Exam 4: B: Product Design

A certain product is comprised of two components: X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that component Y will perform reliably for a year?

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.If the company includes both a backup light bulb and a backup battery with each flashlight,what is the probability that the flashlight will perform reliably for one hour (excluding replacement time)?

The probability that a product will fail within a given amount of time is often described by the:

An early warning security fence has three major components which must each perform in order for the system to perform.Their reliabilities are .4,.3,and .2.The system reliability is equal to:

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If they were to connect an identical,backup gyroscope with a perfectly reliable switch to the primary gyroscope,what would be the reliability of the gyroscope function during a launch?

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If they were to connect an identical,backup gyroscope with a .90 reliable switch to the primary gyroscope,what would be the reliability of the gyroscope function during a launch?

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If he were to add both a backup generator and a backup transformer,what would be the probability that this system would perform reliably for a period of one year?

A certain product is comprised of two components: X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What would be the reliability of this product if component Y were backed up with an identical component?

One operational definition of reliability is the probability that a product or system will function when activated.

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.Devices,Inc.supplies Readylite with the on-off switch for this flashlight.These switches,on average,fail in fifty hours with a standard deviation of four hours.What service life should Devices specify to have a .8944 probability that a switch will last at least that long before failing?

A certain product is comprised of two components: X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What would be the reliability of this product if both components were redundant?

An important dimension of reliability relates to "prescribed set of conditions".

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.If the temperature drops below the desired level,what is the probability the system will perform reliably for one hour?

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.If the pressure drops below the desired level,what is the probability the system will perform reliably for one hour?

A certain product is comprised of two components: X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that component X will perform reliably for a year?

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.What is the probability that the battery will perform reliably for one hour?

The probability that a product will perform its intended function under prescribed conditions is:

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.What is the probability that this system will perform reliably for a period of one year?

Events can be considered "independent events" if they have no relation to the occurrence or non-occurrence of each other.

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If the battery used to power the computer has a mean time to fail of 60 minutes with a standard deviation of 20 minutes,what is the probability that it will last for a launch of 30 minutes duration without failing?