Periodic Restoration and Imperfect Testing

It is quite unrealistic to assume that inspection and testing processes will detect all failures. In the worst case, assume that testing is not done. In that situation what is the mission time If the equipment is used for the life of an industrial facility, plant life is the mission time. Probability of failure would be modeled with the unreliability function using the plant life as the time interval. 

If the equipment is required to operate only on demand and the demand is independent of system failure, the unreliability function can be averaged as explained in the preceding section. 

When only some failures are detected during the periodic inspection and test, the average probability of failure can be calculated using an equation that combines the two types of failures those detected by the test and those undetected by the test. One must estimate the percentage of failures detected by the test to make this spHt. The equation would be  

Problem A valve used in a safety instrumented system has a failure rate of 0.002 failures per year. The valve is not tested. It will be used during the lifetime of the process unit, 25 years. The demand is estimated to be once every 100 years. What is the probability of failure during a demand  

Solution Equation (4-16) gives the average probability of failure. This is appropriate for this problem using a time interval of 25 years. The average probability of failure = 0.002 x 25 / 2 = 0.025. 

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