The RELIABILITY Procedure

# Overview

The RELIABILITY procedure provides tools for reliability and survival data analysis and for recurrence 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.

Features of the RELIABILITY procedure include

• probability plotting and parameter estimation for the common life distributions: Weibull, exponential, extreme value, normal, lognormal, logistic, and loglogistic. 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 loglogistic, 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

Some of the features provided in the RELIABILITY procedure are available in other SAS procedures.

• You can construct probability plots of life data with the CAPABILITY procedure; however, the CAPABILITY procedure is intended for process capability analysis rather than reliability analysis, and the data must be complete (that is, uncensored).

• The LIFEREG procedure fits regression models with life distributions such as the Weibull, lognormal, and loglogistic to left-, right-, and interval-censored data. The RELIABILITY procedure fits the same distributions and regression models as the LIFEREG procedure and, in addition, provides a graphical display of life data in probability plots.

Lawless (2003) , Meeker and Escobar (1998) , Nelson (1982, 1990) , and Tobias and Trindade (1995) provide many examples taken from diverse fields and describe the analyses provided by the RELIABILITY procedure.

The features of the procedure that deal with the analysis of repair data from systems are based on the work of Doganaksoy and Nelson (1998) , Nelson (1988, 1995, 2002) , and Nelson and Doganaksoy (1989) , who provide examples of repair data analysis.

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