Reliability Test Plan

The Reliability Test Plan feature computes required sample sizes, censor times, or precision, for estimating failure times and failure probabilities.

To launch the Reliability Test Plan calculator, select DOE > Design Diagnostics > Sample Size and Power, and then select Reliability Test Plan. Reliability Test Plan Window shows the Reliability Test Plan window.

Reliability Test Plan Window

The Reliability Test Plan window has the following options:

Alpha

is the significance level. It is also 1 minus the confidence level.

Distribution

is the assumed failure distribution, with the associated parameters.

Precision Measure

is the precision measure. In the following definitions, U and L correspond to the upper and lower confidence limits of the quantity being estimated (either a time or failure probability), and T corresponds to the true time or probability for the specified distribution.

Interval Ratio is sqrt(U/L), the square root of the ratio of the upper and lower limits.

Two-sided Interval Absolute Width is U-L, the difference of the upper and lower limits.

Lower One-sided Interval Absolute Width is T-L, the true value minus the lower limit.

Two-sided Interval Relative Width is (U-L)/T, the difference between the upper and lower limits, divided by the true value.

Lower One-sided Interval Relative Width is (T-L)/T, the difference between the true value and the lower limit, divided by the true value.

Objective

is the objective of the study. The objective can be one of the following two:

–

estimate the time associated with a specific probability of failure.

–

estimate the probability of failure at a specific time.

CDF Plot

is a plot of the CDF of the specified distribution. When estimating a time, the true time associated with the specified probability is written on the plot. When estimating a failure probability, the true probability associated with the specified time is written on the plot.

Sample Size

is the required number of units to include in the reliability test.

Censor Time

is the amount of time to run the reliability test.

Precision

is the level of precision. This value corresponds to the Precision Measure chosen above.

Large-sample approximate covariance matrix

gives the approximate variances and covariance for the location and scale parameters of the distribution.

Continue

click here to make the calculations.

Back

click here to go back to the Power and Sample Size window.

After the Continue button is clicked, two additional statistics are shown:

Expected number of failures

is the expected number of failures for the specified reliability test.

Probability of fewer than 3 failures

is the probability that the specified reliability test will result in fewer than three failures. This is important because a minimum of three failures is required to reliably estimate the parameters of the failure distribution. With only one or two failures, the estimates are unstable. If this probability is large, you risk not being able to achieve enough failures to reliably estimate the distribution parameters, and you should consider changing the test plan. Increasing the sample size or censor time are two ways of lowering the probability of fewer than three failures.

Example

A company has developed a new product and wants to know the required sample size to estimate the time till 20% of units fail, with a two-sided absolute precision of 200 hours. In other words, when a confidence interval is created for the estimated time, the difference between the upper and lower limits needs to be approximately 200 hours. The company can run the experiment for 2500 hours. Additionally, from studies done on similar products, they believe the failure distribution to be approximately Weibull (2000, 3).

To compute the required sample size, do the following steps:

Select DOE > Design Diagnostics > Sample Size and Power.

Select Reliability Test Plan.

Select Weibull from the Distribution list.

Enter 2000 for the Weibull α parameter.

Enter 3 for the Weibull β parameter.

Select Two-sided Interval Absolute Width from the Precision Measure list.

Select Estimate time associated with specified failure probability.

Enter 0.2 for p.

Enter 2500 for Censor Time.

10.

Enter 200 for Precision.

11.

Click Continue. Reliability Test Plan Results shows the results.

Reliability Test Plan Results

The required sample size is 217 units if the company wants to estimate the time till 20% failures with a precision of 200 hours. The probability of fewer than 3 failures is small, so the experiment will likely result in enough failures to reliably estimate the distribution parameters.