Analyzing the Effect of Inspection Intervals on Availability Scheduled inspections can be an important part of a maintenance program because they provide a way to discover dormant failures and/or degradation that is likely to result in the imminent failure of the component. As with other maintenance activities, it is important to determine the appropriate inspection schedule to meet the performance expectations for the system with the lowest possible cost (in terms of personnel, spare parts, downtime, etc.). This article presents an example designed to study the effects of various possible inspection intervals on the availability of a component. Such analyses can contribute to an organization's decisions regarding optimal inspection intervals for components. Please note that this example is fictional and intended for demonstration purposes only. Description of the
Problem
The life vests are stored until they are required for use. Therefore, failures remain dormant until the vests are needed or until they are discovered during scheduled inspections. During each scheduled inspection, all of the vests on the aircraft are tested for failure. Failed vests are discarded and replaced with new vests (with no accumulated age). Non-failed vests are left on the aircraft in their current conditions (with a specific accumulated age equal to the amount of time that the vest has been on the plane). This results in a mix of vests of different accumulated ages aboard an aircraft at any given time. Odyssey Air has collected data on the life vest failures discovered during past inspections. Using ReliaSoft's Weibull++ software for life data analysis, the airline's reliability engineers determined a dormant failure distribution for the vests. The observed failures follow a Weibull distribution with Beta = 2.55 and Eta = 7.89 years. With this information and ReliaSoft's BlockSim 6 software, the analysts can go on to study the effects of the proposed one, two and three-year inspection intervals on the availability of the vests. This analysis, using BlockSim's simulation utility for maintainability and availability analysis, is described next. Preparing the Analysis
in BlockSim As described above, Odyssey Air's maintenance procedures for life vests consist of two types of actions: inspections and corrective maintenance. Specifically, the maintenance crew inspects the vests on a scheduled basis in order to discover any vests that may have failed (inspection) and they replace any failed units with new vests (corrective maintenance). Preventive maintenance (i.e. repairing or replacing vests before they fail) is not part of Odyssey Air's maintenance plan for this component. Figure 1 shows the corrective maintenance characteristics for the life vest, as defined in BlockSim. Because the time required to perform the inspection and replace the failed vests (if necessary) is not of interest in this analysis, we can assume instantaneous replacement of failed vests (i.e. fixed duration for corrective maintenance = 0). The Restoration Factor is set to 1 because failed units are replaced with new ones, thus restoring the accumulated age to zero. Finally, the corrective maintenance policy is set to initiate the maintenance upon inspection. In other words, each life vest will not be replaced unless/until it is found to be failed as the result of an inspection.
Figure 1: Corrective maintenance properties for life vest Figure 2 shows the inspection characteristics for the annual (one year) inspection interval, as defined in BlockSim. The inspection duration is set to zero because it is not of interest for the analysis and the restoration factor is zero because the inspection does not affect the accumulated age of the vests. The inspections are scheduled to be performed upon a fixed time interval - every one year, in this case. The analysis will be repeated with the inspection interval set to two years and three years in order to compare the results. This can be accomplished by creating three different RBDs with a different inspection policy assigned to each analysis.
Figure 2: Inspection properties for life vest When the RBD has been fully defined, BlockSim's simulation utility can be used to obtain maintainability and availability results. For this example, use 15 years as the end time, a fixed number of simulations (10,000), a seed of 1 for the random number generator and compute the point availability in increments of 999.9.
Estimating the
Instantaneous or Point Availability Specifically, the instantaneous (or point) availability is defined as the probability that a system (or component) will be operational (up and running) at any random time, t. At any given time, t, the system will be operational if either of the following conditions are met:
Where m(u) is the renewal density function of the system. Therefore, the point availability is the summation of these two probabilities, or:
Examining the Analysis
Results Inspection Every Year: As shown in Figure 3, when the inspections are performed annually, A(t) goes to 1 after each inspection, implying that 100% of the vests are in a non-failed state after the inspection. After 1.5 years, A(t) is approximately 98%, implying that 2% of the vests on the aircraft are in a failed state at that point in time. Furthermore, the following can be noted:
Figure 3: A(t) vs. time assuming annual inspection Inspection Every Two Years: As shown in Figure 4, when the inspections are performed every two years, the behavior of the availability is similar to the one-year inspection policy. However, it can be seen that lower availability values are experienced between inspections, since the inspection interval is longer, and thus more life vests fail between inspections. Since the availability does not drop below 70%, this inspection policy is a very good candidate and offers substantial cost savings over the one-year inspection policy.
Figure 4: A(t) vs. time assuming inspection every 2 years Inspection Every Three Years: As shown in Figure 5, when the inspections are performed every three years, the availability drops below 70%, which is unacceptable, and this inspection policy is rejected. Figure 5: A(t) vs. time assuming inspection every 3 years Conclusion
Similar analyses can be performed in other types of systems with dormant failure modes or systems that are stored and do not operate until needed. For example, in military applications, missiles are stored until they are requested for operation. Regular inspections can substantially increase the operational readiness of a fleet. Using the same analysis as in this article, an optimum inspection interval can be determined based on the cost of each inspection and the desirable operational readiness goal. See more examples. |