Mathematical Model of the Occurrence of Human Error in Manufacturing Processes

Various types of phenomena contribute to the variability of process results. Their common feature is randomness. Some of them can be described by continuous probability distributions, for example, the performance of machines or the properties of processed material. There are also discretely distributed contributions, such as human errors or machine failures. Six sigma methodology encompasses both continuous and discrete phenomena by expressing measures of variability by the so-called 'sigma measure'. However, this methodology cannot be used directly to assess the individual impact of a specific class of factors, such as human errors in a continuously distributed production process. This paper describes the development of a probabilistic model of human error. The model makes use of classical reliability concepts, such as a failure rate function, to represent substantial phenomena of various types (continuous and discrete) that play a significant role in the creation of errors in human work. The model includes a mechanism that is inherently associated with human work (i.e. the 'bathtub curve' that represents the processes of learning and fatiguing) and mechanisms introduced by the work environment (accumulation of tasks). The hypothesis is formulated that, in industrial processes, special causes of errors are closely related to the assignment of inadequate amounts of time for properly performing the operations. Graphs of error rate functions enable intuitive graphical interpretation of the causes of problems, and they can be used to support some considerations regarding the organization and measurement of workflow during a work shift. Thus, an intuitive graph can be useful for figuring out the potential impact on the risk of errors that will result from certain system events. Such graphs can be applied in a general capability study of a process to assess the variability measures associated with the individual impacts of particular classes of factors, for example, the sigma measure used in the six sigma methodology. It can be used to identify mechanisms of potential failures associated with human error in risk analysis, such as FMEA (Failure Mode and Effect Analysis). Copyright (C) 2010 John Wiley & Sons, Ltd.