quality control chapter 11- reliability powerpoint presentation to accompany besterfield quality...

Quality ControlQuality ControlQuality ControlQuality Control

Chapter 11- ReliabilityChapter 11- ReliabilityChapter 11- ReliabilityChapter 11- Reliability

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Quality Control, 8eQuality Control, 8e

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Quality Control, 8eQuality Control, 8e

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Besterfield: Quality Control, 8th ed.. © 2009 Pearson Education, Upper Saddle River, NJ 07458.All rights reserved

OutlineOutline

Fundamental Aspects Additional Statistical Aspects Life and Reliability Testing Plans Availability and Maintainability


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 ObjectivesLearning Objectives


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.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

Learning Objectives cont’d.Learning Objectives cont’d.


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 will perform its intended function for a stated period of time under specified operating conditions.

ReliabilityReliability


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.



There are four factors associated with Reliability:

1. Numerical Value.The numerical value is the probability

that the product will function satisfactorily during a particular time.




2. Intended Function.Product are designed for particular

applications and are expected to be able to perform those applications.




3. Life. How long the product is expected to last.

Product life is specified as a function of usage, time, or both.




4. Environmental ConditionsIndoors.Outdoors.Storage.Transportation.



Emphasis:

1.The Consumer Protection Act of 1972.

2.Products are more complicated.

3.Automation.

Achieving ReliabilityAchieving 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.

System ReliabilitySystem Reliability


RS = R1 R2 ... Rn

1 2 n

For a series systems, the reliability is the product of the individual components.

As components are added to the series, the system reliability decreases.

Series SystemSeries System


Rs = 1 - (1 - R1) (1 - R2)... (1 - Rn)

1

2

n

When a component does not function, the product continues to function, using another component, until all parallel components do not function.

Parallel SystemParallel System


Convert to equivalent series system

AA BB

CC

CCDD

RRAA RRBB RRCCRRDD

RRCC

AA BB C’C’ DD

RRAA RRBB RRDD

RRC’C’ = 1 – (1-R = 1 – (1-RCC)(1-R)(1-RCC))

Series-Parallel SystemSeries-Parallel System


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).

DesignDesign


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.

DesignDesign


The second most important aspect of reliability is the production process.

Emphasis should be placed on those components which are least reliable.

Production personnel.

ProductionProduction


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.

TransportationTransportation


Distributions Applicable to Reliability: Exponential distribution. Normal distribution. Weibull distribution.

Reliability Curves:Reliability Curves: The curves as a function of time.The curves as a function of time.

Additional Statistical AspectsAdditional 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) .



Failure-Rate Curve: It is important in describing the life-

history curve of a product. See Figure 11-2.

est

number of test failures rλ = =

sum of test times t +(n - r)T



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 CurveLife History Curve


“Infant mortality period”

Debugging Phase

Chance Failure Phase

Wear Out Phase



1. 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.



2. 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.

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 describe this phase.



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.

t

0

R(t)= 1.0 - f(t)dt

R(t)= 1.0 - P(t)

Normal Failure AnalysisNormal Failure Analysis


Exponential distribution:

RRtt = = e e –t/–t/өө

Where:

t: Time or cycles.

ө: Mean life.

Exponential Failure AnalysisExponential 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.

RtRt = = e e –(t/–(t/өө)ß)ß

Where ß is the Weibull slope.

Weibull Failure AnalysisWeibull Failure Analysis


Steps:

1. Assume values for the mean life ө.

2. These values are converted to the failure rate, l =1/ ө.

3. Calculate the expected average number of failures nTl.

4. From Table C of the Appendix using nTl and c value, get Pa.

OC Curve ConstructionOC Curve Construction


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 Life and Reliability Testing PlansPlans


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.



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.



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.



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 H108Handbook H108


The handbook is over 70 pages long. The time-terminated plan:

1. Stipulated producer’s risk, consumer’s risk, and sample size.

2. Stipulated producer’s risk, rejection number, and sample size.

3. Stipulated producer’s risk, consumer’s risk, and test time.

Handbook H108Handbook H108


Define customer performance requirements.

Determine important economic factors and relationship with reliability requirements.

Define the environment and conditions of product use.

Reliability ManagementReliability Management


Select components, designs, and vendors that meet reliability and cost criteria.

Determine reliability requirements for machines and equipments.

Analyze field reliability for improvement.

Reliability ManagementReliability Management


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 and Availability and MaintainabilityMaintainability


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.

AvailabilityAvailability


MTBFA

MTBM MTDT

Where:

MTBM = mean time between maintenance

MDT = mean down time

MTBF = mean time between failures

MTTR = mean time to repair

AvailabilityAvailability


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.

MaintainabilityMaintainability


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.

MaintainabilityMaintainability

quality control chapter 11- reliability powerpoint presentation to accompany besterfield quality...

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