## 1 Introduction  
A critical component of an equipment unit under preventive maintenance (PM) is periodically replaced or repaired, either alone or with other critical components to take advantage of equipment stoppage for that purpose. This PM policy has been replaced over the past few years by a predictive (condition-based) maintenance (PdM) policy, which has proven to be more cost-effective. In the processing industry, PdM is much preferred due to the severe consequences of shutdowns [1; 2; 3]. PdM can be performed on-line and off-line, the latter consisting mainly of periodic inspections and deciding whether to stop or proceed until the next inspection based on the results. This conclusion is often doubtful as a false negative may result, depending on the accuracy of the test and the inspector's confidence in it [4; 5]. In many cases the onset of a failure is not immediately noticed. Instead, the inspection reveals some signal that a failure is about to occur (potential failure). If nothing is done, it will evolve and give rise to a functional failure after some time. This issue is often addressed as the P-F time interval. The more accurate the measuring method, the longer the P-F time interval might be. On the other hand, inspections must be carried out at times when a minimum reliability threshold is observed between successive inspections. This gives rise to decreasing time intervals when a degradation failure mode is addressed to prevent a failure in progress from going unnoticed. If these two concepts (P-F period and decreasing time intervals) are merged, a series of safe and unsafe time windows is obtained. Inspections might represent a high cost, particularly when production must be interrupted, but the voluntary shutdown of an equipment unit for preventive replacement of a critical component might also incur a high cost, which leads to the event's being postponement as much as possible. If this is the case, the likelihood of a failure increases progressively as does the degraded production cost. This suggests that all these costs must be properly equated and balanced in accordance with all safe and unsafe time windows. A particular reliability threshold might exist such that a global minimum cost might be achieved [6; 7]. In this paper, a numerical method to determine an optimum set of dates (\"calendar\") for inspections is demonstrated. The method assumes that the failure mode behavior under consideration is described by a Weibull probability function. The method also takes into consideration the loss of monetary value over time. The method is suitable for a first phase where a preliminary calendar is based on prior probabilities of failure and the cost is evaluated for budgetary or bidding purposes. A second phase will take place if the result of an inspection is negative at which time the calendar will be reformulated in view of the accuracy of the test and the inspector's confidence in the prevailing test conditions. In other words, the calendar must be adjusted to consider the subsequent probabilities of failure, given the results of the test observations. The recalculation of the calendar after each inspection is definitively a dynamic attribute of the proposed method. In the literature, several researchers have addressed this issue. Cost optimization is often the main approach for determining time inspection intervals. [PERSON] [8] developed an optimization model for a process with two types of inspections and repairs to minimize the expected cost from a time delay. [PERSON] and [PERSON] (2009) [9] aimed at optimizing a non-periodic inspection policy by evaluating the expected lifetime costs with the use of a multivariate stochastic process. [PERSON] and [PERSON] [10] proposed a model to estimate the optimum policy for minimizing the average long-run maintenance cost rate for systems with multiple competing processes.