Reliability Reliability is the probability that a product will perform its intended function satisfactorily for a prescribed life under certain stated environmental conditions.Reliability is the probability that a product will perform its intended function satisfactorily for a prescribed life under certain stated environmental conditions. Generally defined as the ability of a product to perform as expected over time.Generally defined as the ability of a product to perform as expected over time. Four factors associated with reliability:Four factors associated with reliability: 1. Numerical Value - The numerical value is the probability that the - The numerical value is the probability that the product will function satisfactorily during a particular product will function satisfactorily during a particular time. time. - Say, a probability of 0.93 represent the probability that 93 - Say, a probability of 0.93 represent the probability that 93 out of 100 of product function after prescribed time. out of 100 of product function after prescribed time.

2. Intended Function - Product are designed for particular applications and are expected to be able to perform those applications. - Product are designed for particular applications and are expected to be able to perform those applications. - Products designed for specific applications, example: intended use of screwdriver not for opening paint cans or hammering. - Products designed for specific applications, example: intended use of screwdriver not for opening paint cans or hammering. 3. Life - How long the product is expected to last. Product - How long the product is expected to last. Product life is specified as a function of usage, time, or both. life is specified as a function of usage, time, or both. - Example, automobiles – 10 years. - Example, automobiles – 10 years. 4. Environmental Conditions - Operating conditions – outdoor, indoor – chair, high pressure hose. - Operating conditions – outdoor, indoor – chair, high pressure hose. - Environment – cold or hot climate, dusty. - Environment – cold or hot climate, dusty. - Conditions must include storage and transportation (shipping, freight). - Conditions must include storage and transportation (shipping, freight).

Emphasis on Reliability – Why It Is Important Human safety health and convenience depends on reliability of uninterrupted services of our power supply, water, communications, drugs, food, and other products and services.Human safety health and convenience depends on reliability of uninterrupted services of our power supply, water, communications, drugs, food, and other products and services. Consumer Protection Act.Consumer Protection Act. Increased product complexity – washing machines.Increased product complexity – washing machines. Automation in product – not manual, so if fail cannot operate.Automation in product – not manual, so if fail cannot operate. System Reliability As products become more complex (have more components), the chance that they will not function increases.As products become more complex (have more components), the chance that they will not function increases. The method of arranging the components affects the reliability of the entire system.The method of arranging the components affects the reliability of the entire system. Components can be arranged in series, parallel, or a combination.Components can be arranged in series, parallel, or a combination.

Series Arrangement The reliability is the product of the individual components.The reliability is the product of the individual components. As components are added to the series, the system reliability decreases.As components are added to the series, the system reliability decreases. Reliability in Series is, R S = (R A x R B x R C x …R n )Reliability in Series is, R S = (R A x R B x R C x …R n ) R S = (R A x R B x R C )R S = (R A x R B x R C ) = (0.955 x x 0.999) = (0.955 x x 0.999) = = What happen if one component fail?What happen if one component fail? What happen if number of components increase?What happen if number of components increase? R A R B R C 0.999

Parallel Arrangement When a component does not function, the product continues to function, using another component, until all parallel components do not function.When a component does not function, the product continues to function, using another component, until all parallel components do not function. Reliability in Parallel is, R P = 1 – (1 – R I )(1 – R J )Reliability in Parallel is, R P = 1 – (1 – R I )(1 – R J ) R P = 1 – (1 – R I )(1 – R J )R P = 1 – (1 – R I )(1 – R J ) = 1 – (1 – 0.750)(1 – 0.840) = 1 – (1 – 0.750)(1 – 0.840) = = R I R J 0.840

Combination Arrangement Most complex products are a combination of series and parallel arrangement.Most complex products are a combination of series and parallel arrangement. Reliability in combination is,Reliability in combination is, R C = (R A )(R I,J )(R C ) = (0.955)(0.960)(0.999) = (0.955)(0.960)(0.999) = = R I R J R C R A 0.955

Design The most important aspect of reliability is the design.The most important aspect of reliability is the design. It should be as simple as possible.It should be as simple as possible. The fewer the number of components, the greater the reliability.The fewer the number of components, the greater the reliability. Another way of achieving reliability is to have a backup or redundant component (parallel component).Another way of achieving reliability is to have a backup or redundant component (parallel component). Reliability can be achieved by overdesign.Reliability can be achieved by overdesign. The use of large factors of safety can increase the reliability of a product.The use of large factors of safety can increase the reliability of a product. When an unreliable product can lead to a fatality or substantial financial loss, a fail-safe type of device should be used.When an unreliable product can lead to a fatality or substantial financial loss, a fail-safe type of device should be used. The maintenance of the system is an important factor in reliability.The maintenance of the system is an important factor in reliability.

Production The second most important aspect of reliability is the production process.The second most important aspect of reliability is the production process. Emphasis should be placed on those components which are least reliable.Emphasis should be placed on those components which are least reliable. Production personnel.Production personnel.Transportation The third most important aspect of reliability is the transportation.The third most important aspect of reliability is the transportation. - Packaging - Shipment Performance of the product by the customer is the final evaluation.Performance of the product by the customer is the final evaluation. Good packaging techniques and shipment evaluation are essential.Good packaging techniques and shipment evaluation are essential.

Additional Statistical Aspects Types of continuous probability distributions used in reliability studies are exponential, normal, and Weibull.Types of continuous probability distributions used in reliability studies are exponential, normal, and Weibull. Exponential, R = R t = e –t/ ө ; t=time or cycles; ө =mean lifeExponential, R = R t = e –t/ ө ; t=time or cycles; ө =mean life Weibull, Rt = e –(t/ ө )ß ; ß =Weibull slopeWeibull, Rt = e –(t/ ө )ß ; ß =Weibull slope Failure Rate,Failure Rate, r = no. of test failures t = test time for failed item n = no. of items tested T = termination time

Example – Time Terminated No Replacement Determine the failure rate for an item that has the test of 9 items terminated at the end of 22 hour. Four of the items failed after 4, 12, 15, and 21 hour, respectively. Five items were still operating at the end of 22 hour.Determine the failure rate for an item that has the test of 9 items terminated at the end of 22 hour. Four of the items failed after 4, 12, 15, and 21 hour, respectively. Five items were still operating at the end of 22 hour. λ est = r / [ ∑ t + (n – r) T]λ est = r / [ ∑ t + (n – r) T] = 4 / ( ) + ((9 – 4) 22) = Example – Time Terminated Replacement Determine the failure rate for 50 items that are tested for 15 hour. When a failure occurs, the item is replaced with another unit. At the end of 15 hour, 6 of the items had failed.Determine the failure rate for 50 items that are tested for 15 hour. When a failure occurs, the item is replaced with another unit. At the end of 15 hour, 6 of the items had failed. λ est = r / [ ∑ t + (n – r) T] = r / ∑ tλ est = r / [ ∑ t + (n – r) T] = r / ∑ t = 6 / 50(16) = * total test time equal to ∑ t.

Example – Failure Terminated Determine the failure rate for 6 items that are tested to failure. Test cycles are 1025, 1550, 2232, 3786, 5608 and 7918.Determine the failure rate for 6 items that are tested to failure. Test cycles are 1025, 1550, 2232, 3786, 5608 and λ est = r / [ ∑ t + (n – r) T] = r / ∑ tλ est = r / [ ∑ t + (n – r) T] = r / ∑ t = 6 / ( ) = * total test time equal to ∑ t. For the exponential and Weibull when the shape parameter, ß = 1, there is a constant failure rate. We can use, θ = 1/λ, where θ = mean life or mean time to failures (MTTF).For the exponential and Weibull when the shape parameter, ß = 1, there is a constant failure rate. We can use, θ = 1/λ, where θ = mean life or mean time to failures (MTTF). MMTF for previous 3 problems are:MMTF for previous 3 problems are: 1. θ = 1/λ = 1/0.025 = 40 hours. 2. θ = 1/λ = 1/0.008 = 125 hours. 3. θ = 1/λ = 1/ = 3704 hours.

Life History Curve The curve, sometimes referred to as the “bathtub” curve, is a comparison of failure rate with time.The curve, sometimes referred to as the “bathtub” curve, is a comparison of failure rate with time. Debugging Phase Chance Failure Phase Wear Out Phase

It has three distinct phase:It has three distinct phase: 1. The debugging phase: - It is characterized by marginal and short-life parts that - It is characterized by marginal and short-life parts that cause a rapid decrease in the failure rate. cause a rapid decrease in the failure rate. - It may be part of the testing activity prior to shipment for - It may be part of the testing activity prior to shipment for some products. some products. - The Weibull distribution ß<1 is used to describe the - The Weibull distribution ß<1 is used to describe the occurrence of failures. occurrence of failures. 2. The chance failure phase: - Failures occur in a random manner due to the constant - Failures occur in a random manner due to the constant failure rate. The Exponential and the Weibull distributions failure rate. The Exponential and the Weibull distributions β= 1 are best suited to describe this phase. β= 1 are best suited to describe this phase. 3. The wear-out phase: - Is depicted by a sharp raise in failure rates. The Normal distribution and the Weibull distribution ß >1 are used to distribution and the Weibull distribution ß >1 are used to describe this phase. describe this phase.

Life and Reliability Testing Plans Types of Tests: Failure-Terminated: These life-test sample plans are terminated when a pre-assigned number of failures occurs to the sample.Failure-Terminated: These life-test sample plans are terminated when a pre-assigned number of failures occurs to the sample. Time-Terminated: This life-test sampling plan is terminated when the sample obtains a predetermined test time.Time-Terminated: This life-test sampling plan is terminated when the sample obtains a predetermined test time. Sequential: A third type of life-testing plan is a sequential life-test sampling plan whereby neither the number of failures nor the time required to reach a decision are fixed in advance.Sequential: A third type of life-testing plan is a sequential life-test sampling plan whereby neither the number of failures nor the time required to reach a decision are fixed in advance. Tests are based on one or more of the following characteristics: Mean life: the average life of the product.Mean life: the average life of the product. Failure rate: the percentage of failures per unit time or number of cycles.Failure rate: the percentage of failures per unit time or number of cycles. Hazard rate: the instantaneous failure rate at a specified time.Hazard rate: the instantaneous failure rate at a specified time. Reliable life: the life beyond which some specified portion of the items in the lot will survive.Reliable life: the life beyond which some specified portion of the items in the lot will survive.

Handbook H108 Quality Control Reliability Handbook H108 gives sampling procedures and tables for life and reliability testing.Quality Control Reliability Handbook H108 gives sampling procedures and tables for life and reliability testing. Sampling plans in the handbook are based on the exponential distribution.Sampling plans in the handbook are based on the exponential distribution. Provides for the three different types of test: failure- terminated, time-terminated, and sequential.Provides for the three different types of test: failure- terminated, time-terminated, and sequential. Reliability Management Define customer performance requirements.Define customer performance requirements. Determine important economic factors and relationship with reliability requirements.Determine important economic factors and relationship with reliability requirements. Define the environment and conditions of product use.Define the environment and conditions of product use. Select components, designs, and vendors that meet reliability and cost criteria.Select components, designs, and vendors that meet reliability and cost criteria. Determine reliability requirements for machines and equipments.Determine reliability requirements for machines and equipments. Analyze field reliability for improvement.Analyze field reliability for improvement.

Availability For long-lasting products and services such as refrigerators, electric power lines, and front-line services, the time-related factors of availability, reliability, and maintainability are interrelated.For long-lasting products and services such as refrigerators, electric power lines, and front-line services, the time-related factors of availability, reliability, and maintainability are interrelated. It is a time-related factor that measures the ability of a product or service to perform its designated function.It is a time-related factor that measures the ability of a product or service to perform its designated function. The product or service is available when it is in the operational state, which includes active and standby use.The product or service is available when it is in the operational state, which includes active and standby use.Maintainability Maintainability is the probability that a system or product can be retained in, or one that has failed can be restored to, operating condition in a specified amount of time.Maintainability is the probability that a system or product can be retained in, or one that has failed can be restored to, operating condition in a specified amount of time. Maintainability is the totality of design factors that allows maintenance to be accomplished easily.Maintainability is the totality of design factors that allows maintenance to be accomplished easily. Preventive maintenance reduces the risk of failure.Preventive maintenance reduces the risk of failure. Corrective maintenance is the response to failures.Corrective maintenance is the response to failures.