Maintenance , Reliability , Availability , Bath tub curve , Standards and quality , General studies , UPSC ESE

Reliability 

• The reliability of a product or a system can be defined as the probability that the product will perform its required function under specific condition for a certain period of time. 
• 
  The reliability of a system depend upon reliability of individual component. 
• For series connection. 
  

Question :a product has two component both of which must work for the product to function ,component one has reliability of 80% and component two has reliability of 90%, compute the reliability of system. 

Note: reliability of system is always less than or equal to reliability of individual component when they are connected in series. 

For equal 

• When all component have 100% reliability. 
• When there is a single component. 

Note: as the component increases in series the reliability of system will decrease. 

How to increase reliability of system ?

For parallel connection 

Question : two power generator provide electricity to a facility that is main and backup generator. The main generator has reliability of 95% and the backup has a reliability of 90% ,compute the reliability of system. 

Note: reliability of system is greater than reliability of individual component when they are connected in parallel. 

Note: as the number of component in parallel increases the reliability of system will increase. 

Reliability prediction using exponential distribution. 

• It is one of the most commonly used distribution in the reliability prediction, it is used to predict  the probability of survival to a particular time. 

MTTF (mean time to failure) 

• It referred as the average time an item may be expected to function before the failure. 
• It is used for non repairable item. 
• Example bulb 
  

MTBF (mean time between failure) 

• It referred as time between two failure. 
• It is used for repairable item. 

MTTR (Meantime to repair) 

• ti = the repair time for ith failure. 

Note: MTBF can be used for both repairable as well as non repairable items. 

Problem :a system has two component in series with mtbf of  20 hour and 10 hour respectively ,what is 400 hour system reliability. 

Question :the reliability of a repairable product by exponential distribution is given in hours as 

and mttr is 20 hour. What is the mttf for system in hour. 

Availability

• It is the probability that a product or a system is performing its required function at a given point of time when it is used under the stated operating condition. 

Maintainability 

• It is the probability that a product or system is being failed or system will be restored to a specific condition within a period of time when the maintenance is performed according to prescribed procedure. 
  

Question: suppose that a certain software product has a mean time between failure of 10000 hour and has a mean time to repair 20 hour. If the product is used by hundred customer what is the availability. 

Question :an engine is to be designed to have a minimum reliability of 0.8 and minimum availability of 0.98 over a period of 2000 hrs. The mttr is nearly. 

For series connection 

Question :the automatic focus unit of a TV camera has 10 component in series ,each component has exponential time to failure distribution with a constant failure rate of 0.05/ 4000 hour. What is its mttf for the system. 

Bathtub curve 

• It is a graphical representation of life time of population of product. It does not depict the failure rate of single item ,it describe the relative failure rate of entire  failure rate over a time. 
  

Region 1 infant mortality

• It is also known as early failures or debugging stage.
• The failure rate decreases with respect to time .
• In beginning of infant mortality rate the failure is high and than decreases with respect to time.

Region 2 useful life

• It is middle stage of bathtub curve.
• Failure rate remain constant 
• It is most significant period for reliability prediction.

Region 3 wear out life

• It is final stage of bath tub curve.
• The failure rate increases as product began to wear out because of age or lack of maintenance.

Maintenance are of three types:

1. Reactive maintenance or break down maintenance : it is basically run it till its break , no action or effort taken to maintain the equipment.
2. Preventive maintenance: routine servicing id planned to prevent the failure.
3. Predictive maintenance : timely replacement of component based on the condition monitoring before it cause any break down.