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## Quality Control

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**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.