## Introduction

Reliability is an important consideration for engineers and product designers. It is also very context specific. For example consider a car, which is made from lots of individual components. If the radio antenna should fail, the car still operates. However this is not the case if the engine stops working. Some features are more important than others, especially with safety systems such as the car’s brakes.

In relation to vibration motors and their typical applications we can consider them as individual components or entire systems. Haptic feedback on a user interface is comprised of the input system (such as a touchscreen), the microcontroller, the motor drive circuit, and the vibration motor. If any one of these should fail, then the vibration feature will no longer work.

As with any component, our vibration motors will eventually stop working. The key therefore is accurately estimating when, and determining if it is an acceptable period of time. To do this, we can use one of a number of different methods for calculating the probability of a component's life expectancy.

Below we discuss the main causes for failure, some statistical approaches to determining motor lifetime, and offer a ‘real-life’ example using one of our ERM vibration motors.

## Main Causes of Failure with Vibration Motors

Of course it’s not just the vibration motor that can fail, but the drive circuitry can also stop working. As we explained in the introduction, it can depend on where you draw the boundary of the system. If you are using a motor drive IC that fails, the vibration motor could still be operational, but as a feature the vibration effect no longer works.

Other external factors include control signal failure, improper mounting or enclosure impeding the rotation of the eccentric mass, or power source issues.

As a motor manufacturer, our focus remains on the vibrating motor part of such systems, and although we do recommend driver IC's andmounting methods, we'll only be covering longevity issues related of the motor itself.

Typically vibration motors will fail in one of two ways:

- Overheating (rarely)

This will either cause shorting as the wire lacquer disintegrates and fails to insulate, or cause the winding connection to the commutator to break as the solder melts.

- Mechanical Wear (more common)

The precious metal brushes and copper commutator are subject to mechanical wear, these debris and particles can fill the gaps between the commutator segments and cause the motor to short. In extreme cases of wear the brush can snap off, losing the connection all together (open circuit).

## Measuring Failure Rates

### Mean Time To Failure (MTTF)

The MTTF assumes the component cannot be repaired or serviced, and is a variation of the common Mean Time Between Failure (MTBF) figure, which assumes the component can be repaired. MTTF is more applicable to miniature vibration motors, because they're generally too fragile and small to be repaired.

The formula that defines the MTTF is:

$$ MTTF \approx \frac{Total \: Time}{Number \: Of \: Failures} $$

\(Total \: Time \) can use any unit of time desired, although we will stick with hours as they are most common. It includes all the motors that were still operational at the end of the test, plus the time that failed motors ran for before dying. This gives us the total successful hours and when divided by the number of failures, we have the Mean Time To Failure.

However this can lead to artificially high numbers, especially when testing a large quantity of vibration motors for shorter time periods. As an example, say we tested 1000 motors for 1000 hours. Only 10 of the motors failed, all after completing 900 hours. The MTTF would be calculated as follows:

$$ MTTF \approx \frac{Total \: Time}{Number \: Of \: Failures} $$

$$MTTF \approx \frac{(9,990*1,000)+(900*10)}{10}$$

$$MTTF \approx \frac{9,999,000}{10}$$

$$MTTF \approx 999,900 \: hours$$

No DC motor would run for 999,900 hours, that’s over 114 years!

In fact, for every additional vibration motor that runs the entire course, the MTTF is increased by the length of the test divided by the number of failures. In the above example, that’s 100 hours for every additional motor tested.

With MTTF there is an element of uncertainty when the sample number is low or when the failure number is low. MTTF can become much more accurate if the test period is long enough such that every vibration motor under test fails. Unfortunately that would take a very long time to complete and most companies have limited resources to dedicate to testing. Instead there are other statistical calculations we can do that are designed to improve the reliability calculations.

### Failures In Time (FIT)

The FIT rate shows how many failures can be expected from one billion hours of operation. It effectively presents the MTTF in a different format. These two numbers express the same failure rate, it simply depends on what you are more familiar with or if you are required to use one figure in further analysis. FIT is calculated as follows:

$$FIT = \frac {1,000,000,000}{MTTF}$$

Using the numbers we used for the MTTF example:

$$FIT = \frac{1,000,000,000}{999,900}$$

$$FIT \approx 1000$$

We can see that FIT depends upon the reliability of the MTTF, which means it is subject to the same misrepresentation.

### Weibull Analysis

Weibull Analysis helps improve the accuracy of MTTF and FIT rates for vibrating motors when there are small sample sizes or a low failure rate from the test. It is based around the ‘Weibull distribution’, which is a probability density function. This sounds complicated, but it’s fairly simple to understand.

If we are testing a motor over a period of time, we do not know when (or if) the motor will fail. In probability terms, the time at which a motor will fail is known as a ‘continuous random variable’. It is a variable because it will change for each motor and random because we cannot predict or calculate when that specific motor will fail.

A probability density function is a way of representing the probability of the continuous random variable having a specific value. In our example, the probability density function shows when the motor is most likely to fail (and therefore when it is least likely to fail). It is often shown as a graph, with the failure rate on the vertical axis and a unit of measurement on the horizontal axis (in our case - time):

The above graph is known as the ‘bathtub curve’. It is a common probability distribution showing that for certain devices, some will fail at the very start of their lives or after a length of time when they will start to wear out.

Weibull analysis uses some fairly complicated maths, which is beyond the scope of this Application Bulletin. However we will explain its process. The Weibull analysis takes your test data and attempts to model it so it fits a Weibull distribution. It does this by finding two distribution parameters, eta and beta. Then, with appropriate values for eta() and beta() they are used to calculate a new MTTF, and subsequently a new FIT rate.

## An Example Case - 307-001 Pico Vibe™

### The Setup

With our custom longevity test machine we are able to test multiple vibrations motors in a variety of test situations, including duration and drive sequence. From the output, we are not only able to see which vibration motors failed, but we can pinpoint the exact time.

We mounted 43 units of the Pico Vibe™ 307-001 into individual vibration sleds for testing. Half of the motors were driven on for two seconds while the other half stayed off. They then swapped as the first half switched off and the second half vibrated for two seconds. This ‘2 seconds on - 2 seconds off’ drive sequence was repeated for 2 months, 1440 hours for each vibration motor.

The machine would detect a motor had failed through the accelerometer attached to each vibration sled. The time of failure (accurate to within 4 seconds) was then registered and presented in the summary at the end of testing.

### The Data

From our longevity machine’s report, we were able to see that all of the vibration motors except 6 were still operational after the 1440 hour test period.

The failure times were as follows:

Motor Failure # |
Time (h) |
Total Succesful Hours from Failed Motors (h) |

1 | 860 | 860 |

2 | 912 | 1772 |

3 | 921 | 2693 |

4 | 1168 | 3861 |

5 | 1273 | 5134 |

6 | 1388 | 6522 |

The failed motors accumulated 6,522 hours of successful operation. The other 37 vibration motors that were still operational amassed 53,280 hours (1440 x 37). This gave a total of 59,802 operational hours from 43 units under test.

Now we can re-calculate the MTTF and FIT as per their definitions. First, Mean Time To Failure:

$$MTTF \approx \frac{Total \: Time}{No. \: of \: Failures}$$

$$MTTF \approx \frac{6,522+53,280}{6}$$

$$MTTF \approx \frac{59,802}{6}$$

$$MTTF \approx 9967 hours$$

Remember, Failure In Time rate is the amount of devices that would fail during one billion hours of operation:

$$FIT = \frac {1,000,000,000}{MTTF}$$

$$FIT = \frac {1,000,000,000}{9967}$$

$$FIT \approx 100,331$$

These results are not realistic because our test returned a very small failure rate. As explained above, we can make our results more representative by using Weibull analysis. Our estimated values for eta( \( \eta \) ) and beta( \( \beta \) ) are:

$$\eta = 2000$$

$$\beta = 4.4$$

Next we use these parameters to calculate our new mean time to failure and failures in time rates:

$$MTTF \approx 1822.77 \: hours$$

$$FIT \approx 548,615$$

## Discussion of Results

From our initial calculation of MTTF and FIT we can see the problem with having a low failure rate. The original MTTF estimate predicted that our motors would run for over a year, this would be extremely unlikely for any brushed DC electrical motor.

Our Weibull analysis produces much more realistic results. A further important point to take away, is that our vibration motors like any DC motor fits a Weibull distribution. A common mistake is for customers to read the MTTF figure and assume that their motor will fail ‘around this time’. If that was the case, the motor failure rate would have ‘normal probability distribution’:

Vibration motor failures **do not** follow this distribution. They follow the bathtub curve as mentioned earlier. If one of our vibration motors has a MTTF of 2000 hours on the datasheet, it does not mean that if you purchase one it will "last around 2000 hours". Instead, you should interpret the figure as if you buy 1000 you will receive approximately two million operational hours.

## Conclusion

We have explained how failure rates are calculated, highlighting their drawbacks and explaining what the figures mean. For this we first looked at the Mean Time To Failure and Failure in Time rates.

When using small sample sizes or if we have low failure rates calculate the MTTF and FIT differently by using Weibull analysis. This allows us to provide our customers with more reliable data on the lifetime of vibration motors.

Using the testing of our 307-001 we demonstrated the process we use in-house for generating the MTTF that we're starting to provide in our datasheets.

We're in the process of determining MTTF figures for several key products in our range, and are the only vibration motor manufacturer to do so. As figures are calculated they will be added to their respective datasheets.

If there's no data for a motor that you're interested in, or If you have questions about this article, please contact us using the box below.