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.

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.