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CPS1167 Indrani B.
resulting prediction. ̂ is given by (13) with the denominator modified to .
Then, the linearized UMVUE ̂ corresponding to ̂ is obtained by solving (10)
1
when is substituted by this ̂ .

Case 2 : ( = and = 1, … , 1) The CMP : of : is given by (18) in
1
which the linearized UMVUE ̂ given by (16) with the denominator modified
to and the linearized UMVUE ̂ is obtained by solving (15) when in there
1
is substituted by this ̂.

Case 3 : (0 ≤ ≤ − 1 and = + 1, … , ) The CMP : of : is given
1
1
by
− ̂ 2

= ̂ + ̂ log [ ̂ + ]
2
: ,
(19)

3. Results
Progressive Type-II censored data under the step-stress setting are
generated and the values of MLP and CMP of are computed under Khamis

and Higgins Model. A numerical study is carried out to compare the
performances of these MLP and CMP in terms of their Mean Square Prediction
Errors (MSPEs) and Prediction Intervals (PIs). Derivations of the MSPEs and PIs
of the MLP and CMP are complicated and so we used simulations to get those.
Using simulation studies, standard errors of these were generated and the

PIs were constructed for each of the predictors MLP and CMP.

4. Discussion and Conclusion
In this article, we have derived the MLP and CMP for the survival times of units
from the Weibull distribution which are progressively Type II censored under the
Khamis and Higgins model for the simple step-stress data. Simulation studies are
used to illustrate and compare the methods developed in this article. Simulation
studies show that the predicted values for CMP are generally closer to their actual
values than the corresponding predicted values for MLP. This is particularly true
for larger sample size, larger number of uncensored observations and for delayed
censoring scheme as long as the number of predicted observations are not very
small.

References
1. Banerjee, A. and Kundu, D. (2008). Inference Based on Type-II Hybrid
Censored Data from a Weibull Distribution, IEEE Transactions on
Reliability 57, pp. 369-378.
2. Khamis, I. H. and Higgins, S. H. (1998). A new model for step-stress
testing, IEEE Transactions on Reliability 47, pp. 131-134.

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