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Robot Reliability MeasuresTable of Contents:
There are various types of reliability measures. Four of these measures are as follows [9,11,16]: Robot ReliabilityRobot reliability may simply be defined as the probability that a robot will perform its stated function satisfactorily for the specified time period when used as per designed conditions. The general formula for obtaining timedependent robot reliability is expressed by [9,11].
where R_{r} (t) is the robot reliability at time t. X_{r} (r) is the timedependent failure rate (hazard rate) of the robot. Equation (5.1) can be used to obtain the reliability function of a robot for any failure times probability distribution (e.g., exponential, Rayleigh, or Weibull). Example 5.1 Assume that the timedependent failure rate of a robot is defined by where a is the distribution parameter. t is the time. A,. (?) is the hazard rate (timedependent failure rate) of the robot when its times to failure follow the Rayleigh distribution. Obtain an expression for the robot reliability. By inserting Equation (5.2) into Equation (5.1), we obtain Thus, Equation (5.3) is the expression for the robot reliability. Example 5.2 Assume that the constant failure rate of a robot is 0.0005 failures per hour. Calculate the robot reliability for a 10 hours mission. By inserting the robot specified failure rate value into Equation (5.1), we get
Substituting the stated mission time value of the robot into Equation (5.4) yields
Thus, the robot reliability for the stated mission period is 0.9950. Mean Time to Robot Failure (MTTRF)MTTRF can be obtained by using any of the following three equations: where MTTRF is the mean time to robot failure. R_{r}(t) is the robot reliability at time t. R_{r} (,v) is the Laplace transform of the robot reliability function, R,. (t). s is the Laplace transform variable. RPH is the robot production hours. NRF is the number of robot failures. DDTRF is the downtime due to robot failures expressed in hours. Example 5.3 Assume that the constant failure rate of a robot is 0.0008 failures per hour and its reliability is expressed by
where R_{r} (/) is the robot reliability at time t. A_{r} is the robot constant failure rate. Calculate the mean time to robot failure by using Equations (5.5) and (5.6) and comment on the final result. By substituting Equation (5.8) into Equation (5.5), we obtain By taking the Laplace transform of Equation (5.8), we get By inserting Equation (5.9) into Equation (5.6), we obtain
In both cases, the end result (i.e., MTTRF = 1250 hours) is the same. It proves that both equations (i.e., Equations (5.5) and (5.6)) yield exactly the same end result. Example 5.4 Assume that a robot’s annual production hours and its annual downtime due to failures are 5000 hours and 250 hours, respectively. During that period, the robot failed four times. Calculate the mean time to robot failure. By substituting the given data values into Equation (5.7), we get
Thus, the mean time to robot failure is 1187.5 hours. Robot Hazard RateThe robot hazard rate or timedependent failure rate is expressed by [9,11] where A,. (7) is the robot hazard rate (i.e., timedependent failure rate). R_{r} (7) is the robot reliability at time t. It is to be noted that Equation (5.10) can be used to obtain the hazard rate of a robot when its times to failure follow any timecontinuous probability distribution (e.g., exponential, Weibull, and Rayleigh). Example 5.5 Assume that the reliability of a robot is expressed by where R_{r} (/) is the robot reliability at time t. в is the distribution parameter. Obtain an expression for hazard rate of the robot. By inserting Equation (5.11) into Equation (5.10), we obtain
Thus, Equation (5.12) is the expression for the hazard rate of the robot. Mean Time to Robot ProblemsThis is the average productive robot time before the occurrence of a robotrelated problem. It is expressed by
where NRP is the number of robotrelated problems. RPH is the robot production hours. DDTRP is the downtime due to robotrelated problems expressed in hours. MTTRP is the mean time to robotrelated problems. Example 5.6 Assume that at an industrial facility the annual robot production hours and downtime due to robotassociated problems are 4000 hours and 200 hours, respectively. During the oneyear period, there were 20 robotassociated problems. Calculate the mean time to robot problems. By inserting the specified data values into Equation (5.13), we obtain
Thus, the mean time to robot problems is 190 hours. Reliability Analysis of Electric and Hydraulic RobotsAs both electric and hydraulic robots are used in the industry, this section presents reliability analysis of two typical electric and hydraulic robots by employing the block diagram approach/method [79]. Generally, for the purpose of design evaluation in the industrial sector, it is assumed for both electric and hydraulic robots that all robot parts form a series configuration (i.e., if any one part/component fails, the robot fails). 
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