The effect of failure-distribution specification-errors on maintenance costs

This paper examines the problem of determining and evaluating optimal fixed-length inspection intervals for a single machine that operates continuously subject to nonobvious, random failures. Good-as-new repairs are performed when the machine is found to be failed. Both the fixed-interval inspection and replacement times are instantaneous. Two possible single parameter failure time distributions are used in this investigation: exponential and 2-Erlang. The focus of this paper, however, is on the consequences of mis-specifying the form of the failure distribution or the parameter value(s) of the failure distribution. Robustness analysis indicates that long run expected cost per unit time is extremely robust to moderate errors in the specification of the expected time to failure (cost increases of less than 0.6% for ±20% error in expected failure time), when the form of the failure distribution is correct. Conversely, accurately specifying the mean time between failures, but incorrectly specifying the form of the failure distribution, results in significant increases in long run expected cost per unit time. Mistaking an exponential for a 2-Erlang, or vice versa, can result in cost increases of over 20% for reasonable values of cost parameters