An optimal inspection and diagnosis policy for a multi-mode system

This paper considers a multi-mode system that is inspected periodically, and the period of inspection is a random variable. The system has three modes: normal (N), abnormal (A) and failure (F), where F is a self-announcing mode whereas, N and A are non-self-announcing and operating modes. When the system is operating, it is inspected once every random time T to make sure whether it is in N or A until it attains F, or until it is detected to be in A. Each inspection consists in measuring a value taken by a diagnostic parameter. The diagnostic parameter, which is a random variable, has a close relation with the operating modes. If it is found to have exceeded a certain critical value, a preventive maintenance (or repair) is performed. By using the supplementary variable technique, the reliability indices and an optimal inspection and diagnosis policy for the system are obtained.     

An evaluation of costs and benefits of a vehicle periodic inspection scheme with six-monthly inspections compared to annual inspections

Although previous research suggests that safety benefits accrue from periodic vehicle inspection programmes, little consideration has been given to whether the benefits are sufficient to justify the often considerable costs of such schemes. Methodological barriers impede many attempts to evaluate the overall safety benefits of periodic vehicle inspection schemes, including this study, which did not attempt to evaluate the New Zealand warrant of fitness scheme as a whole. Instead, this study evaluated one aspect of the scheme: the effects of doubling the inspection frequency, from annual to biannual, when the vehicle reaches six years of age. In particular, reductions in safety-related vehicle faults were estimated together with the value of the safety benefits compared to the costs. When merged crash data, licensing data and roadworthiness inspection data were analysed, there were estimated to be improvements in injury crash involvement rates and prevalence of safety-related faults of respectively 8% (95% CI 0.4–15%) and 13.5% (95% CI 12.8–14.2%) associated with the increase from annual to 6-monthly inspections. The wide confidence interval for the drop in crash rate shows considerably statistical uncertainty about the precise size of the drop. Even assuming that this proportion of vehicle faults prevented by doubling the inspection frequency could be maintained over the vehicle age range 7–20 years, the safety benefits are very unlikely to exceed the additional costs of the 6-monthly inspections to the motorists, valued at $NZ 500 million annually excluding the overall costs of administering the scheme. The New Zealand warrant of fitness scheme as a whole cannot be robustly evaluated using the analysis approach used here, but the safety benefits would need to be substantial – yielding an unlikely 12% reduction in injury crashes – for benefits to equal costs.     

An optimal inspection strategy for randomly failing equipment

This paper addresses the problem of generating optimal inspection strategies for randomly failing equipment where imminent failure is not obvious and can only be detected through inspection. Inspections are carried out following a condition-based procedure. The equipment is replaced if it has failed or if it shows imminent signs of failure. The latter state is indicated by measuring certain predetermined control parameters during inspection. Costs are associated with inspection, idle time and preventive or corrective actions. An optimal inspection strategy is defined as the inspection sequence minimizing the expected total cost per time unit over an infinite span. A mathematical model and a numerical algorithm are developed to generate an optimal inspection sequence. As a practical example, the model is applied to provide a machine tool operator with a time sequence for inspecting the cutting tool. The tool life time distribution and the trend of one control parameter defining its actual condition are supposed to be known.     

A study of a two-phase inspection policy for a preparedness system with a defective state and heterogeneous lifetime

This paper considers an inspection policy for a single component protection or preparedness system, in which the component arises from a heterogeneous population. At any point in time, the system may be in one of three states, good, defective or failed. The system is only required in an emergency, and in order to ensure high availability of the system on-demand, the system undergoes a sequence of inspections. Inspection determines the system state, so that if a transition from the good state occurs between inspections it is not revealed until subsequent inspection. When a defect or failure is revealed, the component is replaced. At the final inspection the component is replaced. We suppose that a component may be either weak or strong, so that the time in the good state has a distribution that is a mixture. In these circumstances, the efficacy of a two-phase inspection policy, with an anticipated high inspection frequency in early life and low inspection frequency in later life, is considered using availability and cost criteria. The policy is investigated in the context of a valve in a natural gas supply network. If the lifetime distributions in the mixture are quite distinct, then cost savings of the order of 5% can be achieved by using the two-phase policy in place of the simpler single phase policy. Furthermore, only if the mean time in the defective state is small or the required availability is very high does the two-phase policy tend to mimic a burn-in policy.     

A nonlinear mixed-effects model for degradation data obtained from in-service inspections

Monitoring of degradation and predicting its progression using periodic inspection data are important to ensure safety and reliability of engineering systems. Traditional regression models are inadequate in modeling the periodic inspection data, as it ignores units specific random effects and potential correlation among repeated measurements. This paper presents an advanced nonlinear mixed-effects (NLME) model, generally adopted in bio-statistical literature, for modeling and predicting degradation in nuclear piping system. The proposed model offers considerable improvement by reducing the variance associated with degradation of a specific unit, which leads to more realistic estimates of risk.     

A process targeting model for a product with two dependent quality characteristics using 100% inspection

The purpose of this paper is to develop a process targeting model for a product with two quality characteristics produced by two processes in series. The first quality characteristic is determined by the setting of the first process, whereas the second quality characteristic depends on the setting of the two processes. The quality of the product is controlled by a 100% inspection plan, and inspection is assumed to be error free. The objective of the model is to determine the optimal target for both processes that maximizes the profit. A realistic case study has been used to demonstrate the utility of the model. The results have shown that the model results improve the profit per lot and aid the factory in conducting cost/benefit analysis for reducing the variances of the two processes. In addition, sensitivity analysis has been performed to study the effect of different parameters on the expected profit and optimal processes means. It has been shown that the results of the model are sensitive to the variances of the two processes, selling prices, and rework costs.     

An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not ‘as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

On the inspection policy of a two-component parallel system with failure interaction

In this paper we study a two-component standby system which can successfully operate upon a demand if at least one component is not failed. We assume that failures can be detected only by periodic inspections. We consider that the failure of one component can modify the (conditional) failure probability of the component still alive with probability p and do not interact with probability 1−p. For that failure interaction scheme we obtain the system reliability function for the case of staggered inspections. We compare staggered and non-staggered inspections through numerical examples considering constant hazard rates.     

An inspection model for a multi‐component system subject to 2 types of failures

Group maintenance is common and of significant importance for complex systems in industrial applications. This paper proposes a novel inspection and replacement model for a multi‐component system whose components are all subject to 2 typical failure modes, ie, catastrophic failure and minor failure. A catastrophic failure stops the system immediately, whereas a minor failure is not fatal and could only be identified by periodic inspection. At either a catastrophic or a minor failure, replacement is immediate. The maintenance cost model could be constructed through calculating the distribution of the “forward time”, which denotes the time elapse to a catastrophic failure since the previous inspection. The objective of this paper is to minimize the expected cost per unit time of the system via the optimization of the inspection interval. A case study on offshore wind turbine blades is presented to illustrate the maintenance model.     

A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis

In periodic monitoring, the main problem is determining the inspection interval of condition monitoring. For this problem, the decision variable is represented by the time of next inspection of condition monitoring. There are several studies that deal with prescribing inspection intervals. But only a few of these allow the decision maker to observe simultaneously more than one aspect. This does not accord with the natural tendency of the decision maker who desires to see the decision problem from a broader perspective, by having different viewpoints or dimensions of choices. Therefore, the main objective of this paper is to propose a decision model, which can simultaneously determine inspection intervals for condition monitoring regarding the failure behavior of equipment to be inspected, features of maintainability and decision maker preferences about cost and downtime.     

On a dynamic preventive maintenance policy for a system under inspection

The purpose of this article is to propose both state and time-dependent preventive maintenance policy for a multi-state deteriorating system, which is equipped with inspection equipment(s) connected to a computer center. After the system being identified as state x at nd through computation by the computer center after inspection (or measurement) via equipment(s), one maintenance action with the minimum expected total cost since nd till Nd (where N=n+K for a fixed integer 0<K<∞) will be chosen from the set A_x of alternatives also with the help of the computer center. In real case, the expected total costs since nd till Nd will be time-dependent and so is the maintenance action chosen at nd. A numerical example is given to illustrate such a maintenance policy for a Markovian deteriorating system to describe its state dependent aspect only for simplicity reason. Due to the fact that both equipment measurement and computer computation take time, the preventive maintenance policy for a sufficiently small d may be used in fact as the one under continuous inspection.     

Impact of inspection errors on the performance measures of a general repeat inspection plan

Multi-characteristic critical components exist in many systems. Such components may be a part of an aircraft, space shuttle or a gas ignition system. An inspection plan for such components has been proposed in quality control that deals with several types of classification errors made by the inspector. In this paper, performance measures for this plan are defined and the statistical and economic impact of the several types of inspection errors on these measures is investigated. The impact of the errors is studied by conducting sensitivity analysis on the errors utilizing computer software which implements an algorithm that determines the optimal parameters of the model of the plan. The behaviour of the performance measures upon variation in the levels of errors is investigated. The results indicate that these errors have a considerable effect on the performance measures of the inspection plan.     

A delay-time model with safety constraint

We consider the basic delay-time model in which a system has three states, the perfect functioning state, a defective state and the failure state. The system is deteriorating and to reduce the number of failures, preventive replacements are carried out when the system is in the defective state. The time in the defective state is referred to as the delay time. Inspections are required to check whether the system is in the defective state. System failures are safety critical and to control the risk, management considers two types of safety constraints: (i) the probability of at least one failure in the interval [0,A] should not exceed a fixed probability ω₁ and (ii) the fraction of time the system is in the defective state should not exceed a fixed limit ω₂. The problem is to determine optimal inspection intervals T, minimizing the expected discounted costs under the safety constraints. Conditions are established for when the safety constraints affect the optimal inspection time and causes increased costs.     

Optimal inspection policies with predictive and preventive maintenance

A model is proposed to study the inspection and maintenance policy of systems whose failures can be detected only by periodic tests or inspections. Using predictive techniques, the time of the system failure can be predicted for some failure modes. If the system is found failed in an inspection, a corrective maintenance action is carried out. If the system is in a good condition but the predictive test diagnoses a failure in the period until the next inspection, then the system is replaced. The cost rate function is obtained for general distribution function of the signal time of a future failure and for one specific distribution function recently proposed. An algorithm is presented to find the optimal time between inspections and predictive tests and the optimal system replacement times for an age replacement policy. Numerical experiments illustrate the model.     

Economic design of offline inspections for a batch production process

We consider a batch production process that can be either stable or unstable, in which inspection is performed offline after production of the batch is completed. The quality of a batch can be estimated with a desired level of certainty by inspecting only a sample of its units. In order to minimise the expected total cost per batch, which includes the costs of inspection, of false acceptance and of false rejection, we propose an economic inspection plan in which only a fraction of the batches, rather than each batch, is inspected. We prove that the expected total cost is a strictly quasiconvex function of the inspection interval. We establish necessary and sufficient conditions for the optimal inspection interval to be finite and propose an efficient algorithm to obtain its value. We demonstrate for the case of a single-sampling plan where the proposed economic approach outperforms the common procedure of inspecting every batch, and the proposed algorithm is very efficient.     

An integrated production-inventory model with reprocessing and inspection

Competitive pressures continually force management to examine cost and quality levels of production systems. In this paper these issues are addressed via a model that synthesizes several potential features of production systems: production processes, quality control procedures, in-process inventory and reprocessing. For any specified inspection configuration the model can be used, for serial production systems, to obtain closed-form expressions for two important decision variables: optimal lot size and reprocessing batch size, which minimize the total system costs. A numerical example highlights the interdependencies and the role of various system features in determining the values of the decision variables and hence in reducing the total costs. The paper also discusses the managerial implications of the model.     

Integrated approach to part scheduling and inspection policies for a job shop manufacturing system

The quality of a product greatly depends on the quality of its components. This requires that manufacturing specifications have to be met in the manufacturing environment and as a consequence inspection stations are present in many manufacturing systems and inspection policies must be adopted. One problem, which has been widely investigated, concerns the detection of the inspection points in the hypothesis that the action to be taken is known when a defective part is detected. If different jobs are to be produced, then operation scheduling becomes yet another complex problem needing to be solved. And while the problem of scheduling has received a great amount of attention from researchers, to our knowledge the interaction between the two problems has not been treated in job-shop environment. In the present paper three different control policies are preliminarily examined: they differ both in terms of the number of operations that are inspected, and with regard to the type of intervention carried out on detection of a defect. Each control policy affects the optimal inspection locations, which, in their turn, influence operation scheduling. As will be shown in the present paper, a sequential decision process based on separate optimization steps can lead to very poor final results. For this reason, an integrated approach is proposed, in an attempt to identify an optimal solution using a genetic algorithm.     

A joint spare part and maintenance inspection optimisation model using the Delay-Time concept

Spare parts and maintenance are closely related logistics activities where maintenance generates the need for spare parts. When preventive maintenance is present, it may need more spare parts at one time because of the planned preventive maintenance activities. This paper considers the joint optimisation of three decision variables, e.g., the ordering quantity, ordering interval and inspection interval. The model is constructed using the well-known Delay-Time concept where the failure process is divided into a two-stage process. The objective function is the long run expected cost per unit time in terms of the three decision variables to be optimised. Here we use a block-based inspection policy where all components are inspected at the same time regardless of the ages of the components. This creates a situation that the time to failure since the immediate previous inspection is random and has to be modelled by a distribution. This time is called the forward time and a limiting but closed form of such distribution is obtained. We develop an algorithm for the optimal solution of the decision process using a combination of analytical and enumeration approaches. The model is demonstrated by a numerical example.     

Estimating manufacturing cycle time and throughput in flow shops with process drift and inspection

Process drift is a common occurrence in many manufacturing processes where machines become dirty (leading to more contamination) or processing parameters degrade, negatively affecting system performance. Statistical process control tracks process quality to determine when the process has gone out of control (has drifted beyond its specifications). This paper considers the case where parts examined at a downstream inspection station are used to determine when the upstream process is out of control. The manufacturing cycle time from the out of control process to the downstream inspection process influences the detection time that elapses until the out of control process is noticed and repaired. Because an out of control process produces more bad parts, the detection time affects the number of good parts produced and the throughput of the manufacturing system. This situation is common in many industries but no models of the phenomena exist. This paper presents a novel manufacturing system model based on queueing network approximations for estimating the manufacturing cycle time and throughput of such systems. These are important performance measures since they influence economic measures such as inventory costs and revenue. The model can be used for a variety of system design and analysis tasks. In particular, the model can be used to evaluate the placement of inspection stations in a process flow.