Open AccessOpen Access


Modeling Reliability Engineering Data Using Scale-Invariant Quasi-Inverse Lindley Model

Mohamed Kayid*, Tareq Alsayed

Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia

* Corresponding Author: Mohamed Kayid. Email:

Computers, Materials & Continua 2022, 72(1), 1847-1860.


An important property that any lifetime model should satisfy is scale invariance. In this paper, a new scale-invariant quasi-inverse Lindley (QIL) model is presented and studied. Its basic properties, including moments, quantiles, skewness, kurtosis, and Lorenz curve, have been investigated. In addition, the well-known dynamic reliability measures, such as failure rate (FR), reversed failure rate (RFR), mean residual life (MRL), mean inactivity time (MIT), quantile residual life (QRL), and quantile inactivity time (QIT) are discussed. The FR function considers the decreasing or upside-down bathtub-shaped, and the MRL and median residual lifetime may have a bathtub-shaped form. The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization (EM) algorithm. The EM algorithm is an iterative method suitable for models with a latent variable, for example, when we have mixture or competing risk models. A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them. The simulation study shows that the EM approach provides a better estimation of the parameters. Finally, the proposed model is fitted to a reliability engineering data set along with some alternatives. The Akaike information criterion (AIC), Kolmogorov-Smirnov (K-S), Cramer-von Mises (CVM), and Anderson Darling (AD) statistics are used to compare the considered models.


Cite This Article

M. Kayid and T. Alsayed, "Modeling reliability engineering data using scale-invariant quasi-inverse lindley model," Computers, Materials & Continua, vol. 72, no.1, pp. 1847–1860, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1042


  • 649


  • 0


Share Link