There are certain items such as fluorescent tubes, bulbs and fuse which do not deteriorate but fail suddenly and completely after a certain amount of use. This kind of failure is analysed by the method called group replacement theory. Group replacement involves periodic and simultaneous replacements along with individual replacements. In this research, a technique for calculating the current probabilistic group replacements using only one equation, without referring to past replacements, as it is currently done, has been developed. A more general form of this one-equation model is difficult to obtain. Hence a tabular of a small sample for practical purposes has been suggested and demonstrated in this research. A sequence of replacement-survivor trees has also been developed. This is an alternative to the tabular failure-tree approach that is already in use. It is easier in that there are only two branches at every trunk of the tree as opposed to the existing one with many branches which are not easily followed. Using cumulative probability to calculate replacements shows a normal-probability-distribution tendency with a maximum turning point or maximum number or replacements. This information about maximum number of replacements can be very useful to managers in making replacement policy decisions.
Alabi-Labaika, Abraham B.
"Probabilistic Group Replacement Models: Retrospective and Prospective Approaches,"
Annals of Management Science: Vol. 4
, Article 3.
Available at: https://digitalscholarship.tnstate.edu/ams/vol4/iss2/3