In reliability censored data. The reader should refer more

In the field of lifetime modeling, exponential distribution
(ED) has superior status to study the reliability characteristics of any
lifetime phenomenon. The admiration of this model has been conferred by a
number of authors. Although it became greatest widespread due to its persistent
hazard rate, but in numerous real-world situation this distribution is not
suited to study the phenomenon where hazard rate is not constant. In recent
years, some fresh classes of models were presented based an amendment of an
exponential distribution. For example, Gupta and Kundu (1999) 56 presented an
extension of the exponential distribution typically called the generalized
exponential (GE) distribution.

Reliability
(Survival) has regularly remained a main part in the design of any kind of
systems. Analyzing of reliability in life time distribution is discussed by
Ezzatallah Baloui Jamkhaneh 36, 37. Gonzalez. D-Gonzalez David et al. 51
were presented an analysis of reliability censored data. The reader should
refer more detail of survival analysis for statistical model in 76.

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Oxytocin is a Nano peptide synthesized in the hypothalamus and
stored in and secreted from the posterior pituitary gland. Oxytocin is liable
for uterine contractions and milk letdown and has been recognized more recently
to performance a role as a neurotransmitter. Clinically, oxytocin infusion is
used for induction and augmentation of labor and for the prevention and
treatment of postpartum hemorrhage (PPH). Increasing induction rates
representations more women to protracted, incessant infusion of oxytocin, which
is related with dysfunctional labor and increased rate of cesarean delivery.
Haemodynamic changes caused by oxytocin during caesarean conversed by 96, 115,
and the postpartum haemorrahage in the third stage labour were discussed by 25-27.
The identification of a model to assess the effect of Oxytocin in diverse
consequence is a too aspiring task because different individuals (due to
different body conditions, emotive states, oldness, masculinity, etc.) show
different biological responses (assessed by evaluating the heart rate signal)
under the administration of the drug Oxytocin.

The objective of this chapter to present a mathematical model
using ENH distribution in fuzzy environment and that model can be used to
calculate the effect of oxytocin. Further, compute the hazard rate and survival
rate for the different time interval after administration of the medicine.

6.1.1.        
ENH
Distribution

A random variable T said to follow the GE
distribution then its density function is given by

such
that

and

and
the development of GE was discussed in 2007 by Gupta and Kundu 57. Also
Nadarajah and Haghighi (2011) 95 presented alternative extension of the
exponential model. According to Nadarajah and Haghighi’s, if a random variable
T follows the exponential distribution (NHE) then its probability density
function is given by

Most
recently Artur J. Lemonte (2013) 78 introduced a new three-parameter family
of distribution called the exponentiated NH ENH distribution. Let a random
variable T follows the ENH distribution is denoted by

 and the density
function of ENH distribution is defined by

where

 are shape
parameter and

is the scale parameter. The cumulative
function of ENH distribution is given by

The
survival function of ENH distribution by using equation (5.14), (5.15) and
(5.16),

The
ENH hazard (failure) rate function is given by using equation (5.18) and (5.19)

6.1.           
 Fuzzy ENH Distribution

In our model 122, we developed a fuzzy-based
modeling technique using Exponentiated Nadarajah and Haghighi distribution. The
proposed technique of a fuzzy model assesses the effect of oxytocin for women
by evaluating the survival and hazard rate of their heart rate under the
administration of oxytocin.

We may consider the ENH distributions with fuzzy
parameters

that is replaced

in ENH distribution. A random variable T follows fuzzy
ENH distributionwith fuzzy parameter is known as fuzzy ENH distribution and it
is denoted by


The fuzzy probability of a random variable

in the interval c, d, c?0 is as

and compute its

cut
as follows:The Fuzzy survival (or fuzzy reliability) function

is the fuzzy probability of an item survives beyond
time t. Let the random variable T denote lifetime in a model and T ~FENHD with
density function

then the fuzzy cumulative distribution is

In these conditions the fuzzy survival function at time t of the
fuzzy ENH distribution is defined asOne fuzzier characterizes of the lifetime distribution is the
fuzzy hazard function.  This function is
also known as instantaneous failure rate function. We propose the theory of
fuzzy hazard function based on the fuzzy probability measures and

 –
cut hazard band. The fuzzy hazard function of

is the fuzzy conditional probability of an item
failing in the short time interval t
to t + dt 
given that it has not failed at time t. We would define the fuzzy
hazard function asA fuzzy mathematical model for the effect of the
drug oxytocin is established successfully. The fuzzy probability logic for ENH
distribution hazard rate and survival rate have been effectively assessed in
this paper.  The results shows that the survival
rate is increased and the hazard rate is decreased in the lower

 –
cut values. Similarly the survival rate is decreased and the
hazard rate is increased in the upper

 –
cut values.