Page 103 - Contributed Paper Session (CPS) - Volume 1

CPS1167 Indrani B.

Prediction for censored lifetimes from Weibull
distribution in Khamis and Higgins
Step-Stress Model
Indrani Basak
Penn State Altoona, Altoona, USA

Abstract
We consider the problem of prediction of lifetimes of units from the
Weibull distribution which are censored under a simple step-stress testing
experiment in this article. We considered Progressive Type-II censoring as
the form of censoring. Cumulative Exposure Model (CEM) is the most
popular model for analyzing step-stress data. In case of the Weibull
distribution, the CEM becomes quite complicated. Due to this reason,
Khamis and Higgins (1998) proposed a step-stress model based on the
hazard functions and we will use that model in this article. Two kinds of
predictors - the maximum likelihood predictors (MLP) and the conditional
median predictors (CMP) - are derived. These two prediction methods are
numerically illustrated using simulation studies along with generating
mean squared prediction error (MSPE) and prediction intervals (PI). We
then compare the MLP and the CMP with respect to MSPE and PI.

Keywords
Conditional median predictor; Khamis and Higgins Model; Maximum
likelihood predictor; Mean squared prediction error; Prediction Interval.

1. Introduction
Items made in industrial production these days have become very
reliable with large mean survival times under normal operating
conditions. Complete data are not observed by the experimenter for the
items under study in order to reduce cost and experimental time. Those
items are usually censored. For Weibull distributed lifetimes, inferential
methods are developed by Kundu (2007), Banerjee and Kundu (2008) and
Mokhtari, Rad and Yousefzadeh (2011) for various kind of censored data.
But, the prediction of actual survival times (which are censored) has not
been discussed much. Prediction of unobserved or censored observations
is an interesting topic. It is usually difficult to obtain adequate information
about lifetime distribution and its associated parameters In conventional
industrial life-testing experiment, even with these efficient censoring
schemes. In order to obtain information on the parameters of the lifetime
distribution more rapidly than under normal operating conditions,
accelerated life tests allow the experimenter to expose the experimental

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