Handbook of Reliability Prediction Procedures for Mechanical Equipment. This unique document is the only existing standard for parametrically modeling the reliability of a mechanical component. Developed under the direction of the United States Navy, The Handbook of Reliability Prediction Procedures for Mechanical Equipment provides models for predicting the reliability of many different mechanical components.
• Weibull Analysis. If field failure data has been collected for a mechanical component, Weibull analysis can be used to determine the best-fit distribution for these failure data points. This information can then be used to estimate the parameters of the failure distribution and determine component reliability.

NPRD and EPRD Databases

The Reliability Analysis Center utilized its existing infrastructure for the collection of field failure data to create two databases of failure rate information: the Nonelectronic Parts Reliability Databook (NPRD-95) and the Electronic Parts Reliability Databook (EPRD-97). The NPRD database supplies failure rate information for actuators, bearings, brakes, clutches, connectors, gears, inductive components, optoelectronic devices, pumps, relays, seals, solenoids, splines, springs, and valves. The EPRD database supplies merged failure rate information for electronic parts as well as all of the mechanical parts in the NPRD database. When a model is not available for a particular component, you can search the NPRD or EPRD database to find failure rate information for that part.

The failure rate unit in the NPRD and EPRD databases is failures per million calendar hours rather than the more traditional failures per million operating hours. The primary difference between the NPRD and EPRD databases is that the NPRD database provides a failure rate for each line item displayed for a part while the EPRD database provides a merged failure rate based on all line items displayed for a part. For example, Figure 1 displays NPRD failure rate information for a ball bearing.

Figure 1. NPRD Database with Single Line Item Failure Rates for Ball Bearings

Part types or subtypes followed by a "(Summary)" label indicate a grouping of all part types or subtypes to provide average failure rates for a part based on quality level and environment. For example, when Ball (Summary) is selected as the part subtype for the bearing, the failure rates provided are averages of all ball bearings based on quality level and environment. When dashes appear in the Quality and/or Environment fields, the failure rate shown is the average failure rate of all parts, regardless of quality and/or environment. If a check mark appears in the Miles field, the failure rate unit is measured in failures per million miles rather than failures per million calendar hours.

Figure 2 displays the EPRD merged failure rate data for a ball bearing. There are no longer Summary part types and subtypes or dashes in the Quality and/or Environment fields. Instead, the second and third level part subtype and part quality, environment, and hermeticity fields are used to filter the failure rate data shown. The individual failure rates for all parts listed in the table are used to generate the merged failure rate shown.

Figure 2. EPRD Database with a Merged Failure Rate for all Ball Bearing Part Types

Mechanical Component Modeling

The Handbook of Reliability Prediction Procedures for Mechanical Equipment (Document No. NSWC-98/LE1) provides information about and failure rate calculation models for the following mechanical devices:

• Seals and Gaskets
• Springs
• Solenoids
• Valve Assemblies
• Bearings
• Gears and Splines
• Actuators
• Pumps
• Filters
• Brakes and Clutches
• Compressors
• Electric Motors
• Accumulators, Reservoirs
• Threaded Fasteners
• Mechanical Couplings
• Slider-Crank Mechanisms
• Sensors and Transducers

According to this handbook, all mechanical components are composed of some combination of the above devices. Consequently, the reliability prediction results for these individual devices can be combined to determine the total reliability of any mechanical component in its operating environment.

The models in this handbook were developed after attempts to collect failure data for seemingly similar mechanical components yielded wide-ranging failure rates. These large fluctuations were primarily due to the ability of most mechanical components to perform multiple functions in many different applications. For example, there are more than 100 types of hydraulic valves. The same hydraulic value might be used in automotive, industrial, and aerospace applications, where operating environments vary greatly. The vendor may also offer this hydraulic valve in a base configuration and in configurations with a manual shut-off feature and/or automatic control mechanism. Failure data for specific applications of non-standard components is seldom available. When this data is available, its usefulness depends on whether your application for the component is the same as or similar to the application for which the failure rate was calculated.

The failure rates of mechanical components also differ from those of electronic components in that they are not usually described by a constant failure rate. Wear, fatigue, and other stress-related failure mechanisms result in equipment degradation. Because mechanical components are much more sensitive to impact loading, operating mode, and utilization rate, models for these components must take stress levels, total operating hours, and total failures into account. Thus, the mechanical component models in The Handbook of Reliability Prediction Procedures for Mechanical Equipment consider many different variables that affect component reliability, including material properties, operating environment, and critical failure modes at the component part level.

Figure 3 shows the parameters required for calculating the failure rate of a threaded fastener. Each mechanical component model has its own set of required parameters. The values that you supply for the parameters requested are used to estimate the failure rate of the component based on stress/strength and environmental relationships for your particular application. The values to enter can be located on engineering drawings or in design standards. Some can also be obtained by taking actual measurements.

Figure 3. Parameters for a Threaded Fastener

The failure rate models for a few mechanical components require a base failure rate as one of the parameters. Figure 4 shows the parameters required for calculating the failure rate of a gear. First, the failure rate supplied by the manufacturer of the gear is entered as the base failure rate. The values that are then entered for the other parameters are used to adjust this base failure rate to account for any differences in your usage as compared to that for which the gear was designed. Factors taken into account in the failure rate adjustment include load, alignment, lubrication, speed, temperature, and service (which considers the expected extent of usage in vibration and shock environments).

Figure 4. Parameters for a Gear

Weibull Analysis of Failure Data

Weibull analysis refers to graphically analyzing probability plots to find the distribution that best represents a set of failure data points for a given failure mode. If field failure data has been collected for a mechanical component, Weibull analysis can be used to determine the statistical distribution that best "fits" or presents these failure data points. Although the Weibull distribution is the leading method worldwide for examining failure data to determine best-fit distributions, other distributions occasionally used for failure data analysis include the exponential, lognormal, and normal. Figure 5 shows the plotting of time-to-failure data for a unique failure mode on a Weibull probability plot.

Figure 5. Weibull Probability Plot

By "fitting" a statistical distribution to the failure data, Weibull analysis provides for making predictions about the life of the products in the population. The parameterized distribution for this representative sample can be used to estimate product reliability, probability of failure at a specific time, mean life for the product, and failure rate, which can be incorporated in your system-level reliability predictions.

Summary

The NPRD and EPRD databases, The Handbook of Reliability Prediction Procedures for Mechanical Equipment, and Weibull analysis all provide methods that you can use to estimate the reliability of a mechanical component. All three of these methods for obtaining failure rate estimates are supported in Relex Reliability Prediction. You can quickly search the NPRD or EPRD database for the failure rate for any part and insert it for the component. Because Relex Reliability Prediction supports the mixing of calculation models for the different components in a system, you can use The Handbook of Reliability Prediction Procedures for Mechanical Equipment as the calculation model for supported mechanical components and MIL-HDBK-217, Telcordia, and/or any other calculation model for supported electronic components.

If Relex Weibull is licensed, it is possible to use it to analyze any failure data that you have collected for a component. Wrapped in a user-friendly, flexible interface, this powerful statistical tool has a powerful, behind-the-scenes calculate engine that automatically handles the complexity of the statistical methodology. In Relex Reliability Prediction, you can link directly to Weibull calculation results for a component so that it can be used to calculate a failure rate for the part. The ability to use all of these methods to model the reliability of mechanical and electronic components in Relex Reliability Prediction ensures that your system-level reliability predictions are robust. For additional information about Relex Reliability Prediction and other Relex modules, visit http://www.relex.com/products/index.asp.