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The RELIABILITY Procedure This Document Is an Individual Chapter from SAS/QC® 13.2 User’S Guide SAS/QC® 13.2 User’s Guide The RELIABILITY Procedure This document is an individual chapter from SAS/QC® 13.2 User’s Guide. The correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. 2014. SAS/QC® 13.2 User’s Guide. Cary, NC: SAS Institute Inc. Copyright © 2014, SAS Institute Inc., Cary, NC, USA All rights reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a Web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated. U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computer software developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use, duplication or disclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a) and DFAR 227.7202-4 and, to the extent required under U.S. federal law, the minimum restricted rights as set out in FAR 52.227-19 (DEC 2007). 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Discover all that you need on your journey to knowledge and empowerment. support.sas.com/bookstore for additional books and resources. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies. © 2013 SAS Institute Inc. All rights reserved. S107969US.0613 Chapter 16 The RELIABILITY Procedure Contents Overview: RELIABILITY Procedure............................. 1158 Getting Started: RELIABILITY Procedure.......................... 1160 Analysis of Right-Censored Data from a Single Population . 1160 Weibull Analysis Comparing Groups of Data . 1164 Analysis of Accelerated Life Test Data . 1168 Weibull Analysis of Interval Data with Common Inspection Schedule . 1173 Lognormal Analysis with Arbitrary Censoring . 1178 Regression Modeling................................... 1183 Regression Model with Nonconstant Scale . 1189 Regression Model with Two Independent Variables . 1192 Weibull Probability Plot for Two Combined Failure Modes . 1196 Analysis of Recurrence Data on Repairs . 1199 Comparison of Two Samples of Repair Data . 1204 Analysis of Interval Age Recurrence Data . 1211 Analysis of Binomial Data................................ 1214 Three-Parameter Weibull................................. 1217 Parametric Model for Recurrent Events Data . 1220 Parametric Model for Interval Recurrent Events Data . 1222 Syntax: RELIABILITY Procedure............................... 1225 Primary Statements ................................... 1225 Secondary Statements.................................. 1225 Graphical Enhancement Statements........................... 1227 PROC RELIABILITY Statement ............................ 1227 ANALYZE Statement .................................. 1227 BY Statement ...................................... 1233 CLASS Statement.................................... 1233 DISTRIBUTION Statement............................... 1234 EFFECTPLOT Statement ................................ 1235 ESTIMATE Statement.................................. 1236 FMODE Statement.................................... 1237 FREQ Statement..................................... 1237 INSET Statement..................................... 1238 LOGSCALE Statement ................................. 1242 LSMEANS Statement.................................. 1242 LSMESTIMATE Statement............................... 1243 MAKE Statement .................................... 1244 1158 F Chapter 16: The RELIABILITY Procedure MCFPLOT Statement .................................. 1245 MODEL Statement.................................... 1255 NENTER Statement................................... 1263 NLOPTIONS Statement................................. 1263 PROBPLOT Statement.................................. 1264 RELATIONPLOT Statement .............................. 1278 SLICE Statement..................................... 1291 STORE Statement.................................... 1291 TEST Statement..................................... 1292 UNITID Statement.................................... 1292 Details: RELIABILITY Procedure............................... 1293 Abbreviations and Notation ............................... 1293 Types of Lifetime Data.................................. 1293 Probability Distributions................................. 1293 Probability Plotting ................................... 1296 Nonparametric Confidence Intervals for Cumulative Failure Probabilities . 1305 Parameter Estimation and Confidence Intervals . 1307 Regression Model Statistics Computed for Each Observation for Lifetime Data . 1323 Regression Model Statistics Computed for Each Observation for Recurrent Events Data 1328 Recurrence Data from Repairable Systems . 1329 ODS Table Names.................................... 1341 ODS Graphics...................................... 1343 References........................................... 1344 Overview: RELIABILITY Procedure The RELIABILITY procedure provides tools for reliability and survival data analysis and for recurrent events data analysis. You can use this procedure to • construct probability plots and fitted life distributions with left-censored, right-censored, and interval- censored lifetime data • fit regression models, including accelerated life test models, to combinations of left-censored, right- censored, and interval-censored data • analyze recurrence data from repairable systems These tools benefit reliability engineers and industrial statisticians working with product life data and system repair data. They also aid workers in other fields, such as medical research, pharmaceuticals, social sciences, and business, where survival and recurrence data are analyzed. Most practical problems in reliability data analysis involve right-censored, left-censored, or interval-censored data. The RELIABILITY procedure provides probability plots of uncensored, right-censored, interval- censored, and arbitrarily censored data. Overview: RELIABILITY Procedure F 1159 Features of the RELIABILITY procedure include • probability plotting and parameter estimation for the common life distributions: Weibull, three- parameter Weibull, exponential, extreme value, normal, lognormal, logistic, and log-logistic. The data can be complete, right censored, or interval censored. • maximum likelihood estimates of distribution parameters, percentiles, and reliability functions • both asymptotic normal and likelihood ratio confidence intervals for distribution parameters and percentiles. Asymptotic normal confidence intervals for the reliability function are also available. • estimation of distribution parameters by least squares fitting to the probability plot • Weibayes analysis, where there are no failures and where the data analyst specifies a value for the Weibull shape parameter • estimates of the resulting distribution when specified failure modes are eliminated • plots of the data and the fitted relation for life versus stress in the analysis of accelerated life test data • fitting of regression models to life data, where the life distribution location parameter is a linear function of covariates. The fitting yields maximum likelihood estimates of parameters of a regression model with a Weibull, exponential, extreme value, normal, lognormal, logistic and log-logistic, or generalized gamma distribution. The data can be complete, right censored, left censored, or interval censored. For example, accelerated life test data can be modeled with such a regression model. • nonparametric estimates and plots of the mean cumulative function for cost or number of recurrences and associated confidence intervals from data with exact or interval recurrence ages • maximum likelihood estimation of the parameters of parametric models for recurrent events data • horizontal plots of failure times
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