arrow_back_ios

Main Menu

See All Software See All Instruments See All Transducers See All Vibration Testing Equipment See All Electroacoustics See All Acoustic End-of-Line Test Systems See All Academy See All Resource Center See All Applications See All Industries See All Services See All Support See All Our Business See All Our History See All Global Presence
arrow_back_ios

Main Menu

See All nCode - Durability and Fatigue Analysis See All ReliaSoft - Reliability Analysis and Management See All Test Data Management See All DAQ Software See All Drivers & API See All Utility See All Vibration Control See All High Precision and Calibration Systems See All DAQ Systems See All S&V Hand-held Devices See All Industrial Electronics See All Power Analyzer See All S&V Signal Conditioner See All Acoustic See All Current and Voltage Sensors See All Displacement See All Force sensors See All Load Cells See All Pressure See All Strain Gauges See All Temperature Sensors See All Torque Sensors See All Vibration See All Accessories for Vibration Testing Equipment See All Vibration Controllers See All Measurement Exciters See All Modal Exciters See All Power Amplifiers See All LDS Shaker Systems See All Test Solutions See All Actuators See All Combustion Engines See All Durability See All eDrive See All Production Testing Sensors See All Transmission & Gearboxes See All Turbo Charger See All Training Courses See All Acoustics See All Asset & Process Monitoring See All Custom Sensors See All Data Acquisition & Analysis See All Durability & Fatigue See All Electric Power Testing See All NVH See All Reliability See All Smart Sensors See All Vibration See All Weighing See All Automotive & Ground Transportation See All Calibration See All Installation, Maintenance & Repair See All Support Brüel & Kjær See All Release Notes See All Compliance See All BKSV Worldwide Contacts
arrow_back_ios

Main Menu

See All API See All Microphone Cartridges See All Microphone Sets See All Microphone Pre-amplifiers See All Sound Sources See All Acoustic Calibrators See All Special Microphones See All Accessories for acoustic transducers See All Experimental testing See All Transducer Manufacturing (OEM) See All Piezoelectric Charge Accelerometers See All Piezoelectric CCLD (IEPE) accelerometers See All Electroacoustics See All Noise Source Identification See All Environmental Noise See All Sound Power and Sound Pressure See All Noise Certification See All Industrial Process Control See All Structural Health Monitoring See All Electrical Devices Testing See All Electrical Systems Testing See All Grid Testing See All High-Voltage Testing See All Vibration Testing with Electrodynamic Shakers See All Structural Dynamics See All Machine Analysis and Diagnostics See All Dynamic Weighing See All Vehicle Electrification See All Calibration Services for Transducers See All Calibration Services for Handheld Instruments See All Calibration Services for Instruments & DAQ See All On-Site Calibration See All Resources See All Software License Management

Reliability meassure

Although useful to some degree, the mean life function (often denoted as "MTTF" or "MTBF") is not a good measurement when used as the sole reliability metric. Instead, the specification of a reliability value with an associated time, along with an associated confidence requirement when possible, is a more versatile and powerful metric for describing a product's reliability.

The Mean Life Function

The mean life function, such as the mean time to failure (MTTF), is widely used as the measurement of a product's reliability and performance. This value is often calculated by dividing the total operating time of the units tested by the total number of failures encountered. This metric, which is valid only when the data is exponentially distributed (a poor assumption which implies that the failure rate is constant), is then used as the sole measure of a product's reliability.

One problem that arises from the use of this metric stems from confusion over the differentiation between the "mean" and the "median" values of a data set. The mean is what would normally be called the average, or the most likely value to be expected in a group of data. The mathematical definition is:

 

Mathematical definition equation

 

where f(T) is the probability density function of the data. The median, on the other hand, is the value that splits the data. Half of the data will be greater than the median and half will be less than the median. The mathematical definition of the median involves solving the equation:

 

Mathematical definition of the median equation

for

 

, where f(T) is the probability density function of the data. If the data in question is from a symmetrical distribution, such as the normal or Gaussian distribution, the values for the mean and median are equal. However, when dealing with an asymmetrical distribution, such as the exponential or Weibull, there can be a large difference between the mean and median.

To give a discreet example, suppose we have a data set consisting of five values: (1,2,3,4,100). The mean value of this data set is (1+2+3+4+100)/5=110/5=22. However, the median value for this data set is 3, as it is the "middle number" in the set of five. Clearly, there is a sizable difference in the values of the mean and the median for this data set.

Reliability is a Function of Time

Because reliability is a function of time, in order to properly define a reliability goal or test result, the reliability value should be associated with a time. For example, "the reliability at 50,000 cycles should be 50%" is a more meaningful reliability goal than "the MTTF should be 50,000 cycles."

The MTTF is not an appropriate metric because the reliability value associated with the MTTF is not always 50% and can vary widely. The following example illustrates how the actual reliability can vary with a given MTTF. Suppose we are testing the reliability of products from three suppliers. We obtain eight samples from each supplier and test them until they fail. The next table gives the time-to-failure results for the three test lots.

 

  Test Lot 1 Test Lot 2 Test Lot 3
Failure #1
Failure #2
Failure #3
Failure #4
Failure #5
Failure #6
Failure #7
Failure #8
8664.8
22439.4
38713.4
57981.8
82098.1
113631.4
160445.0
248891.5
3.1
74.1
456.6
1755.2
5595.1
16533.2
52213.7
225630.0
59857.5
75933.3
87025.1
96272.5
105017.6
113907.9
124168.3
138573.9

 

We determine that these three data sets follow the Weibull distribution and the probability plot of the data, generated with ReliaSoft's Weibull++ software, is displayed in Figure 1. For the Weibull distribution,

 

the MTTF is calculated with the equation:

MTTF equation

 

where

 

 

and

 

 

are the Weibull location and shape parameters and

 

(*) is the Gamma function.

Probability plot

Figure 1: Probability Plot

Based on this analysis (utilizing Rank Regression - RRX), we determine that even though the three Weibull-distributed data sets are quite different, they have the same MTTF of 100,000. The actual reliability values, however, are quite different at different times as can be seen in the reliability vs. time plot in Figure 2. At the MTTF of 100,000 for data set 2, over 85% of the units are expected to fail while for data sets 1 and 3, 63% and 49% of the units are expected to fail respectively.

Reliability vs. Time plot

Figure 2: Reliability vs. Time Plot

This example illustrates the potential pitfalls of using the MTTF as the sole reliability metric. Attempting to use a single number to describe an entire lifetime distribution can be misleading and may lead to poor business decisions when a non-exponential lifetime distribution is assumed. The reliability of a product should be specified as a percentage value with an associated time. Ideally, a confidence level should also be associated, which allows for consideration of the variability of data being compared to the specification.

Support Content