Bath Tub Curve


Replacement model is the part of operation research mostly used in the industries when a purchased items like machinery, buildings efficiency is reduced or wear out due to much usage.

Bathtub CurveMachine or equipment or facility life can be classified into three stages. They are

(a)   Infant stage,

(b)   Youth stage or Youth phase and

(c)    Old age stage or Old age phase.

 Infant stage or phase

(a)   This is also known as early failure stage.

(b)   When new equipment is purchased and installed in the existing system, it has to cope up with the operating efficiency of the existing system.

(c)    Also it has to accustom to operating skill of the operator.

(d)   Perhaps when a new vehicle is purchased, due to mechanical conditions of the machine and the operating skill of the person, the vehicle may give trouble in the early stages.

(e)   Once an age of 10 to 15 years is reached, the death rate or failure rates will reduce. In this stage the safety of machine is covered by the guarantee period given by the manufacturer. This is represented by a curve on the left hand side of the Bathtub curve.

 Youth stage or random failure stage

(a)   In this stage the equipment or machine is accustomed to the system in which it is installed and works at designed operating efficiency.

(b)   Regular maintenance such as overhauling, oiling, greasing, cleaning keep the machine working. Now and then due to wear and tear of components or heavy load or electrical voltage fluctuations, breakdown may occur, which can be taken care of by repair maintenance.

(c)    The machine or equipment works for longer periods without any trouble.

(d)   This is like youth stage in human life that is full of vigor and energy and the person will be healthy and work for longer periods without any diseases.

(e)   This is shown as a horizontal line in bathtub curve. Here repair maintenance; preventive maintenance or other maintenance techniques are used to keep the machine or equipment in working condition.


Old age stage or Old age phase or Wear out failures

(a)   Due to continuous usage and age of the machine, there will be wear and tear of various components.

(b)   Not only this, during youth stage, some of the components might have been replaced due to wear and tear.

(c)    These replaced components may not suit well in the system if they are not from original manufacturer.

(d)   As the manufacturers are changing the design, one has to go for spares available in the market.

(e)   All this may reduce to operating efficiency of the machine or equipment and the management has to face frequent failures. This is very similar to old age in human life.

(f)     Due to old age, people will get diseases and old age weakness and many a time they have to go to hospitals for treatment before the life fails.

(g)   This is shown on the right side of the bath- tub curve. Here one will think of replacement of the equipment or machine. When all the above three curves are assembled, we get a curve which is in the form of a bathtub and is known as bathtub curve,