Failed Item Research Articles

Preventive maintenance for the constrained multi-attempt minimal repair

In practice, at some instances, the repair of a failed item can be unsuccessful and should be repeated due to various reasons. This can happen in practice with a minimal repair when a failed part of a system is replaced, e.g., by the faulty spare. The corresponding stochastic model that takes into account this possibility can be described probabilistically in terms of the Polya-Aeppli process, which is a generalization of the Poisson process to the case of multiple occurrences of events. Some useful properties for considering optimal preventive maintenance problems are derived. The optimal replacement policy for a system with the multi-attempt minimal repairs is defined and analysed. The characteristic feature of this policy is that the system is replaced not only on reaching the predetermined age but also after a fixed number of unsuccessful minimal repairs. The detailed numerical examples illustrate our findings.

On a problem of calculating a set of spare parts that have two types of failures

Aim. The paper, that continues [24], aims to develop an algorithm that would allow finding the required number of spare items (SPTA) for a complex system, whose elements may or may not be maintainable. Unlike in [24], as a generalisation, the paper introduces additional inoperable states. Those states are characterised by system downtime associated with the replacement of a failed element with an element from the SPTA. If the time of replacement of a failed element is not a negligibly small value as compared to other time indices of the serviced system, it becomes necessary, as suggested, to account for additional inoperable states. Methods. Markov models are used for describing the technical system under consideration. The final probabilities were obtained using a developed system of Kolmogorov equations. A stationary solution was obtained for the system of Kolmogorov equations. Classical methods of the probability theory and mathematical theory of dependability, some special functions were used. Conclusions. The paper formalizes the problem of determining the required number of SPTAs for a system with items that may fail at a random moment in time. The failures may be of two types. The first type of failures leaves an item in an inoperable repairable state. In this case, the item can be repaired in the maintenance unit of the company that operates such item. The second type of failures, a more catastrophic one, leaves the item in an inoperable non-repairable state, and it can be repaired only by the manufacturer or a specialized maintenance company. A Markov graph was built for the respective birth and death process. Equations were formalised for typical states of the Markov graph. A stationary solution was obtained for the system of Kolmogorov equations using induction. The theorem of general solution was proven for all the states of the Markov graph. In case of unlimited repair, the solution is significantly simplified. It was shown that, on an assumption of unlimited repair and momentary replacements, the solution matches the one earlier obtained in a simplified form in [24]. The limit values of the probabilities of inoperable critical and non-critical states were found. They allow concluding that, in case of unlimited repair, the growth of the size of SPTA causes the probability of a critical state of insufficient SPTA to tend to and become zero. Additionally, the probability of an inoperable state associated with the replacement of a failed item with an equivalent from the SPTA that takes a certain time is defined by a stationary unavailability of the alternating repair process. The general solution of the problem allows formalising the SPTA sufficiency coefficient. The required number of SPTAs is identified by progressively increasing the number of SPTAs until the probability of inoperable critical states is below the defined probability of SPTA shortage. An example of finding the required number of SPTAs is given

The CCAS-scale in hereditary ataxias: helpful on the group level, particularly in SCA3, but limited in individual patients

BackgroundA brief bedside test has recently been introduced by Hoche et al. (Brain, 2018) to screen for the Cerebellar Cognitive Affective Syndrome (CCAS) in patients with cerebellar disease.ObjectiveThis multicenter study tested the ability of the CCAS-Scale to diagnose CCAS in individual patients with common forms of hereditary ataxia.MethodsA German version of the CCAS-Scale was applied in 30 SCA3, 14 SCA6 and 20 FRDA patients, and 64 healthy participants matched for age, sex, and level of education. Based on original cut-off values, the number of failed test items was assessed, and CCAS was considered possible (one failed item), probable (two failed items) or definite (three failed items). In addition a total sum raw score was calculated.ResultsOn a group level, failed items were significantly higher and total sum scores were significantly lower in SCA3 patients compared to matched controls. SCA6 and FRDA patients performed numerically below controls, but respective group differences failed to reach significance. The ability of the CCAS-Scale to diagnose CCAS in individual patients was limited to severe cases failing three or more items. Milder cases failing one or two items showed a great overlap with the performance of controls exhibiting a substantial number of false-positive test results. The word fluency test items differentiated best between patients and controls.ConclusionsAs a group, SCA3 patients performed below the level of SCA6 and FRDA patients, possibly reflecting additional cerebral involvement. Moreover, the application of the CCAS-Scale in its present form results in a high number of false-positive test results, that is identifying controls as patients, reducing its usefulness as a screening tool for CCAS in individual patients.

Optimizing the timeframe of scheduled repairs using valuation techniques

Aim. The paper examines technical systems (machinery and equipment), whose condition deteriorates in the course of operation, yet can be improved through repairs (overhaul). The items are subject to random failures. After another failure, an item can be repaired or disposed of. A new or repaired item is to be assigned the date of the next scheduled repairs. Regarding a failed item, the decision is to be taken as to unscheduled repairs or disposal. We are solving the problem of optimization of such repair policy. At the same time, it proves to be important to take into consideration the effect of repairs, first, on the choice of appropriate indicators of item condition that define its primary operational characteristics, and second, on a sufficiently adequate description of the dynamics of items’ performance indicators. Methods. Assigning the timeframe of scheduled repairs normally involves the construction of economic and mathematical optimization models that are the subject matter of a vast number of publications. They use various optimality criteria, i.e., probability of no failure over a given period of time, average repair costs per service life or per unit of time, etc. However, criteria of this kind do not take into account the performance dynamics of degrading items and do not fully meet the business interests of the item owners. The criterion of maximum expected total discounted benefits is more adequate in such cases. It is adopted in the theory of investment projects efficiency estimation and the cost estimation theory and is, ultimately, focused on maximizing a company’s value. The model’s formulas associate the item’s benefit stream with its primary characteristics (hazard of failure, operating costs, performance), which, in turn, depend on the item’s condition. The condition of non-repairable items is usually characterized by their age (operating time). Yet the characteristics of repairable items change significantly after repairs, and, in recent years, their dynamics have been described by various models using Kijima’s virtual age indicator (a similar indicator of effective age has long been used in the valuation of buildings, machinery and equipment). That allows associating the characteristics of items in the first and subsequent inter-repair cycles. However, analysis shows that this indicator does not allow taking into consideration the incurable physical deterioration of repaired items. The paper suggests a different approach to describing the condition of such objects that does not have the above shortcoming. Conclusions. The author constructed and analysed an economic and mathematical model for repair policy optimisation that is focused on maximizing the market value of the company that owns the item. It is suggested describing the condition of an item with two indicators, i.e., the age at the beginning of the current inter-repair cycle and time of operation within the current cycle. It proves to be possible to simplify the dependence of an item’s characteristics on its condition by using the general idea of Kijima models, but more adequately taking into consideration the incurable physical deterioration of such item. The author conducted experimental calculations that show a reduction of the duration of planned repairs as machinery ages at the beginning of an inter-repair cycle. Some well-known repair policies were critically evaluated.

An inventory system with replacement and refurbishment of failed items

We consider a continuous review inventory system with two types of inventory, namely type-I and type-II. Type-I and type-II inventory, respectively, contain fresh and refurbished items. Two streams of customers, called type-A and type-B customers arrive to the system in which type-A customer demands for an item either from type-I or type-II inventory according to a Bernoulli trial and type-B customer occurs to replace the failed item with new one from type-I inventory. The arrival time points of type-A and type-B customers follow independent Poisson Processes. Failed items are stored in a place, called pool, of infinite size for refurbishment. After refurbishment, these items are kept in type-II inventory. The refurbishment of pooled item is stopped once type-II inventory reaches its maximum level S 2 and is again commenced only when type-II inventory level falls to s 2. The refurbishment time follows exponential distribution. Type-I inventory is replenished according to a (s, S) policy with exponential lead time. The joint pdf of number of items in the pool, type-II inventory level, status of refurbishment and type-I inventory level is obtained in the steady state. Various system performance measures are derived and total expected cost rate is calculated. Results are illustrated numerically.

Determination of Optimal Warranty Period with Preventive Maintenance Actions for Items from Heterogeneous Populations

In this study, we develop an optimal maintenance policy with replacement service and minimal repair service for items from heterogeneous populations and determine the optimal warranty length and repair time threshold. We consider the information-based repair-replacement policy model and develop the formula to evaluate the expected cost rate during the product life cycle. A general formulation is derived for the expected cost rate under a warranty policy for items of heterogeneous populations. When a replacement service and minimal repair service are provided for a failed item, then an item from a weak population has the property of an item from a weak population after service. Similarly, an item from a strong population has the property of an item from a strong population after service. We define the optimal maintenance strategies to minimize the expected cost rate with failure time and repair time for items with heterogeneous reliability characteristics. The effects of parameters of the intensity function for the failure times on the optimal length of the warranty period are studied numerically. Assuming that the product deteriorates, we illustrate the proposed approach using numerical applications and observe the impacts of relevant parameters on the optimal length of the warranty period.

New failure and minimal repair processes for repairable systems in a random environment

AbstractMost often, minimal repair is defined as a replacement of a failed item by an operable item that has the same distribution of the remaining lifetime as the failed one just prior a failure. This is the so‐called statistical minimal repair extensively explored in the literature. Another well‐known type of minimal repair takes into account the state of a system prior to a failure (the information‐based minimal repair). In this paper, we suggest the new type of minimal repair to be called conditional statistical minimal repair. Our approach goes further and deals with the corresponding minimal repair processes for systems operating in a random environment. Moreover, we also consider heterogeneous populations of items, which makes the model more realistic. Both of these aspects that affect the failure mechanism of items are studied. Environment is modeled by the nonhomogeneous Poisson shock process. Two models for the failure mechanism defined by the extreme shock model and the cumulative shock model, respectively, are considered. Some examples illustrating our findings are presented.

Modelling upgrading maintenance policy in the one-dimensional renewing warranty period

In the one-dimensional renewing warranty period, the quality of the spares for product is likely to be improved during the warranty period. Therefore, upgrading maintenance becomes more and more common. Then the manufacturers (customers) may have to decide whether or not to provide (buy) the warranty considering upgrading maintenance. This paper presents a mathematical model considering upgrading maintenance for products with multiple failure modes. Upgrading maintenance is taken into account with the assumption that the warranted item is upgraded one time during the warranty cycle. The upgrading maintenance is carried out, when the corrective maintenance is taken place. After upgrading maintenance, the high-quality spares are used to replace the failed item. In the numerical example, the results of the models are calculated. Monte Carlo simulation results are compared with the analytical results to demonstrate the correctness and efficiency of the proposed models considering upgrading maintenance.

Defining line replaceable units

Defective capital assets may be quickly restored to their operational condition by replacing the item that has failed. The item that is replaced is called the Line Replaceable Unit (LRU), and the so-called LRU definition problem is the problem of deciding on which item to replace upon each type of failure: when a replacement action is required in the field, service engineers can either replace the failed item itself or replace a parent assembly that holds the failed item. One option may be fast but expensive, while the other may take longer but against lower cost. We consider a maintenance organization that services a fleet of assets, so that unavailability due to maintenance downtime may be compensated by acquiring additional standby assets. The objective of the LRU-definition problem is to minimize the total cost of item replacement and the investment in additional assets, given a constraint on the availability of the fleet of assets. We link this problem to the literature. We also present two cases to show how the problem is treated in practice. We next model the problem as a mixed integer linear programming formulation, and we use a numerical experiment to illustrate the model, and the potential cost reductions that using such a model may lead to.

Repair systems with exchangeable items and the longest queue mechanism

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: At the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions.

WARRANTY SERVICING WITH A BROWN–PROSCHAN REPAIR OPTION

Reducing warranty servicing costs are of great interest to product manufacturers or sellers who are contractually bound to provide post-sales support, up to a specified warranty period, usually in the form of some remedial action that restores a failed item to a functioning condition. Here, in the spirit of Jack et al. (2009) strategy based on partitioning the effective warranty period into three intervals, we consider and analyze the cost of a new two-dimensional warranty servicing strategy, that probabilistically exercises a choice between a replacement and a minimal repair to rectify the first failure if any, in the middle interval. The behavior of the expected cost is numerical illustration with Weibull failure model.

On optimal replacement-repair policy for multi-state deteriorating products under renewing free replacement warranty

In this paper a replacement-repair model is developed to study a renewing free replacement warranty (RFRW) for a class of multi-state deteriorating repairable products. After a replacement, the product warranty is renewed. Two parameters affect the manufacturer’s decision to minimally repair or replace a failed item: the product deterioration level at the time of failure and the remaining warranty time. We derive an optimal replacement-repair policy to minimise the expected warranty servicing cost per item sold. In the case of a product with two different working states, we are able to explicitly find the optimal values of the replacement-repair parameters using the Adomian decomposition method. In general, for N > 2 , it is impossible to find the optimal parameter values analytically. Hence, a computational procedure for finding these optimal values is proposed. For more clarification, numerical examples are also presented.

Dynamic pricing and warranty policies for products with fixed lifetime

Abstract We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.

Warranty servicing with imperfect repair

A manufacturer of a product sold with warranty incurs additional costs from the servicing of warranty claims made by customers. These costs depend on several factors such as the reliability of the product, the warranty terms, the maintenance actions of the customers, and the servicing strategy used by the manufacturer. Through effective warranty servicing strategies the manufacturer can reduce the warranty costs. In the case of repairable items, several different warranty servicing strategies involving minimal repair and replace by new have been studied. For expensive products, servicing strategies involving minimal and imperfect repairs should result in lower warranty costs than strategies studied in the past. Imperfect repair results in the reliability of a repaired item being better than it was just before failure but less than that of a new item and it is much cheaper than the cost of a new item. In this paper, we look at two new warranty servicing strategies (strategies 1 and 2) involving minimal and imperfect repairs. In both strategies, a failed item is subjected to at most one imperfect repair over the warranty period. In Strategy 1, the level of improvement in reliability under imperfect repair depends on the age of the item at which imperfect repair is carried out whereas, in Strategy 2, the level of improvement does not depend on the age. As a result, Strategy 1 involves a functional optimisation to determine the optimal improvement in reliability when an imperfect repair is carried out. In contrast, Strategy 2 involves only a parameter optimisation to determine the optimal reliability improvement. In a numerical example, we compare the two new servicing strategies with two other strategies reported in the literature.

A new repair–replace strategy for items sold with a two-dimensional warranty

For repairable items, the manufacturer has the option to either repair or replace a failed item that is returned under warranty. In this paper, we look at a new warranty servicing strategy for items sold with two-dimensional warranty where the failed item is replaced by a new one when it fails for the first time in a specified region of the warranty and all other failures are repaired minimally. The region is characterised by two parameters and we derive the optimal values for these to minimise the total expected warranty servicing cost. We compare the results with other repair–replace strategies reported in the literature.

Replacement–repair policy for multi-state deteriorating products under warranty

In this paper we study a warranty servicing policy for a class of multi-state deteriorating and repairable products. The manufacturer's decision to repair or replace a failed item depends on two parameters, the deterioration degree of the item and the length of the residual warranty period. We examine the optimal value of these two parameters to minimize the manufacturer's expected warranty servicing cost per item sold.

The marginal cost analysis and its application to repair and replacement policies

The concern of this paper is twofold: (i) elaboration on the role of the marginal cost analysis (MCA) method in the study and optimization of maintenance policies; (ii) the study of a repair and replacement policy where the decision whether to repair a failed item or replace it is based on the repair costs: those encountered now and those anticipated in the future (the policy is an extension of another one which bases this decision solely on the present repair costs). The situation of incomplete information on the underlying life distribution is also considered in which case a Bayesian inference procedure is associated to the failure process and its results incorporated into the repair or replace decision process at failures. These two goals are interlinked in that on one hand the repair and replacement policy is analyzed and optimized by using the MCA, and on the other hand this provides yet another illustration for the application of the MCA and its adaptability to model and policy generalizations.

Customer Delay in M/G/∞ Repair Systems with Spares

The exchangeable-item repair systems considered here are characterized by customers who bring failed items to the system, and are prepared to take in return any serviceable item of the same kind. This exchangeability feature enables the system to keep spare items, either those repaired by the facilities the system operates or newly acquired ones. Rather than only considering the common number of backorders as a measure, the focus of this research is on the delay experienced by customers in an “ample-service” repair system, where repair of a failed item commences upon arrival at the system. The stationary and the nonstationary distributions of this delay are obtained in an analytic closed form in terms of the basic model parameters—the (Poisson) arrival rate, the (arbitrary) repair distribution of an item, and the initial number of spares in the system. The results are applicable to a variety of models that incorporate factors such as item scrapping, replenishment of new items, different modes of failure, and customers bringing several failed items. Successive use of the formulas can extend the spectrum of potential applications to multiechelon systems.

Exchangeable Items in Repair Systems: Delay Times

We compute the delay time distribution for a customer who delivers a failed item to a repair system, when the items are exchangeable and the customer accepts any repaired item that is offered when he is at the head of the customer queue.

Optimal replace-repair strategy for servicing products sold with warranty

For repairable products sold with warranty, the manufacturer has the option of either repairing a failed item or replacing it by a new one should the failure occur during the warranty period. This paper formulates a model to make optimal decisions regarding replace-repair strategies for a fairly general warranty policy.