General Failure Time Research Articles

Variable selection for case-cohort studies with informatively interval-censored outcomes

Variable selection has recently attracted a great deal of attention and in particular, a couple of methods have been proposed for general interval-censored failure time data or the interval-censored data arising from case-cohort studies. However, all of them have some limitations or apply only to limited situations. Corresponding to these, a new, more general variable selection approach is proposed under a class of flexible semiparametric transformation models that allows for dependent interval censoring. In particular, the oracle property of the method under the broken adaptive ridge penalty function is established and for its implementation, a novel EM algorithm is developed. Also a simulation study is performed and suggests that the proposed approach works well in practical situations. Finally the method is applied to a HIV trial that motivated this study.

Accelerated failure time model for data from outcome-dependent sampling.

Outcome-dependent sampling designs such as the case-control or case-cohort design are widely used in epidemiological studies for their outstanding cost-effectiveness. In this article, we propose and develop a smoothed weighted Gehan estimating equation approach for inference in an accelerated failure time model under a general failure time outcome-dependent sampling scheme. The proposed estimating equation is continuously differentiable and can be solved by the standard numerical methods. In addition to developing asymptotic properties of the proposed estimator, we also propose and investigate a new optimal power-based subsamples allocation criteria in the proposed design by maximizing the power function of a significant test. Simulation results show that the proposed estimator is more efficient than other existing competing estimators and the optimal power-based subsamples allocation will provide an ODS design that yield improved power for the test of exposure effect. We illustrate the proposed method with a data set from the Norwegian Mother and Child Cohort Study to evaluate the relationship between exposure to perfluoroalkyl substances and women's subfecundity.

An Automated Smart EPQ-Based Inventory Model for Technology-Dependent Products under Stochastic Failure and Repair Rate

With the ever-growing technology development, high-tech products such as mobile phones, computers, electromagnetic devices and smart devices are facing high design and production modification requirements with relatively shorter life cycles. For instance, every forthcoming smart phone goes out of production in a shorter period after its launch, followed by its next generation. The design of high-tech products requires high investments in smart and automated manufacturing technology to ensure higher production efficiency. For high-tech products with short life spans, the manufacturing performance-quality variable is an important design parameter that affects system reliability, production efficiency and manufacturing costs. Major performance-quality factors of a manufacturing system which affect productivity and reliability of the manufacturing process are discussed in this research. The study investigates an integrated smart production maintenance model under stochastic manufacturing reliability for technology dependent demand and variable production rate. The smart unit production cost is a function of manufacturing reliability and controllable production rate, as a manufacturing system can be operated at different production rates within designed limits μ ϵ [ μ m i n , μ m a x ] . Manufacturing reliability is increased through investment in smart manufacturing technology and resources. The integrated smart production maintenance model is formulated under general failure and repair time distributions and the optimal production maintenance policy is investigated under specific failure and repair time distributions. A mathematical model is developed to optimize the manufacturing quality-performance parameter, variable production rate, per unit technology investment and production lot size. The total cost function is optimized through the Khun–Tucker method. The mathematical model is also validated with numerical analysis, comparative study, and sensitivity analysis for model key parameters.

A regularized estimation approach for case‐cohort periodic follow‐up studies with an application to HIV vaccine trials

This paper discusses regression analysis of the failure time data arising from case-cohort periodic follow-up studies, and one feature of such data, which makes their analysis much more difficult, is that they are usually interval-censored rather than right-censored. Although some methods have been developed for general failure time data, there does not seem to exist an established procedure for the situation considered here. To address the problem, we present a semiparametric regularized procedure and develop a simple algorithm for the implementation of the proposed method. In addition, unlike some existing procedures for similar situations, the proposed procedure is shown to have the oracle property, and an extensive simulation is conducted and it suggests that the presented approach seems to work well for practical situations. The method is applied to an HIV vaccine trial that motivated thisstudy.

Inference on semiparametric transformation model with general interval-censored failure time data

ABSTRACTFailure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided.

Point estimation of distribution parameters of overhaul period of imported hydraulic valves for agricultural machinery

As a result of researches of operational reliability of imported hydraulic valves in ordinary conditions of operation, lower confidence limit of the average value of operating life for the general mean failure time corresponding to specified confidence probability was determined.

Pointwise availability of a system having a general failure time distribution

This paper considers the behaviour of a system having a general failure time distribution with probability density S(x). the Laplace transforms of various joint probabilities have been obtained and the corresponding results for some particular cases are deduced. In the end the behaviour of the system under steady state is examined.

Joint effect of stock threshold level and production policy on an unreliable production environment

In this article we develop an economic manufacturing quantity (EMQ) model subject to stochastic machine breakdown, repair and stock threshold level (STL). Instead of constant production rate, in this model production rate is considered as a decision variable. Since, the stress of the machine depends on the production rate, failure rate of the machine will be a function of the production rate. Again, in this article consideration of safety stock in all existing literature is replaced by the concept of stock threshold level (STL). Further, extra capacity of the machine is considered to buffer against the possible uncertainties of the production process where machine capacity is predetermined. The basic model is developed under general failure and general repair time distributions. Since, the assumption of variable production rate makes the objective function quite complex, so main emphasis is given on computational methodology to solve the present problem. We suggest two computational algorithms for the determination of production rate and stock threshold level which minimize the expected cost rate in the steady state. Finally, through numerical examples we illustrate the key insights of our model from managerial point of view.

Confidence Intervals for the Difference of Median Failure Times Applied to Censored Tumor Growth Delay Data

In tumor xenograft experiments, tumor response to the anticancer agents is often assessed by tumor growth delay, the difference in median tumor quadrupling times between treatment and control. Tumor quadrupling time is often subjected to right censoring because death of the experimental mice or limitations of the follow-up period. In the literature, tumor growth delay is simply reported without a standard error or confidence interval being given, which ignores the noise in the experimental data. Here, we present seven confidence intervals for the difference of medians in a general right-censored failure time framework. Simulation studies are conducted to compare the coverage probability of these intervals for small samples. The proposed intervals are applied to tumor growth delay data from an actual tumor xenograft experiment.

Optimising age-replacement and extended non-renewing warranty policies in lifecycle costing

This paper analyses the life cycle cost of equipment protected by both base and extended warranty policies from a consumer's perspective. We assume that the equipment has two types of failure: minor and catastrophic. A minor failure can be corrected with minimal repair whereas a catastrophic failure can only be removed by a replacement. It is assumed that equipment is maintained at no charge to the consumer during the warranty period, whereas the consumer is fully charged for any maintenance on failures after the extended warranty expires. We formulate the expected life cycle cost of the equipment under a general failure time distribution, and then for special cases we prove that the optimal replacement and extended warranty policies exists where the expected life cycle cost per unit time is minimised. This is examined with numerical examples.

Optimal preventive maintenance for equipment with two quality states and general failure time distributions

We present an economic model for the optimization of preventive maintenance in a production process with two quality states. The equipment starts its operation in the in-control state but it may shift to the out-of-control state before failure or scheduled preventive maintenance. The time of shift and the time of failure are generally distributed random variables. The two states are characterized by different failure rates and revenues. We first derive the structure of the optimal maintenance policy, which is defined by two critical values of the equipment age that determine when to perform preventive maintenance depending on the actual (observable) state of the process. We then provide properties of the optimal solution and show how to determine the optimal values of the two critical maintenance times accurately and efficiently. The proposed model and, in particular, the behavior of the optimal solution as the model parameters and the shift and failure time distributions change are illustrated through numerical examples.

Optimal Lot Sizing Policy for an Unreliable Manufacturing System Under Cost-Effectiveness Criterion

The traditional method of determining the optimal Economic Manufacturing Quantity (EMQ) policy for an unreliable production system is the minimization of the expected cost per unit time in the steady state which does not consider the reliability of the system in true sense. The purpose of this article is to introduce an alternative criterion of optimality called cost effectiveness which takes into account both cost and reliability aspects of the production system. The proposed EMQ model is formulated under general failure and general repair time distributions. The criteria for the existence and uniqueness of the optimal production time which maximizes the cost effectiveness are derived. Finally, a numerical example is taken to compare the cost effective production policy with the corresponding average cost one.

Statistical Analysis of General Degradation Path Model and Failure Time Data with Multiple Failure Modes

ABSTRACT This article considers degradation and failure time models with multiple failure modes which used to study the problem of longevity and aging in survival analysis and reliability. Degradation process is modeled using general nonparametric, nonlinear path models. Semi-parametric models for the intensities of the traumatic failures are used supposing that these intensities depend on degradation level. Semi-parametric estimators of various reliability characteristics are proposed and asymptotic properties of the estimators are obtained. The theoretical results are illustrated using simulated data.

Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.

Optimal design of unreliable production–inventory systems with variable production rate

In this article, we study an economic manufacturing quantity (EMQ) problem for an unreliable production facility where the production rate is treated as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate of the machine is assumed to be dependent on the production rate. The unit production cost is also taken as a function of the production rate, as the machine can be operated at different production rates resulting in different unit production costs. The basic EMQ model is formulated under general failure and general repair time distributions and the optimal production policy is derived for specific failure and repair time distributions viz., exponential failure and exponential repair time distributions. Considering randomness of the time to machine failure and corrective repair time, the model is extended to the case where certain safety stocks in inventory may be useful to improve service level to customers. Optimal production policies of the proposed models are derived numerically and the sensitivity of the optimal results with respect to those parameters which directly influence the machine failure and repair rates is also examined.

Computational aspects of an extended EMQ model with variable production rate

The paper considers a generalized economic manufacturing quantity (EMQ) model with stochastic machine breakdown and repair in which the time to machine failure, corrective and preventive repair times are all assumed to be random variables. The model is formulated under general failure and general repair time distributions, treating the machine production rate (speed) as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate is assumed to be dependent on the production rate. The model is further extended to the case where certain safety stocks are hold in inventory to protect against possible stockout during machine repair. The solution procedure and computational algorithms of the associated constrained optimization problems are provided. Numerical examples are taken to determine the optimal production policies by the proposed algorithms and examine the sensitivity of the model parameters. Several economic manufacturing quantity (EMQ) models for unreliable manufacturing systems have been developed in the literature even for general failure and general repair (corrective) time distributions. In these studies, preventive repair has not been considered in a general way and efforts have been made to derive the production control and maintenance policy for inflexible manufacturing systems, where the machine capacity is pre-determined. The purpose of this article is to formulate a generalized EMQ model for a flexible unreliable manufacturing system in which (i) the time to machine failure and repair (corrective and preventive) times follow general probability distributions and (ii) the machine failure rate is dependent on the production rate. Consideration of a variable production rate makes the model hard to analyze completely. So, attempt has also been made to get into its computational aspects by developing solution algorithms.

Optimal lot sizing for an unreliable production system under partial backlogging and at most two failures in a production cycle

The paper considers an economic manufacturing quantity problem for an unreliable manufacturing system where the machine is subject to random failure and at most two failures can occur in a production cycle. Upon first failure, the repair action is started immediately and the demand is met first from the on-hand inventory. The shortages, if occur due to longer repair time, are backlogged partially by resuming the production run after machine repair. While backlogging, if failure occurs again then the accumulated shortages until completion of the second repair are assumed to be lost. The model is formulated under general failure and general repair time distributions. Some characteristics of the model with exponential failure and exponential/constant repair times are studied. The optimal lot sizing policies are derived and the sensitivity of some model parameters is examined with the help of numerical examples.

Semiparametric Failure Time Regression With Replicates of Mismeasured Covariates

This article proposes a general strategy for the regression analysis of univariate and multivariate failure time data when a subset of covariates cannot be measured precisely but replicate measurements of their surrogates are available. Multivariate failure time data include recurrent events and clustered survival data. The number of replicate measurements can vary from subject to subject and can even depend on the failure time. No parametric assumption is imposed on the error or on any other random variable. Several semiparametric regression models are considered, including the Cox proportional hazards model for univariate failure time data, multiplicative intensity/rate models for recurrent events data, and marginal Cox proportional hazards models for general multivariate failure time data. The existing estimating functions in the absence of measurement error are corrected to yield consistent and asymptotically normal estimators of the regression parameters. The estimation of the underlying failure time distribution is also studied. The operating characteristics of the proposed estimators are assessed through extensive simulation studies. An application to multiple tumor recurrences from a cancer prevention trial is provided.

Optimal lot sizing for an unreliable production system based on net present value approach

The paper considers the net present value (NPV) approach to determine the economic manufacturing quantities for an unreliable production system over an infinite planning horizon. The NPV of the expected total cost is obtained under general failure time and general repair time distributions and its asymptotic characteristics are examined by perturbation of the instantaneous discount rate. The criteria for the existence and uniqueness of the optimal production time (lot size) are derived under exponential failure and constant/zero repair time. The performance of the NPV model is compared with the traditional long-run average cost model in terms of the NPV of the expected total cost based on the optimal decisions of the two models. From numerical experiments, it is observed that the decision based on the average cost can be 10% worse than the decision based on the NPV depending upon the machine failure rate.

Production planning problem in manufacturing systems with general failure and repair time distributions

We study the optimal flow control for a manufacturing system subject to random failures and repairs. In most previous work, it has been proved that, for constant demand rates and exponential failure and repair times distributions of machines, the hedging point policy is optimal. The aim of this study is to extend the hedging point policy to non-exponential failure and repair times distributions and random demand rates models. The performance measure is the cost related to the inventory and back order penalties. We find that the structure of the hedging point policy can be parametrized by a single factor representing the critical stock level or threshold. With the corresponding hedging point policy, simulation experiments are used to construct input-output data from which an estimation of the incurred cost function is obtained through a regression analysis. The best parameter value of the related hedging point policy is derived from a minimum search of the obtained cost function. The extended hedging point policy is validated and shown to be quite effective. We find that the hedging point policy is also applicable to a wide variety of complex problems (i.e. non-exponential failure and repair times distributions and random demand rates), where analytical solutions may not be easily obtained.