A typical proportional, integral, and derivative (PID) controller consists of a stand-alone regulator (which adjusts the...

A typical proportional, integral, and derivative (PID) controller consists of a stand-alone regulator (which adjusts the control variable of a process), a front end where the controller constants are manually entered, and a processor (or a computer) where the control algorithm is implemented. When a controller observes deviations in a process output from predefined reference values, the regulator automatically adjusts the process parameter to compensate for such deviations. The regulator is a mechanical, electrical, or an electromechanical system that implements the appropriate control action on the process parameter. Twenty controllers are placed in service, and the times to failure of the regulators are recorded as follows:

551, 571, 571, 575, 583, 588, 590, 592, 594, 598, 606, 610, 611, 611, 613, 615, 615, 626, 629 and 637

a. Assuming that the failure data follow and exponential distribution, find the MLE for the MTTF

b. Assuming that the failure data follow a Webull distribution, find the MLE for the MTTF

c. Compare the results of a and b. What do you conclude about the failure-time distribution?

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Expert Solution

orchestra answered 1 year ago

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