Reliability Activities And Their Impact On Weibull Shapes

EP Editorial Staff | January 2, 2006

There’s been a shift in the maintenance and reliability marketplace towards more analytical software that takes predictive maintenance and equipment history data and then provides optimum solutions for a company’s assets.

The Weibull distribution is a widely recognized statistical model created by Swedish-born Waloddi Weibull to describe life distributions. Its primary advantage is that it requires very small amounts of data when compared with other forms of statistical analysis. It could be said that the primary job of physical asset managers is to prevent failures. Stated another way, the primary job of physical asset managers is to develop and then analyze data points for improved decision making. A statistical method that is effective using small amounts of data is a very useful tool. There is a direct relationship between maintenance and operating activities performed on equipment and the Weibull shapes that are developed for the equipment. This article discusses basic Weibull shapes, how operating and maintenance activities impact the reliability of equipment and the steps organizations can take to change those shapes to meet the needs of the business for equipment availability.

The bathtub curve
The bathtub curve consists of three distinct regions. Each region contains its own unique values for the Weibull parameters, Eta, Beta, and Gamma. The Weibull parameters provide insight into the failure mechanism that is present. (See Table I.)

What Beta values tell us
Beta values are extremely important because they tell us the failure behavior of the component. Knowledge of the failure behavior will lead us down a certain path when trying to improve overall reliability and availability. This will aid in decisions as to whether to apply preventive or predictive maintenance techniques to the equipment component.

Infant failures
Beta less than one, or infant failure, indicates that there may be a quality issue present among our maintenance, operating or spare parts acquisition programs. There is not a time-based maintenance activity for these types of failures until the root cause or causes of the infant failures are determined. The goal is to eliminate or minimize the high early failure rate represented by the curve.

There is a large laundry list of possible causes of infant failure mechanisms. Table II gives examples of the sources of infant failures. When examining these failure causes, it we can readily see that there is little benefit from investing in advanced predictive technologies to prevent infant failures.

High failure rate random failures
Random failures are characterized by a Beta value of approximately one. High failure rate random failures have a shorter than expected, or shorter than desired characteristic life, or Eta. Random failures typically lend themselves to either route-based, or constant condition monitoring, but still may have a greater than desired negative impact on the goals of the organization if the failure rate is too high.

Random failures are usually caused by some outside action that induces failures into the component. The organizational activities listed in table three are some likely sources of higher than expected or desired random failure rates. When examining the failure causes for random failures, it is easy to see that increasing the focus on the preventive maintenance program, particularly the basics, would eliminate many random failures.

Short life wearout failures (early wearout)
Generally, wearout failures lend themselves to some type of time-based replacement or overhaul strategy. While wearout is predictable, it can have a significant negative impact on the goals of the organization if components are not lasting as long as expected or desired. This is the area where a substantial return on investment can be realized when deploying predictive maintenance tools and techniques.

Early wearout is often caused by a lack of understanding of the stresses present in the equipment during the design phase, but there also are organizational activities that can lead to early component wearout. Again, the proper utilization of predictive techniques, such as vibration analysis, thermography, and spectrographic oil analysis can provide significant benefits.

How you know what you have (build-ing Weibull shapes without data)
Many companies do not have the complete data to perform a full Weibull analysis on their failing components. They do, however, have some data from their CMMS/EAM system, their predictive software systems and even information from experienced maintenance and operations personnel who are knowledgeable about what fails—and how. The trick to building Weibull shapes without complete CMMS/EAM system and predictive system data is to learn what questions to ask the maintainers and operators.

This isn’t perfect
The questioning method for building Weibull shapes is not a perfect replacement for a CMMS/EAM system or predictive system data. Still, it does provide a good starting point until an organization is able to build a complete database. The goal should be to eventually develop a database of predictive information that will allow for the development of maintenance tactics and strategies to eliminate undesired failures that keep you from meeting your business goals.

The key things to remember here are that the failure mechanisms present in equipment are a reflection of the maintenance, operating and procurement activities present within your organization. Furthermore, there is a direct link between best maintenance and operating practices and changing the Weibull behavior of your equipment. As an organization develops the preventive and predictive maintenance data necessary to properly analyze, it will progress to using analytical predictive software. The Weibull techniques discussed in this article help provide an understanding of how the analytical software utilizes this data to optimize preventive and predictive maintenance policies and procedures. MT

Bill Keeter, CMRP, is president of BK Reliability Engineers, Inc. (BK). Based in Titusville, FL, BK provides services that help facilities improve asset performance through Weibull analysis, RCM, availability simulation and life cycle cost analysis. Keeter has over 25 years of experience in maintenance engineering and management. He has successfully implemented maintenance improvement programs in a variety of manufacturing and production facilities, across a range of industry segments, and has authored and presented a number of articles and papers on practical applications. He holds degrees in Business Administration and Electrical Engineering. Telephone: (888) 673-8360 ext. 3; Internet:


Table I: Weibull Parameters
Weibull Parameter Description
Gamma (g) or Location Parameter Gives the location of each section of the Weibull curve. Gamma 3 is particularly important for items with a wearout mechanism because it marks the beginning of the zone of increasing failure rate.
Beta (b) or Shape Factor Beta values are an indicator of the failure behavior of the component. Beta values less than one represent infant failures, Beta values equal to one represent random failures, and Beta values greater than one represent wearout failures.
Eta (h) or Characteristic Life Eta gives an estimate of how long components might last after being put into service. It represents the point in time where 63.2% of the components in service are likely to have failed.


Table II: Potential Organizational Causes for Infant Failures
Source Causes
Maintenance Activities
  • No or inadequate quality of work control procedures and policies
  • Unskilled or untrained maintainers
  • No or Poorly written maintenance procedures
  • Poor organizational communication
  • No focus on precision maintenance
  • Inadequate Maintenance Supervision
Operating Activities
  • No or inadequate operating procedures, especially start up procedures
  • Unskilled or untrained operators
  • Inadequate Operations Supervision
Procurement Activities
  • Procurement focused solely on price
  • No or inadequate quality control procedures for incoming spares, especially custom manufactured parts from third party vendors
  • Parts procured from a wide variety of vendors


Table III. Potential Causes for High Random Failure Rates
Source Causes
Maintenance Activities
  • Lubrication routes not well designed
  • Inconsistent torque applied to bolts
  • Poor maintenance cleanliness practices
  • Inadequate lightening protection
Operating Activities
  • Equipment occasionally operated outside its design envelope
  • Process upsets created by inadequate quality control of incoming raw materials
  • Process upsets created by unskilled or untrained operators
Procurement Activities
  • Parts procured from a wide variety of vendors
  • Parts specifications not clear


Table IV. Potential Causes for Early Wearout
Source Causes
Maintenance Activities
  • Under-Lubrication of bearings
  • Using Incorrect Lubricant for the Service
  • Over-Lubrication of bearings
  • Service intervals too long for:
    • Lubrication
    • Adjustments
  • Consistent Over Tightening of Belts
  • Consistent Over-Torquing of Bolts
  • Using Parts Below Required Specifications
Operating Activities
  • Consistently operating the equipment outside its design envelope
Procurement Activities
  • Purchasing spares below needed specifications


Table V. Some Simple Questions for Determining Weibull Failure Mechanisms
Question Answer What The Answer Tells Us
1. How many times have you repaired this particular failure in the last three years? Three or Four The answer gives us an approximation of the mean time between failures or the characteristic life. It may not be exact, but it will be close enough for us to make a reasonable decision.
2. If you work on it today do you know you have to warn others that you worked on it because it may not get through till day after tomorrow? Yes There is probably an infant failure mechanism present. You will need to do some Root Cause Analysis (RCA) to determine why and eliminate the cause.
3. If you work on it today do you know you won’t have to come back to work on it again until sometime near the mean time to failure you determined in question one? If you wait too long after that will it probably fail? Yes This is probably a wearout failure. It can most likely be addressed with a time based replacement or overhaul strategy, but RCA should be performed to find root cause if the wearout is occurring sooner than desired.
4. If you work on it today is it likely to fail sometime between now and the mean time to failure determined in question one, but you can’t be certain that it will last that long? Yes This is most likely a random failure. It can be handled by condition monitoring unless the failure rate is higher than is tolerable for the organization. If the rate is too high, then RCFA should be performed to find and eliminate cause.


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