Application of the mixed Weibull distribution in machine reliability analysis for a cell formation problem

Purpose The purpose of this paper is to understand the consequence of the use of mixed Weibull distribution in the cell formation problem. In reliability theory, a mixed distribution is used for more than one hazard cause, and the Weibull distribution can be used for ascendant, monotonous and descendant failure rate. Here, the authors mixed these two theme and use it in a common problem in group technology. Design/methodology/approach In this paper, the authors made a non-polynomial-hard mathematical model based on past research and solved it with an exact algorithm. The algorithm is coded and solved in GAMS to illustrate the model, and the authors use simulation. A common numerical example is solved with the model, and the results are compared. Findings Reliability analysis model based on the mixed Weibull distribution approach will give options to a user to select the suitable failure rate and modes for a specific situation. If the user uses the exponential or Weibull distribution instead of the mixed Weibull distribution, the calculated cost and reliability are wrong; therefore, it leads to user making wrong decisions. Originality/value The model the authors use is the one used in past research, but in the past, researchers did not use the mixed distribution for explaining failure time. Therefore, the model can be considered as a new and more complete model.