On the Mean Inactivity Time Ordering With Reliability Applications

We study further the quantile mean inactivity time order. Relations between the proposed stochastic order and the other transform stochastic orders are obtained. Besides, sufficient conditions for the stochastic order are provided. Then, preservation of the order under monotone transformations, series, and parallel systems and mixtures of a general family of semiparametric distributions is studied. Examples are also given to illustrate the results.

show abstract

“…For a nonnegative random variable with distribution function , the mean inactivity time (MIT) of is defined as (cf. Kayid and Ahmad [20])…”

Section: Resultsmentioning

confidence: 98%

Increasing Mean Inactivity Time Ordering: A Quantile Approach

Kayid

Izadkhah

Alfifi

2018

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, if r = 1, thenm 1 (t) represents a function called the mean idle time or inactivity time (MIT) or reversed residual life (MRRL) function that indicates the expected inactive life length for a unit which is first observed down at age t. The properties of MIT function have been explored by Ahmad et al (2005) and Kayid and Ahmad (2004).…”

Section: Definition 471 Let X Be a Random Variable Denoting The Lifmentioning

confidence: 99%

The Generalized Additive Weibull-G Family of Distributions

Hassan¹,

Hemeda²,

Maiti³

et al. 2017

IJSP

View full text Add to dashboard Cite

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

show abstract

“…The MRRL of X can be obtained by setting n = 1 in the above equation. The properties of the mean inactivity time have been considered by many authors, see e.g., Kayid and Ahmad (2004) and Ahmad et al (2005).…”

Section: Reversed Residual Life Functionmentioning

confidence: 99%

The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

Afify¹,

Hamedani²,

Ghosh³

et al. 2015

IJSP

View full text Add to dashboard Cite

This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.

show abstract

On the Mean Inactivity Time Ordering With Reliability Applications

Cited by 92 publications

References 12 publications

Increasing Mean Inactivity Time Ordering: A Quantile Approach

Increasing Mean Inactivity Time Ordering: A Quantile Approach

The Generalized Additive Weibull-G Family of Distributions

The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

Contact Info

Product

Resources

About