Volume 4, Issue 2

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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.

Airplane

Description of the Problem
Odyssey Air, a fictional commercial airline, uses inflatable life vests aboard its aircraft. The airline is considering three possible inspection schedules for this equipment: every year, every two years or every three years. More frequent inspections are, obviously, more expensive to the airline. However, insufficient inspections can result in the inability to provide functioning life vests to passengers and crew in the event that they are needed, which carries serious consequences that are important to avoid. In order to choose the inspection interval that meets the company's performance requirements with the lowest cost, Odyssey Air must study the effects of different inspection intervals on the likelihood that the vests will be found operational (or non-failed) when needed. That is, they must study and compare the availability of the vests under the three possible maintenance scenarios. An availability goal of at least 70% is sought between inspections. That is, at least 70% of the life vests must be available in any given aircraft between inspections.

Life vest

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
To perform this analysis in BlockSim, the first step is to define a reliability block diagram (RBD) to describe the "system" of interest. For this analysis, the RBD consists of a single block defined with the reliability and maintenance characteristics of the life vests used by Odyssey Air. The reliability of the block is defined by the dormant failure distribution and parameters that have been calculated for this item: Weibull with Beta = 2.55 and Eta = 7.89 years.

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 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

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.

Simulation utility

Estimating the Instantaneous or Point Availability
For this analysis, the instantaneous (or point) availability, A(t), is the metric of interest because it describes (within the context of this analysis) the probability that a vest will be operational (non-failed) at a specific point in time.

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:

  • The item has functioned properly from 0 to t with probability R(t).
     
  • The item has functioned properly since the last repair at time u, 0 < u < t, with probability:

Equation

Where m(u) is the renewal density function of the system.

Therefore, the point availability is the summation of these two probabilities, or:

Equation

Examining the Analysis Results
Figures 3, 4 and 5 present the point availability versus time for each of the three potential inspection intervals (based on results estimated via the simulation). This provides a graphical way to compare the three inspection interval options that Odyssey Air is considering.

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:

  • The percentage of non-failed life vests decreases after each inspection.
     
  • The rate of decrease of A(t) continues to increase after each subsequent inspection (since non-failed vests are not replaced and the population ages) until a periodic reversal point is reached at which most vests are replaced with newer ones, thus yielding a younger population.
     
  • The availability does not drop below 70% between inspections.

Figure 3: A(t) vs. time assuming annual inspection

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

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
By comparing the three inspection policies, it is decided that the two-year inspection policy is the optimum one. It offers the desirable availability goal and lower cost.

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.

End Article See more examples.

 

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