JEDEC
STANDARD
LOGNORMAL ANALYSIS OF
UNCENSORED DATA AND OF
SINGLY RIGHT-CENSORED DATA
UTILIZING THE PERSSON AND
ROOTZEN METHOD
JESD37A
(Revision of JESD37, October 1992)
AUGUST 2017
JEDEC SOLID STATE TECHNOLOGY ASSOCIATION
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JEDEC Standard No. 37A
-i-
LOGNORMAL ANALYSIS OF UNCENSORED DATA AND OF SINGLY RIGHT-
CENSORED DATA UTILIZING THE PERSSON AND ROOTZEN METHOD
Contents
Page
Foreword ii
Introduction ii
1 Scope 1
2 Normative references 2
3 Terms, definitions, and symbols 2
4 Summary of techniques 4
5 Inferences 4
6 Procedure for complete sample data 6
7 Persson-Rootzen procedure for singly right-censored data 8
8 Data graphing, and presentation 10
9 Reporting 11
Annex A (informative) Non-censored data example 12
Annex B (informative) Singly right-censored data example 14
Annex C (informative) Data graphing example for singly right-censored data 16
Annex D (informative) Bibliography 26
Annex E (informative) Differences between JESD37A and its predecessor JESD37 27
JEDEC Standard No. 37A
-ii-
Foreword
This standard is intended for use by those involved with reliability, lifetime estimation or failure
data analysis. This standard enables the user to estimate the parameters of a two parameter
lognormal distribution from complete or singly right-censored independent failure data. The
methods described were chosen because they can be easily done with a calculator or spreadsheet
and are as accurate as more complex iterative techniques for the cases described.
Interferences or issues that can complicate and/or invalidate the analysis are discussed. One
section discusses analysis of failure data where all units from within the sample have a known
failure time. Another section discusses analysis of failure data for the case where the life
experiment was stopped and the failure times for the surviving unis are not known. Graphical
presentation is discussed and sample calculations are presented in several annexes.
Introduction
Analysis of reliability experiments depends extensively on failure statistics and commonly used
failure distribution is the normal distribution after natural logarithms of the failure times have
been calculated. Lognormal distributions and the associated statistics are used by analysts
working in semiconductor reliability to interpret and communicate results from failure
experiments. Unfortunately, many individuals who lack a sufficient background in statistical
methods are using the techniques; errors in usage and interpretation are abundant.
This document was written to provide a very basic set of tools for determining the parameters of
the lognormal distribution for cases where sophisticated tools or expertise do not exist. The
techniques handle a majority of the experimental cases experienced by contributors. The step-
by-step standard and annexes are intended to instruct and to help ensure proper analysis.
JEDEC Standard No. 37A
Page 1
STANDARD FOR LOGNORMAL ANALYSIS OF UNCENSORED DATA AND OF
SINGLY RIGHT-CENSORED DATA UTILIZING THE PERSSON AND ROOTZEN
METHOD
(From JEDEC Board Ballot JCB-17-28, formulated under the cognizance of the JC-14.2 Committee on
Wafer-Level Reliability)
1 Scope
1.1 Intent
This standard enables the user to estimate the parameters of a two-parameter lognormal
distribution from complete or singly right-censored independent data samples.
Specifically, this standard is intended for analyzing failure-time (t
f
) data obtained from a stress
test of a sample of units when the natural logarithm of the failure-time (ln t
f
) follow a normal
distribution.
This standard is not intended to describe techniques used to determine how well the failure data
fits a lognormal distribution. However, if points lie along a straight line for plots generated in
section 8 the lognormal distribution estimators will describe the points along the line.
1.2 Results
The results of the analysis provide bias-corrected sample estimates for the median time-to-failure
(t
50
), mean of the ln t
f
values (ln t
50
), and the standard deviation (σ) of the ln t
f
value of the
lognormal distribution. Additionally, confidence intervals are provided for complete data
samples (no censoring). These are all obtained from the failure time values (t
f
)
1.3 Complete data case
This standard may be used to analyze complete data where the failure-time data for the entire
sample population is known and used. The analysis uses the most efficient estimators for
obtaining estimates of the two primary parameters (t
50
, σ) of the distribution.
1.4 Right-censored case
This standard may be used to analyze singly right-censored (Type II censored) data where the
test has been stopped before all the parts have failed. The analysis uses the Persson and Rootzen
Estimators [1] corrected for bias [2, 3]. These estimators can be calculated with a hand
calculator and are as accurate as more complex estimators.
