Quality Control Chapter 11- Reliability PowerPoint presentation to accompany Besterfield Quality Control, 8e PowerPoints created by Rosida Coowar
Fundamental Aspects Additional Statistical Aspects Life and Reliability Testing Plans Availability and Maintainability Outline
Learning Objectives When you have completed this chapter you should be able to: • Know the definition of reliability and the factors associated with it. • Know the various techniques to obtain reliability. • Understand the probability distributions, failure curves, and reliability curves as a factor of time.
Learning Objectives cont’d. When you have completed this chapter you should be able to: • Calculate the failure rate under different conditions. • Construct the life history curve and describe its three phases. • Calculate the normal, exponential, and Weibull failure rate.
Learning Objectives cont’d. When you have completed this chapter you should be able to: • Construct the OC Curve • Determine life and reliability test curves • Calculate the normal, exponential, and Weibull failure rate • Understand the different types of test design • Understand the concepts of availability and maintainability
Reliability • Generally defined as the ability of a product to perform as expected over time. • Formally defined as the probability that a product, piece of equipment, or system willperform its intended function for a stated period of time under specified operating conditions.
Reliability • Means quality over the long run. • A product that “works” for a long period of time is a reliable one. • Since all units of a product will fail at different times, reliability is a probability.
Reliability There are four factors associated with Reliability: • Numerical Value. • The numerical value is the probability that the product will function satisfactorily during a particular time.
Reliability There are four factors associated with Reliability: • Intended Function. • Product are designed for particular applications and are expected to be able to perform those applications.
Reliability There are four factors associated with Reliability: • Life. • How long the product is expected to last. Product life is specified as a function of usage, time, or both.
Reliability There are four factors associated with Reliability: • Environmental Conditions • Indoors. • Outdoors. • Storage. • Transportation.
Achieving Reliability Emphasis: • The Consumer Protection Act of 1972. • Products are more complicated. • Automation.
System Reliability • 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. • Components can be arranged in series, parallel, or a combination.
1 2 n Series System • For a series systems, the reliability is the product of the individual components. RS = R1 R2 ... Rn • As components are added to the series, the system reliability decreases.
1 2 n Parallel System Rs = 1 - (1 - R1) (1 - R2)... (1 - Rn) • When a component does not function, the product continues to function, using another component, until all parallel components do not function.
Series-Parallel System • Convert to equivalent series system C RA RB RD RC A B D C RC RA RB RD A B C’ D RC’ = 1 – (1-RC)(1-RC)
Design • The most important aspect of reliability is the design. • It should be as simple as possible. • 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).
Design • Reliability can be achieved by overdesign. • 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. • The maintenance of the system is an important factor in reliability.
Production • The second most important aspect of reliability is the production process. • Emphasis should be placed on those components which are least reliable. • Production personnel.
Transportation • The third most important aspect of reliability is the transportation. • Packaging • Shipment • Performance of the product by the customer is the final evaluation. • Good packaging techniques and shipment evaluation are essential.
Additional Statistical Aspects Distributions Applicable to Reliability: • Exponential distribution. • Normal distribution. • Weibull distribution. Reliability Curves: • The curves as a function of time.
Additional Statistical Aspects Reliability Curves: • The reliability curves for the exponential, normal and Weibull distributions as a function of time are given in Figure 11-2(b) .
Additional Statistical Aspects Failure-Rate Curve: • It is important in describing the life-history curve of a product. • See Figure 11-2.
Life History Curve • The curve, sometimes referred to as the “bathtub” curve, is a comparison of failure rate with time. • It has three distinct phases: • The debugging phase. • The chance failure phase. • The wear-out phase.
Life History Curve Wear Out Phase Chance Failure Phase Debugging Phase “Infant mortality period”
Life History Curve • The debugging phase: It is characterized by marginal and short-life parts that cause a rapid decrease in the failure rate. It may be part of the testing activity prior to shipment for some products. The Weibull distribution ß<1 is used to describe the occurrence of failures.
Life History Curve • The chance failure phase: Failures occur in a random manner due to the constant failure rate. The Exponential and the Weibull distributions β= 1 are best suited to describe this phase. • 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 describe this phase.
Normal Failure Analysis • The Weibull distribution is usually uses. • The Normal distribution. R(t):Reliability at time t P(t): Probability of failure or area of the normal curve to the left of time t. Table A.
Exponential Failure Analysis Exponential distribution: Rt = e –t/ө Where: t: Time or cycles. ө: Mean life.
Weibull Failure Analysis • Can be used for the debugging phase (ß<1) and the chance failure phase (ß=1). • By setting = 1, the Weibull equals the exponential. • By setting ß=3.4, the Weibull approximates the Normal. Rt = e –(t/ө)ß Where ß is the Weibull slope.
OC Curve Construction Steps: • Assume values for the mean life ө. • These values are converted to the failure rate, l =1/ ө. • Calculate the expected average number of failures nTl. • From Table C of the Appendix using nTl and c value, get Pa.
Life and Reliability Testing Plans Type of Tests: • Failure-Terminated: These life-test sample plans are terminated when a preassigned number of failures occurs to the sample. • Time-Terminated: This life-test sampling plan is terminated when the sample obtains a predetermined test time.
Life and Reliability Testing Plans Type of Tests cont’d.: • 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.
Life and Reliability Testing Plans Tests are based on one or more of the following characteristics: • Mean life: the average life of the product. • Failure rate: the percentage of failures per unit time or number of cycles.
Life and Reliability Testing Plans Test are based on one or more of the following characteristics cont’d.: • 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.
Handbook H108 • 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. • Provides for the three different types of test: failure-terminated, time-terminated, and sequential.
Handbook H108 • The handbook is over 70 pages long. • The time-terminated plan: • Stipulated producer’s risk, consumer’s risk, and sample size. • Stipulated producer’s risk, rejection number, and sample size. • Stipulated producer’s risk, consumer’s risk, and test time.
Reliability Management • Define customer performance requirements. • Determine important economic factors and relationship with reliability requirements. • Define the environment and conditions of product use.
Reliability Management • Select components, designs, and vendors that meet reliability and cost criteria. • Determine reliability requirements for machines and equipments. • Analyze field reliability for improvement.
Availability and Maintainability 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.
Availability • 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.
Availability Where: MTBM = mean time between maintenance MDT = mean down time MTBF = mean time between failures MTTR = mean time to repair
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 • Maintainability is the totality of design factors that allows maintenance to be accomplished easily. • Preventive maintenance reduces the risk of failure. • Corrective maintenance is the response to failures.