Life cycle testing is an essential step in the design process of a consumer hardware product. Hi, my name is Chris Thiele and as a member of the Electrical Engineering team here at Thalmic Labs, I work on the electrical design of various life cycle tests for the Myo™ Armband.

It is important to determine what kind of stress the product will be exposed to during use. For example, the Myo armband will need to expand and contract as it is slid on and off the user’s arm.This seemingly gentle process can place a great deal of stress when one considers how often this will occur over the product’s lifetime. The most logical question that follows is, ‘Will the Myo armband withstand being put on and taken off enough times before the product is expected to fail?’ Assuming at estimated 50,000 cycles of taking the band on and off over the product’s lifetime, we can design a life-cycle stress test to help answer this question.

#### The Test Setup

The hardware team at Thalmic designed an autonomous mechanical rig that will expand a Myo armband from the minimum to maximum expected arm size, over and over again (See Figure 1). To analyze the life cycle, we’re interested in finding when each sample fails, and the point of failure. To do this in an automated fashion, we developed a set of electronics and software, which constantly monitors the Myo armband that is being tested for failures. When a failure is encountered, the software stops the testing machine and an engineer can investigate the results.

Figure 1: Myo Armband Expansion Rig

Figure 2: Myo Armband Expansion Rig Block Diagram

Automated testing begins with one module whereas the results are compiled into a chart or a database. The results, in the case of a Myo armband, would include number of cycles the device ran through before it failed as well as the mode of failure.

However, one device’s test results is not a suitable amount of data to get a definite conclusion on how many cycles the average Myo armband will go through until it breaks. When discussing expected failure rates, we’re nearly always speaking in terms of probabilities. The only way to be 100% certain of when a particular unit will fail is to actually test that unit itself to failure, but that is not feasible. Instead we test a sample of the population and use statistical analysis to infer probabilities of any unit in the population failing at a given life-cycle.

#### Gathering Data

The first step in getting a proper statistical analysis to infer probabilities of a device’s failure rate is to gather lots of data. Sample size determination is crucial in this case as we are taking a small percentage of the total population and using them to draw conclusions on every device that will ever be built. As the sample size approaches the population size we get a more accurate representation of the mean value at which the average device fail.

For our example, let’s take a sample size of 20 Myo armbands. The data includes various armbands that failed at different cycles and various locations (See Table 1).

Table 1: Expanded sample stress test data

#### Statistical Analysis

A proper sample size with varying numbers is now available to be further analyzed in a statistical manner. The mean number of cycles before failure can be easily calculated, by adding the total number of cycles before failure and dividing by the number of trials. We also assume the failure will follow a normal in order to estimate the likelihood of devices failing after a certain number of cycles. Standard deviation is used in conjunction with the normal distribution as it shows the dispersion of the data from the average. Our standard deviation is a number that, when subtracted and added to the mean, the data in that range represents where 68% of where the total amount of data falls. Keep in mind that this is only because it is a normal distribution. See [2] and [3] in the Reference section for more information on this topic.

Let’s take the data from above and calculate the parameters of the distribution, then plot it using Excel. Excel has many built in functions that make plotting a normal distribution on your data very simple.

In order to calculate the mean value of your test results use:

“=AVERAGE(**First_Number:Last_Number**)”

In order to calculate the standard deviation of your test results use:

“=STDEV(**First_Number:Last_Number**).”

After these two numbers are calculated we can use them to create a set of data points for the corresponding normal distribution. First we create an x vector covering the range of cycles we’re interested in, eg. (0:70,000):

“=NORMDIST(**x,**$**Mean,**$**StdDev, FALSE***)”

*FALSE as we desire to plot the probability density function (PDF) rather than the cumulative distribution function.

Once you get all of your data you can now graph your normal distribution by graphing this data as a line plot. The NORMDIST will generate your probability of that failure occurring.

Table 2: Calculated Parameters of Series

In a case with very few samples an extreme case could easily throw off the balance of this histogram. Hence the need for testing a larger sample in order to get a better representation of the overall product. Notice how with a sample size of 500 we get an evenly distributed histogram shown in Figure 3 below.

Figure 3: Probability Distribution of Expected Failures

For our problem definition, we had imposed a design constraint that the device must withstand 50,000 cycles. Of course, we can never be 100% sure – so instead we must pick the probability limit we are comfortable with. For example, we could instead specify that we desire a 99% probability that a device will not fail before 50,000 cycles. Using our calculated normal distribution, from the cumulative probability function we can calculate that 7% of the Myo armbands fell under this threshold. Therefore, in this example we would not meet the 99% criteria set out, and we would need to modify the design to meet the goal. Figure 4 shows the probability of failures occurring below 50,000 cycles (eg the area under the curve).

Figure 4: Probability of Failure before 50k Cycles

Life cycle testing is an integral step in the product development process. Ultimately, putting the Myo armband through the paces now will help ensure that our consumers receive a reliable, high-quality product when they have the product in their hands.

##### References

[1] http://en.wikipedia.org/wiki/Sample_size_determination

[2] http://en.wikipedia.org/wiki/Standard_deviation

[3] http://en.wikipedia.org/wiki/68-95-99.7_rule