Publication date: 07/30/2020

Specify the following quantities and test settings:

Alpha

The significance level of the confidence interval used to define the precision measure.

Distribution

The assumed failure distribution. Distributions available are: Weibull, Lognormal, Frechet, Loglogistic, SEV, Normal, LEV, and logistic. For more information about these distributions, see Statistical Details for the Life Distribution Platform in Reliability and Survival Methods.

Location

The location parameter for the failure distribution.

Note: The Location field is denoted Weibull α when the Distribution is set to Weibull.

Scale

The scale parameter for the failure distribution.

Note: The Scale field is denoted Weibull β when the Distribution is set to Weibull.

Precision Measure

The definition of the precision measure. Definitions are based on the expected confidence interval of the quantity being estimated (failure time or probability). The choices for the precision measure are as follows:

Interval Ratio

Defines precision as the square root of the ratio of the upper limit to the lower limit. This ratio is always greater than one since the upper limit is greater than or equal to the lower limit. The interval ratio decreases as the precision in the estimate increases.

Two-sided Interval Absolute Width

Defines precision as the width of the confidence interval or the difference between the upper and lower limits.

Lower One-sided Interval Absolute Width

Defines precision as the width of the lower side of the interval or the difference between the estimate and the lower limit of the confidence interval for the estimate.

Two-sided Interval Relative Width

Defines precision as the width of the confidence interval relative to the estimate. This is the difference between the upper and lower limits divided by the estimate.

Lower One-sided Interval Relative Width

Defines precision as the width of the lower side of the interval relative to the estimate. This is the difference between the estimate and the lower limit divided by the estimate.

Objective

The objective of the study. Select one of the following objectives and enter the corresponding value:

– Estimate time associated with specified failure probability p.

– Estimate failure probability at time t.

Note: The plot is the cumulative distribution function of the failure distribution. The plot is labeled with the estimate of time or probability based on the study objective.

Specify two of the following quantities to calculate the third quantity:

Sample Size

The number of units to include in the reliability test.

Censor Time

The amount of time available to run the reliability test.

Precision

The level of precision. The definition of the units on this value corresponds to the chosen Precision Measure.

Continue

Evaluates the missing value.

Back

Returns to the previous Sample Size and Power launch window.

In addition to calculating the sample size, censor time, or precision, the following quantities are also calculated:

Expected number of failures

The expected number of failures for the specified reliability test.

Probability of fewer than 3 failures

The probability that the specified reliability test results in fewer than three failures. This is important because a minimum of three failures is required to obtain stable estimates for the location and scale parameters of the failure distribution. With only one or two failures, the estimates are unstable. If this probability is large, you risk not observing enough failures to reliably estimate the distribution parameters. Increasing the sample size or censor time are both ways to lower the probability of fewer than three failures.

Large-sample approximate covariance matrix

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

Want more information? Have questions? Get answers in the JMP User Community (community.jmp.com).