Page 104 - Contributed Paper Session (CPS) - Volume 1

CPS1167 Indrani B.
units in industrial experiments to increased levels of stress factors such as
load, pressure, temperature and voltage. Step-stress tests are special class
of accelerated life tests that allow the experimenter to change the stress
levels at pre-fixed times during the life-testing experiment. We consider
a simple step-stress testing with only two stress levels and this model has
been studied extensively in the literature in this article. Developing
statistical prediction theory and procedures for step-stress models under
progressive Type II censoring schemes based on Weibull distribution is
the purpose of this article. Two frequently used predictors which are
called the Maximum Likelihood Predictor (MLP) and the Conditional
Median Predictor (CMP) will be used for prediction purpose.

2. Methodology
In a simple step-stress testing setup, n identical units are tested at
initial stress level of s1 until a pre-fixed time τ, at which point stress level
is changed to s2 and the life-test continues on. Let us denote the hazard
functions at stress levels s1 and s2 by h1 and h2, respectively. Cumulative
Exposure Model is the most popular model for analyzing step-stress data.
The main idea is to assume that the remaining lifetime of the items
depends only on the current accumulated stress, regardless of how it has
been accumulated. In case of the Weibull distribution, the CEM becomes quite
complicated. Khamis and Higgins (1998) proposed the following step-stress model
for the Weibull distribution:

−1
ℎ () = for 0 < < τ
1
ℎ() = { 1
ℎ () = −1 for τ < < ∞
2
2
(1)
The corresponding survival functions are:

̅
() = − 1 for 0 < < τ
̅
() = { 1 −

̅
() = − 2 − 1 for τ < < ∞
2
(2)
We will assume that, at the stress level 1, lifetimes have the distribution
Weibull (, ) with the shape and scale parameters and and at the stress
1
1
level 2, lifetimes have the distribution Weibull (, ) with the shape and scale
2
parameters and . We found that the prediction methods become
2
complicated for the original Weibull distribution and therefore we will be working
with the variable = ln where the hazard function and survival function of the

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