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This work seeks to determine the impact of the ‘bathtub curve’ failure rate on the performance of a fleet of military aircraft. Previous work in this area using a simulation modelling approach (e.g., Mattila and Virtanen, 2014; Marlow et al., 2015) has assumed a constant failure rate for unscheduled maintenance throughout a fleet life. We seek to ascertain whether a fleet is able to absorb the potential impacts of a representative bathtub curve through other actions such as implementing better fleet management policies, and at what point the effect of the bathtub overwhelms any mitigation procedures. The bathtub curve is a concept used in reliability engineering to describe the varying failure rates of a system over time. It consists of three main periods: • the ‘infant mortality’ or ‘burn in’ period, where the failure rate is high as initial faults are identified, before decreasing over time, resembling the left-hand side of a bathtub (viewed in cross-section); • the ‘random failures’ period in the ‘middle’ of the bathtub, where failures occur at a constant rate; and • the ‘wear-out’ period, where the failure rate increases as the system ages, resembling the right-hand side of a bathtub. We incorporate the bathtub curve effect into our aircraft fleet simulation model used in previous work for a naval helicopter fleet (Marlow et al., 2015) but applicable to any fleet. The model represents the movement of aircraft between states for each day of a 30 year fleet life. Aircraft may be embarked on ships or ashore; they may be serviceable (able to fly) or in various types of scheduled or unscheduled maintenance. Aircraft change states once particular criteria are met – e.g., entering maintenance after achieving a certain number of flying hours. The primary measures of effectiveness (MoEs) for the model are to achieve the required number of embarked aircraft each day, and the required annual embarked and ashore flying hours. In order to evaluate the impact of the bathtub curve on fleet performance, we include additional MoEs that calculate the percentage of years that the fleet does not meet its annual embarked and ashore requirements. The model also includes a range of pre-determined policies to assist the fleet in meeting its MoEs. There are six policy categories: flying allocation, maintenance allocation, crew rotation between maintenance areas, tail rotation between multiple squadrons, policies to balance the total flying hours across the fleet, and squadron sharing. The two new input variables to the model represent the ‘height’ of the bathtub (corresponding with an increase in the unscheduled maintenance failure rate of 2height) and the ‘duration’ in years of each end of the symmetrical bathtub. To represent the bathtub curve effect, we use a ‘thinning’ technique (Lewis and Shedler, 1979) to create time-dependent rates over the fleet life. We generate gamma-distributed potential failure events at a rate corresponding to the maximum bathtub height, and accept or reject the generated events with a probability determined by the height of the bathtub at the time of the event. The probability decreases linearly from 1 to 1/2height during the infant mortality period; takes the value 1/2height in the random failures period; and increases linearly from 1/2height to 1 during the wear-out period. In order to test various bathtub heights and durations, we use a designed simulation experiment approach (Sanchez and Wan, 2015) over 512 design points, with the height varying from 0 to 3 and duration varying from 0 to 10 years. We perform statistical analysis of the results on the two new MoEs. For the percentage of years that the embarked annual flying requirements are not met, flying at a higher tempo (up to 7 hours per day) has the largest impact on the results, more so than the bathtub variables. For the percentage of years that the ashore annual flying requirements are not met, various combinations of existing policies, particularly sharing squadron resources, can be implemented to reduce the impact of the bathtub curve. However, if the bathtub effects last for longer than around 5 years at each end, and the height of the bathtub exceeds approximately 1.3 (i.e., slightly more the double the failure rate), negative impacts on the fleet performance eventuate.

Assessing the impact of the bathtub curve failure rate on fleet performance using designed simulation experiments