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Research in the area of financial distress often uses a proportional hazards model to determine the influence of covariates on the duration of time that precedes financial distress. Acritical issue in the use of a proportional hazards model is the use of time‐invariant and time‐dependent covariates. Time‐invariant covariates remain fixed while time‐dependent covariates change during the estimation of the model. Although the choice of covariates might substantially affect the estimation of the proportional hazards model, existing literature often fails to consider the potential effect of this choice on model estimation. This paper reviews the distinction between time‐invariant and time‐dependent covariates and the effect of covariate selection on the estimation of a proportional hazards model. Using a sample of financially distressed and non‐financially distressed firms, this paper suggests the choice of time dependence substantially influences model estimation and that covariate selection should be given more serious consideration in financial distress research.

This study aims to focus on asset management of large‐scale information systems supporting infrastructures and especially seeks to address a methodology of their statistical deterioration prediction based on their historical inspection data. Information systems are composed of many devices. Deterioration process i.e. wear‐out failure generation process of those devices is formulated by a Weibull hazard model. Furthermore, in order to consider the heterogeneity of the hazard rate of each device, the random proportional Weibull hazard model, which expresses the heterogeneity of the hazard rate as random variables, is to be proposed.

Large‐scale information systems comprise many components, and different types of components might have different hazard rates. Therefore, when analyzing faults of information systems that comprise various types of devices and components, it is important to consider the heterogeneity of the hazard rates that exist between the different types of components. In this study, with this in consideration, the random proportional Weibull hazard model, whose heterogeneity of hazard rates is subject to a gamma distribution, is formulated and a methodology is proposed which estimates the failure rate of various components comprising an information system.

Through a case study using a traffic control system for expressways, the validity of the proposed model is empirically verified. Concretely, as for HDD, the service life at which the survival probability is 50 percent is estimated as 158 months. However, even for the same HDD, use environment differs according to usage. Actually, among the three different usages (PC, server, others), failures happen earliest in the case of PCs, which have the highest heterogeneity parameter and a survival probability of 50 percent after 135 months of usage. On the other hand, as for others, its survival probability is 50 percent at 303 months.

To operationally express the heterogeneity of failure rates, the Weibull hazard model is employed as a base, and a random proportional Weibull hazard model expressing the proportional heterogeneity of hazard rates with a standard gamma distribution is formulated. By estimating the parameter of the standard proportional Weibull hazard function and the parameter of the probability distribution that expresses the heterogeneity of the proportionality constant between the types, the random proportional Weibull hazard model can easily express the heterogeneity of the hazard rates between types and components.

The software reliability models to describe the reliability growth phenomenon are formulated by any stochastic point process with state‐dependent or time‐dependent intensity function. On the other hand, to deal with the environmental data, which consists of covariates influencing times to software failure, it may be useful to apply the Cox’s proportional hazards model for assessing the software reliability. In this paper, we review the proportional hazards software reliability models and discuss the problem to determine the optimal software release time under the expected total software cost criterion. Numerical examples are devoted to examine the dependence of the covariate structure in both the software reliability prediction and the optimal software release decision.

The purpose of this research is to undertake an examination of the impacts of socio‐demographic and economic variables on the probability of purchasing financial products. There is relatively little empirical research that has been taken to understand how the underlying economy affects customers' subsequent financial product purchase behaviours. Understanding this influence would improve prediction of when purchases will occur and hence is important for the Customer lifetime value models of financial service organisations.

Two proportional hazard modelling approaches – Cox and Weibull – are compared in terms of predictive ability on a data set from a major insurance company. The risk factors for purchase are both economic and socio‐demographic.

The results show that the external economic environment is an extremely important influence in driving customers' financial products purchasing behaviours. Furthermore, the results also indicate that Cox's proportional hazard models are superior to Weibull proportional hazard models in this case because of an annual purchase effect.

Financial organisations need to consider the current economic conditions before determining how much marketing effort to undertake.

The originality of this paper is that it considers economic conditions and socio‐demographic variables in modelling the long run purchase behaviour of customers for insurance and savings products. It has a large data set from a major insurance company. It is also one of the first papers to make a detailed comparison between the semi‐parametric and parametric proportional hazard models in the bank marketing area.

This paper aims to present a case study where proportional hazards modeling software is used to evaluate the potential benefits of a condition‐based maintenance policy for military vehicle diesel engines.

Maintenance records for diesel engines were supplied by the UK Ministry of Defence. A proportional hazards model based on these data was created using EXAKT software. Covariate parameters were estimated using the maximum likelihood method and transition probabilities were established using a Markov Chain model. Finally, decision parameters were entered to create an optimal decision model.

Two significant covariates were identified as influencing the hazard rate of the engines. In addition, the optimal decision model indicated a potential economic saving of up to 30 per cent.

A model of this nature is particularly useful to predict failures, improve maintenance policies, and possibly reduce maintenance costs. In addition, the cost of implementing maintenance policies based on this model should be balanced with the potential to reduce the risk of danger to personnel.

The model presented provides military personnel with a decision tool that optimizes the maintenance policy for diesel engines installed in military vehicles.

The main purpose of this study is to evaluate the extent of dropout students and identify the relationship between risk factors of dropout and the survival time of students.

The Kaplan–Meier estimator (KM), also known as the product-limit technique, is a nonparametric model function that is commonly used in estimating survival function events (Kaplan and Meier, 1958). The survival function's Kaplan–Meier estimators are used to estimate and graph survival probabilities as a function of time, as well as explanatory data analysis (EDA) for the survival data, including the median survival time, and compare for two or more of the survival events. In addition, Cox proportional hazards model is employed for modelling purpose.

Results of the Kaplan–Meier curves show that male students have lower survival rates than female, researchers have found that there is a difference between the survival times of the student's school types, results show students from English-based schools are higher than Arabic-based schools as suggested by the survival curve. Similarly, there is a difference between the survival times of students aging equal or greater than 25 and students aging less than 25 and survival function estimates of dropout according to high school grade marks has huge difference. These results were confirmed using log rank test as age, school type and marks were statistically significantly different while gender is not statistically significant.

There is no study of this kind from the Somalia context about the student's dropout. Subsequent to the outbreak of civil war in 1988 and the collapse of the central government in 1991, all public social services in Somalia including education centers were severely disrupted.

The statistical methods discussed in the previous section will be applied on a real dataset obtained from different offices of the university; most of the data were extracted from faculty of economics office and admission and record office. The data set comprised of 70 students from SIMAD university, consists of full-time faculty of economics students who enrolled at the university in the academic year of 2017–2018 until two years of diploma, students either complete 24 months of diploma or leave the university and that is the event of interest.

Industry decision makers often rely on a risk-based approach to perform inspection and maintenance planning. According to the Risk-Based Inspection and Maintenance Procedure project for the European industry, risk has two main components: probability of failure (PoF) and consequence of failure (CoF). As one of these risk drivers, a more accurate estimation of the PoF will contribute to a more accurate risk assessment. Current methods to estimate the PoF are either time-based or founded on expert judgement. This paper suggests an approach that incorporates the proportional hazards model (PHM), which is a statistical procedure to estimate the risk of failure for a component subject to condition monitoring, into the risk-based inspection (RBI) methodology, so that the PoF estimation is enhanced to optimize inspection policies.

To achieve the overall goal of this paper, a case study applying the PHM to determine the PoF for the real-time condition data component is discussed. Due to a lack of published data for risk assessment at this stage of the research, the case study considered here uses failure data obtained from the simple but readily available Intelligent Maintenance Systems bearing data, to illustrate the methodology.

The benefit of incorporating PHM into the RBI approach is that PHM uses real-time condition data, allowing dynamic decision-making on inspection and maintenance planning. An additional advantage of the PHM is that where traditional techniques might not give an accurate estimation of the remaining useful life to plan inspection, the PHM method has the ability to consider the condition as well as the age of the component.

This paper is proposing the development of an approach to incorporate the PHM into an RBI methodology using bearing data to illustrate the methodology. The CoF estimation is not addressed in this paper.

This paper presents the benefits related to the use of PHM as an approach to optimize the PoF estimation, which drives to the optimal risk assessment, in comparison to the time-based approach.

Survival analysis is statistical technique that uses longitudinal data to model the process that allows an individual or firm to survive to a particular point in time. Despite a large number of studies that use survival analysis to model the duration of time that precedes financial distress, some criticism has suggested that the application of survival analysis to financial distress research provides limited incremental knowledge. This study uses survival analysis to model the duration of time that precedes a firm's initial payment default. The data set consists of firm financial information obtained from a large credit information company in Finland for a five‐year period split into estimation and holdout samples. Financial ratios, size, industry, and age are used as covariates to model the survival process preceding the initial payment default. The hazard is compared to a logistic risk measure estimated from data one year prior to default. The proportional hazards model is shown to give a more accurate forecast of default for the earlier years prior to the onset of financial distress.

Reviews previous research on predicting financial distress and the effects of US Chapter 11 bankruptcy (C11B); and explains how survival analysis and Cox’s (1972) proportional hazards model can be used to estimate the financial outcome for the shareholders of C11B. Reduces a previous data set (Russel et al 1999) of 154 companies entering C11B between 1984 and 1993 to 59 (54 of which gave no value to shareholders) and estimates two models to predict this: one based on firm‐specific covariates only and the other adding market‐wide covariates. Explains the methodology, presents the results and uses receiver operating characteristic curves to compare the predictive accuracy of the two. Finds little difference between the and suggests using the simpler model. Briefly summarizes the variables which are most useful in predicting the value outcomes of C11B for shareholders and recognizes the limitations of the study.

To a customer, higher quality is synonymous to higher expected life. Therefore, the purpose of this paper is to determine the existing life of the competing brands in a product field and suggest an improvement plan, under cost constraints, so that all the brands can be placed on a comparable scale.

For this, we consider Cox proportional hazard model for estimation of the mean life and suggest an optimization procedure for improving mean life under cost constraint. As the cost of redesigning the product is mostly known, the authors propose to take corresponding repairing cost as their surrogates and optimize the expected life for each brand subject to a fixed level of cost.

From Cox's model one can identify the causes of failure for the brands under consideration. Further, under the optimization techniques proposed herein one can order the brands for comparison purpose.

We have applied the proposed optimization techniques for ordering mobile handsets. In fact, based on the result obtained by our proposed method, the design engineers or the brand planners can take necessary actions to increase the product life, correct product design and improve the product performance.

The cost minimization approach under Cox's cause‐wise setup can provide a tool for comparing different brands of different prices and order them to know the best performer.