Confidence limits on the failure rate and a rapid projection nomogram for the lognormal distribution

In order to predict the sample failure rate from a limited number of early malfunctions, we have developed the rapid lognormal projection nomogram (RLPN) which we present at 1, 5, and 10 years of service. In the core of each diagram is a family of curves showing the variation of failure rate as a function of sample median life and standard deviation. Superimposed are Arrhenius plots for a series of activation energies, all referenced with respect to a fixed time. We also display the standard deviation as a function of relative median life, using cumulative failure as a parameter. The RLPN provides graphical means to estimate the failure rate at the planned service life and operating temperature in an efficient manner from the time to failure at the aging temperature and sample size for known or assumed values of the standard deviation and activation energy. To obtain the confidence limits for the failure rate of the lognormal distribution at the 90% confidence level, we have derived an approximate formula that relates the bounds to the service life and the sample's size, median life, and standard deviation. Then, by an appropriate selection of the independent variables and parameters, the confidence intervals are displayed as a series of curve families. The applications of the diagrams are discussed by means of illustrative examples taken from the field of GaAs FETs.