بازرسی بهینه و تعمیر و نگهداری پیشگیرانه در دستگاه هایی با خرابی های آشکار و نهان

The maintenance of a single unit system that alternates operating and idle periods is studied. In the former case the failures are detected as soon as they occur and only by special testing or inspection in the latter. This paper aims at minimizing the cost per unit of time for an infinite time span by selection of a unique interval, for both inspection and maintenance. A special feature of this model is the possibility of a less than perfect testing as the inspections may fail and give a wrong result. It is further assumed that both preventive and corrective maintenance make the unit as good as new with the durations of inspections and maintenances being negligible. The existence of an optimum interval and how it depends on both the cost parameters and the reliability characteristics of the unit is discussed.

It is well known that the effectiveness of a system depends on both the quality of its design as well as the proper maintenance actions to prevent it from failing. In fact, the choice of scheduled maintenance policies which are optimum from an economic point of view constitutes a predominating approach in reliability theory. A wide and recent study of preventive maintenance models can be found in Ref. [9]. When dealing with maintenance models the features of the failures play a primary role: the classical age and block replacement policies [5] are useful for failures that are detected as soon as they occur (revealed failures); in this situation repairs can be immediately initiated. The opposite case corresponds to unrevealed failures, that is, those, which remain undiscovered unless some kind of inspection or testing is carried out. This usually happens in stored equipment, standby units, or devices that operate rarely as security systems. Badı́a et al. [10] analyzed the existence of a cost optimizing policy within the context of an inspection model which involves corrective maintenance whenever a failure is detected, and having no effect in the unit reliability otherwise. In Ref. [11] a preventive maintenance procedure is considered where inspections and maintenance actions take place at different times. Maintenance policies that can be used under unrevealed failures are found in [2], [3], [4], [7] and [8]. Gertsbakh [1] considers an intermediate situation where failures are sometimes revealed and sometimes not as it often happens in computers. The results of computations may seem reasonable although they are wrong due to a hidden defect in the computer, which will be discovered by means of special checking. Gertsbakh [9] (see chapter 2) presents a failure detecting device which may exhibit an imperfect signaling with α being the probability of sending a signal about the failure. At the same time an inspection policy is proposed and the probability of a failure remaining undiscovered, 1−β, is also assumed. In our work there is no failure signaling mechanism but failures manifest themselves when the unit is operating or are detected by special tests in case the unit is in the standby mode. The parameters denoted in the former model by α and β play now the role of 1−p and 1−β. We introduce the possibility of false alarms during inspections, not considered previously, and deal with a cost function instead of the unit availability. This paper develops an inspection policy along with a maintenance procedure for a single unit system whose failures are revealed or not in a random way. In fact we consider that they are unrevealed with probability p or revealed otherwise. This model turns out to be a mixture of the age-replacement policy and a maintenance procedure for unrevealed failures. The basic assumptions are 1. Unrevealed failures are only detected by inspection or testing. 2. Inspections may not be perfect, that is, they may fail giving an erroneous result: after inspection it can be wrongly concluded that a failure has occurred or, on the contrary, a failure may remain undiscovered. Both types of inspection errors correspond, respectively, to type I and type II statistical errors. Mistaken checks occur, for example, when carrying out tests to detect breast cancer or in assessing the effect that fatigue causes on mechanisms fracture. In general, wrong inspections may happen whenever a system is examined due to testing device failure. 3. Tests have no effect on the unit reliability. Depending on the test result, a preventive or corrective maintenance is carried out. Both types of maintenance restore the unit to an ‘as good as new’ condition. 4. Times of test and maintenance are considered negligible.