A comprehensive review of the lognormal failure distribution with application to LED reliability

Life-test data for many semiconductor devices obey the lognormal law of failure. In this paper we offer a survey of the key statistical properties of the lognormal distribution which are relevant in device engineering. The statistical developments are illustrated throughout by specific examples drawn from life-test data for GaP red LEDs which show lognormal failure behavior. Additional theoretical justification for accepting the lognormal distribution in the case of these devices is provided by the statistical recasting of the diffusion theory of red LED degradation.The treatment of the fundamental concepts of reliability in terms of cumulative failure function, instantaneous failure rate, mean time for failure (MTTF), etc., although concise, is self-contained. Moreover, the estimation of the two characteristic parameters (median life, standard deviation) of the lognormal distribution from sample data by means of a number of alternative procedures (graphical, least-square, maximum likelihood) is discussed in detail. The efficient determination of the MTTF and failure rate is facilitated by convenient charts developed here which relate these quantities to the parameters median life and standard deviation at 5, 10, 20 and 40 years of device service life. In order to assess the uncertainty associated with the estimates, the confidence limits on the median life and standard deviation of the population as a function of confidence level and sample size are given in novel graphical forms. Finally, error bounds for the MTTF and failure rate of the population are also presented.