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AbstractThis paper deals with the repair alert models. They are used for analyzing lifetime data coming from engineering devices under maintenance management. Repair alert models have been proposed and investigated for continuous component lifetimes. Existing studies are concerned with the lifetimes of items described by continuous distributions. However, discrete lifetimes are also frequently encountered in practice. Examples include operating a piece of equipment in cycles, reporting field failures that are gathered weekly, and the number of pages printed by a device completed before failure. Here, the repair alert models are developed when device lifetimes are discrete. A wide class of discrete distributions, called the telescopic family, is considered for the component lifetimes, and the proposed repair alert model is explained in detail. Furthermore, the problem of estimating parameters is investigated and illustrated by analyzing a real data set. [ABSTRACT FROM AUTHOR]

This article deals with the problem of classifying Fréchet populations by proposing a non-linear fixed effects model. Various properties of the proposed model are investigated in detail. Estimations of the effects are achieved in explicit expressions and stochastic properties of the estimators are discussed. Two procedures for testing the homogeneity of populations are proposed. Illustrative examples are also given. The proposed model is an alternative method for situations in which the existing parametric methods such as generalized linear models provide poor efficiency and factor effects are on the response non-linearly. The proposed model is also applicable in situations where the mean response does not exist. [ABSTRACT FROM AUTHOR]

Redundant is used to improve the reliability of a given system and to ensure that it is available to fulfill its duty during a mission time. This paper proposes an algorithmic approach for solving RAPs when component lifetimes are either independent and heterogeneous under a general setting. Two common active and standby schemes for allocations, are considered. Moreover, a new stochastic order is proposed and applied for comparison purposes. Various illustrative examples are also analyzed. This method can be implemented for engineering system networks. [ABSTRACT FROM AUTHOR]

This paper deals with a stress-strength system wherein the strength system has n replaceable components under internal environmental factors. These factors change the strength system and impose different effects on the magnitudes of the component strengths. The stress-strength reliability of the system under various configurations among random strengths of components and random internal environmental factors are studied in details. A characterization result for the stress distribution based on the stress-strength reliability of the system is also obtained. Moreover, some stochastic orders for comparing the system performance are discussed. Under a non-parametric setting, the lower and upper bounds for the stress-strength reliability of system are proposed. Explicit expressions for mean remaining strength functions are also derived. Some illustrative examples are assessed. [ABSTRACT FROM AUTHOR]

This paper proposes a new statistical method for one-way classification which is based on the (reversed) hazard function of the response variable. The model parameters are estimated according the maximum likelihood approach. Several testing procedures, e.g., generalized likelihood ratio test, are investigated to assess homogeneity of populations. A non-parametric method for data analysis is also proposed. Two data sets are studied using the obtained results. [ABSTRACT FROM AUTHOR]

Process capability indices has been widely applied in industry to assess the performance of industrial processes. For the larger‐the‐better lifetimes of products, the lifetime performance index CL$C_L$ is commonly considered by industrial managers. This paper confines itself to the the Bayesian statistical inferences about CL$C_L$ under the Pareto distribution with the progressively Type‐II censored samples. The Bayesian inferences are based on a conjugate continuous prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are given to demonstrate the sensitivity of results to the prior hyperparameters and the underlying distribution of the observations. Finally, a Monte Carlo simulation study is done to evaluate the behavior of the lifetime performance index CL$C_L$. [ABSTRACT FROM AUTHOR]

In manufacturing industries, indices such as the lifetime performance index ( C L ) are utilized to assess whether products' quality meets the required level. This article deals with the Bayesian inferences about C L on the basis of progressively censored data when the product's lifetime follows the Weibull distribution. The Bayesian analysis is based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are studied to assess the sensitivity of results to the prior parameters and the underlying distribution of the observed data. Finally, a simulation study is conducted to carry out the performance of the obtained results. [ABSTRACT FROM AUTHOR]

Comparative lifetime experiments are of particular importance in production processes when one wishes to determine the relative merits of several competing products with regard to their reliability. This paper confines itself to the data obtained by running a joint progressive Type-II censoring plan on samples in a combined manner. The problem of Bayesian predicting failure times of surviving units is discussed in details when parent populations are exponential. Two real data sets are analyzed in order to illustrate all the inferential procedures developed here. When destructive experiments under a censoring scheme finished, the researchers are usually interested to estimate remaining lifetimes of surviving units for sequel experiments. Findings of this paper are useful for these purposes specially when samples are non-homogeneous such as those taken from industrial storages. [ABSTRACT FROM AUTHOR]