Page 105 - Contributed Paper Session (CPS) - Volume 1

CPS1167 Indrani B.
variable Y is given by (1) and (2) respectively. The probability density function g(t)
and the cumulative distribution function G(t) of T are given as
1 − 1 − 1
() = − for y < ln
1
() = ln − 2 ln − 1
1 − 2 − 2 ( − ) (3)

() = − for ln < < ∞
2
{

and

− 1
() = 1 − − for y < ln
1
() = { ln − 2 ln − 1
− 2 ( − ) (4)
() = 1 − − for ln < < ∞
2

1
1
1
Where = ln = ln and σ = .
1, 2
1
2

Suppose a sample of experimental units are placed on a simple step-stress
life test at an initial stress level of s1 and the stress level is changed to at a pre-
2
fixed time . Then, the progressive Type-II censoring is implemented in this
experimental setting in the following manner. At the stress-level and at the time
1
of the first failure, of the − 1 surviving units are randomly removed from the
1
experiment. At the time of the second failure, R2 of the − 2 − surviving units
1
are randomly removed from the experiment, and similarly the test continues until
time . Let be the random number of units that fail at stress level s1 and
1
be the total number of the censored units at stress level where denotes the
1
1
observed value of . Then, after time (at stress level ), at the time of the ( +
1
2
1
1)-th failure, +1 of the − − (1) − 1 surviving units are randomly removed
1
from the experiment. At the time of the ( + 2) -th
1
failure, 1 +2 of the − − (1) 1 +1 −2 surviving units are randomly removed
1
from the experiment, and similarly the test continues at the stress level . Let
2
be the total number of the censored units at stress level for a fixed
2
value of , the total number of observations. Then, let = − denotes
1
2
the random number of units that fail at stress level . With , ( = 1, 2,· · ·

2
, − 1) fixed in advance, the test continues until the -th failure at which time
all the remaining surviving units are removed. Note that =
+ + (1) + (2) where denotes the observed value of . If = ⋯ =
1
1
2
2
2
= 0, = ⋯ = = 0, then = which corresponds to the complete
1 1 +1
sample situation. If = ⋯ = 1 = 0, 1+1 = ⋯ = −1 = 0 and = −

1
then it corresponds to the conventional Type-II right censoring scheme. Note
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