Determining the best maintenance policy in systems exposed to self announcing and non-self announcing failures

In order to maintain the proper functioning of the systems, it is important to check the functionality of the systems in certain periods. When the costs incurred during the control and the costs incurred in system failures are taken into consideration, the determination of the control period is widely available in the literature. Too frequent control periods lead to unnecessary constant control costs, while less frequent control periods result in the cost of undetectable errors other than inspection. For example, in expensive and complex medical devices such as Magnetic Resonance (MR), negative situations that may affect human life as a result of faulty imaging; or simple structured devices such as fire alarm which cannot be detected any failure in normal time. It can be only noticed when it is needed. During the fire, the fire alarm, whose functionality is not checked periodically and which is actually faulty, can cause a huge loss of life and property. In this study, two error types with different probability density distributions are discussed. One of these errors is called "self-announcing failures" or "revealed failures" stops the operation of the system and causes the system to be renewed at that time; The other type of error, which is called "non-self announcing failure"or defined as "hidden failures" or "unrevealed failure" causing the system to malfunction and can only be noticed during the controls. Since this type of error can only be detected during the control, the system runs improperly from fault to control. This defective operating cost, which is called "down-time cost" in the literature, will be one of the important parameters in the mathematical model we will develop. The main purpose of this study is to determine the control period (τ). In addition, after the system has been running without error for a certain period of time, as the probability of error is gradually increasing, the decision maker may want to renew the system instead of performing an inspection and renew the system to avoid possible malfunctions and costs. The determination of the period (n) of preventive system replacement before any error occurs, is another fundamental parameter discussed in this study. In this problem, which can be called as parameter optimization, besides the effect of the change of probability density function parameters on control period which is frequently found in literature; effects of changing inspection and system renewal costs on control period and effects of loosening reliability level constraint on control periods and expected avarage cost per unit time are also focused.