A Linear Model Approach to Time and Cost Analysis

Systems analyses frequently require estimates of the average time that it takes to perform repetitive tasks. These time estimates may be easy to obtain; for example, if one man is performing a single operation, then a simple division of his total working time by the frequency of the task repetition, gives an estimate of the average performance time. However, in many instances, work consolidation requires that individuals be called upon to perform several different operations. For example, crews may be sent into the field to carry out a number of different tasks, for which the relative rate of occurrence may change from day to day. This introduction of multiple operations implies that the required separate time estimates can no longer be obtained by a simple division. This paper discusses linear model estimation of the average time taken to perform specific tasks; the estimation is possible even when a number of different tasks are performed by an individual or group. The models are based on the conceptual relation that the time taken to perform a task multiplied by the rate of occurrence in the considered time period, and summed over all possible tasks, should equal the total time taken by all tasks. Estimation is also possible when direct observations are difficult to obtain (as in stopwatch procedures) because the proposed models do not require direct time observations but rather utilize linear combinations of the individual time parameters. An actual application is discussed.