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The purpose of this paper is to analyze and compare four numerical methods to estimate the most suitable one which describes wind speed distribution of M’Sila, a province of northern Algeria.

The site chosen in this investigation is characterized by calm winds; in this case, the appropriate wind speed distribution is that of hybrid Weibull.

The four numerical methods used in the present paper are the maximum likelihood method, the graphical method, the moment method and the energy pattern factor method. The hybrid Weibull distributions using the abovementioned approaches are compared with the measured data via three statistical parameters, namely, the correlation coefficient, the root mean square error and the Chi-square error.

The obtained results showed that the moment method is the suitable one in describing month and annual wind speed hybrid Weibull parameters of this region.

This article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).

The GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.

The performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.

The proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

Burr distribution has been proved to be a useful failure model. It can assume different shapes which allow it to be a good fit for various lifetimes data. Hybrid censoring is an important way of generating lifetimes data. The purpose of this paper is to estimate an unknown parameter of the Burr type XII distribution when data are hybrid censored.

The problem is dealt with through both the classical and Bayesian point of view. Specifically, the methods of estimation used to tackle the problem are maximum likelihood estimation method and Bayesian method. Empirical Bayesian approach is also considered. The performance of all estimates is compared through their mean square error values. The paper employs Monte Carlo simulation to evaluate the mean square error values of all estimates.

The key findings of the paper are that the Bayesian estimates are superior to the maximum likelihood estimates (MLE).

This work has practical importance. Indeed, the proposed methods are applied to real life data.

The paper is original and is quite applicable in lifetimes data analysis.

In this paper, the authors design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this paper we design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this study, the authors design accelerated life test under Type-I censoring when the lifetime of test items follows PID and also provides its application in the field of warranty policy. The following conclusion is made on the basis of this study. (1) An inverse relationship is shown between the shape parameter with the expected total cost and expected cycle time, while the shape parameter directly relates to the expected cost rate (see Table 5). (2) A direct relationship is shown between the scale parameter with the expected total cost and expected time cycle, while the inverse relationship is shown with the expected cost rate (see Table 5). (3) An inverse relationship is shown between the replacement age and the expected cost rate, while there are direct relationships between expected total cost and expected time cycle (see Table 5).

This paper is neither published or neither accepted anywhere.

The purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.

For Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.

Optimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.

The research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.

Differential search algorithm (DSA) is a new optimization, meta-heuristic algorithm. It simulates the Brownian-like, random-walk movement of an organism by migrating to a better position. The purpose of this paper is to analyze the performance analysis of DSA into two key parts: six random number generators (RNGs) and Benchmark functions (BMF) from IEEE World Congress on Evolutionary Computation (CEC, 2015). Noting that this study took problem dimensionality and maximum function evaluation (MFE) into account, various configurations were executed to check the parameters’ influence. Shifted rotated Rastrigin’s functions provided the best outcomes for the majority of RNGs, and minimum dimensionality offered the best average. Among almost all BMFs studied, Weibull and Beta RNGs concluded with the best and worst averages, respectively. In sum, 50,000 MFE provided the best results with almost RNGs and BMFs.

DSA was tested under six randomizers (Bernoulli, Beta, Binomial, Chisquare, Rayleigh, Weibull), two unimodal functions (rotated high conditioned elliptic function, rotated cigar function), three simple multi-modal functions (shifted rotated Ackley’s, shifted rotated Rastrigin’s, shifted rotated Schwefel’s functions) and three hybrid Functions (Hybrid Function 1 (n=3), Hybrid Function 2 (n=4,and Hybrid Function 3 (n=5)) at four problem dimensionalities (10D, 30D, 50D and 100D). According to the protocol of the CEC (2015) testbed, the stopping criteria are the MFEs, which are set to 10,000, 50,000 and 100,000. All algorithms mentioned were implemented on PC running Windows 8.1, i5 CPU at 1.60 GHz, 2.29 GHz and a 64-bit operating system.

The authors concluded the results based on RNGs as follows: F3 gave the best average results with Bernoulli, whereas F4 resulted in the best outcomes with all other RNGs; minimum and maximum dimensionality offered the best and worst averages, respectively; and Bernoulli and Binomial RNGs retained the best and worst averages, respectively, when all other parameters were fixed. In addition, the authors’ results concluded, based on BMFs: Weibull and Beta RNGs produced the best and worst averages with most BMFs; shifted and rotated Rastrigin’s function and Hybrid Function 2 gave rise to the best and worst averages. In both parts, 50,000 MFEs offered the best average results with most RNGs and BMFs.

Being aware of the advantages and drawbacks of DS enlarges knowledge about the class in which differential evolution belongs. Application of that knowledge, to specific problems, ensures that the possible improvements are not randomly applied. Strengths and weaknesses influenced by the characteristics of the problem being solved (e.g. linearity, dimensionality) and by the internal approaches being used (e.g. stop criteria, parameter control settings, initialization procedure) are not studied in detail. In-depth study of performance under various conditions is a “must” if one desires to efficiently apply DS algorithms to help solve specific problems. In this work, all the functions were chosen from the 2015 IEEE World Congress on Evolutionary Computation (CEC, 2015).

Maintenance managers must often make preventive maintenance (PM) decisions based on limited historical failure data. These small data sets introduce significant uncertainties which can lead to selecting suboptimal (more costly) PM intervals. Examines the performance of two commonly used estimation techniques (MLE and rank regression), and develops a third hybrid technique which improves the PM interval accuracy for small data sets. In addition, characterizes the risks involved in making PM decisions based on small data sets for all three methods, to provide useful guidelines for the practising maintenance engineer.

In order to reduce avoidably lengthy duration required to test highly reliable products under usage stress, accelerated life test sampling plans (ALTSPs) are employed. This paper aims to build a decision model for obtaining optimal sampling plan under accelerated life test setting using Type-I hybrid censoring scheme for products covered under warranty.

The primary decision model proposed in this paper determines ALTSP by minimizing the relevant costs involved. To arrive at the decision model, the Fisher information matrix for Type-I hybrid censoring scheme under accelerated life test setting is derived. The optimal solution is attained by utilizing appropriate techniques following a nonlinear constrained optimization approach. As a special case, ALTSP for Type-I censoring is obtained using the same approach. ALTSP under Type-I hybrid censoring using the variance minimization approach is also derived.

On comparing the optimal results obtained using the above mentioned approaches, it is found that the cost minimization approach does better in reducing the total cost incurred. Results also show that the proposed ALTSP model under cost function setting has considerably lower expected testing time. Interesting findings from the sensitivity analysis conducted using a newly introduced failure dataset pertaining to locomotive controls are highlighted.

The research introduces a model to design optimum ALTSP for Type-I hybrid censoring scheme. The practical viability of the model makes it valuable for real-life situations. The practical application of the proposed model is exemplified using a real-life case.

Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.

The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.

The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.

The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.

These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.

A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

Acceptance sampling plans are a decision-making process on the basis of a randomly selected sampling from a party, where it is not possible to completely scan the products for reasons such as time and cost being limited or the formation of damaged products during the inspection. For some products, the life span (time from beginning to failure) may be an important quality characteristic. In this case, the quality control adequacy of the products can be checked with an acceptance sampling plan based on the truncated life test with a censored scheme for the lifetime of the products. In this study, group acceptance sampling plans (GASPs) based on life tests are studied under the Type-I censored scheme for the compound Weibull-exponential (CWE) distribution.

GASPs based on life tests under the Type-I censored scheme for the CWE distribution are developed by using both the producer's risk and the consumer's risk.

In this study, optimum sample size, optimum number of groups and acceptance number are obtained under the Type-I censored scheme for the CWE distribution. Real data set illustration is given to show GASPs how to be used for the industry applications.

Different from acceptance sampling plans with just considering the producer's risk, GASPs are constructed by using two-point approach included both the producer's risk and the consumer's risk for CWE distribution.