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The formula for the moving average is:Measuring Reliability, AVAILABILITY

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Production and Operations Management­MGT613
VU
Lesson 14
We often come across statementssimilar to these, this bulb(product) is not as reliable as the previous
bulb or my newspaper's analysis and report writing (service) is not as reliable as my friend's newspaper
analysis. These two sentencessummarize what human mind is looking for? That is reliability.
Reliability is sought by customers from allorganizations. Interestingly enough, the personnel working
inside the organization whether engineers or managers also seekreliability of operations, management,
IT, Accounting and other host of functions that help an organization perform its day to day routine
activitieseffectively. Reliability is no longerthat art which was considered to be possessed by a family
of skilled craftsman rather hasnow evolved in to a vast andever increasing field of Engineering.
Reliability in general and reliability engineering in fact play a very criticalpart in an organizations
product or service gaining competitive advantage over the organizations competitors.
Reliability
We often overlook the concept of Reliability and confuse it with the concept of safety. Safety is one
smallaspect of reliability. Reliabilityneeds to be looked into with the important perspective of failure of
a product /service and normal operatingconditions for thatparticular product or service. Lets us briefly
look at the definitions of reliability, alongwith what is termed as failure and what are the normal
operatingconditions for a product.
·Reliability: The ability of a product,part, or system to performits intended function under a prescribed
set of conditions
·Failure: Situation in which a product,part, or system does notperform as intended
·Normaloperating conditions: Theset of conditions underwhich an item's reliability is specified e.g.
an automobile designed for operation in Europe may not fulfillits intended useful service in Pakistan.
SO IT HAS THE POTENTIAL TO FAIL AND BE LESS RELIABLE. Kindly pay more attention to the
wordpotential here, potential refers to something hidden or attached either to the performance or
operations of a product. A bank servicingits client if fails to provide reliable normaloperating service
canlead to disastrous financialconsequences for itscustomers similarly if a pharmacy starts dispensing
expired medicines it can cause serioushealth hazards to itscustomers. All products and servicescarry
with them the potential of doing something harmful if they are unable to function according to normal
operatingconditions. The thing or characteristic or quality that avoids something aberrant happening is
known as RELIABILITY.
MeasuringReliability
Reliabilitycan be measured, quiteeffectively by making use of the concept of chance or probability, in
other words we can quantify the concept of reliability in terms of statisticalprobability. Often products
aremade more reliable (dependable andsafe) by increasing the safe operations of certain criticalparts
by increasing the presence of such importantelements. E.g. a computer beingused as a server may be
havingtwo or more uninterrupted powersupply units ensuring itssafe operations. Similarly,building
code requirements in the past followed a more stringent and increased factor of safety, often leading to
redundancy (subassembly or components or elementswhich were never broughtinto action or play or
operations or never used in the normalroutine operations of an assembly). In ourearlier lectures we
covered the important concept of Tacguchi method which made us realize that a product or service
should be able to provide what it promises under a welldefined range of operating conditions. A car
manufactured in Lahore should be able to provide the same service in northernareas of Pakistan or
coastalbelt with same reliabilityand robustness.
We now quantify Reliability in terms of Probability. E.g. If a component or item has a reliability of 0.9,
it means that it has a 90%probability of functioning as intended, the probability it will fail is 1-0.9 =
0.1which is 10%
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Production and Operations Management­MGT613
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We can use Probability in twofunctions
1. The probability that the product or system willfunction whenactivated.
2. The probability that the product or system willfunction for a given length of time
Reliabilityand ProbabilityBasics
Probability is used to explain reliability by taking into account the factthat the product or systemwill
Functionwhen activated or Functionfor a given length of time.This also means we need to know about
the independent events as well as redundancy.
NowIndependent events are thoseevents whose occurrence or nonoccurrence do not influence each
other,also Redundancy is the use of backupcomponents to increasereliability.
Let'sfirst take into account the fact that Probability that a system will function whenactivated.
RULE 1
If two or more events areindependent and success is defined as probability thatall of
theevents, occur then theprobability of success is equal to the product of probabilities
Lamp
Lamp
.90 x .80 = .72
.80
.90
Boththe lamps should be lighted up in order to ensure visibility.Reliability of the
Systemequals (Reliability of component1)(Reliability of Component 2)
RULE 2
If two events are independent and "success" is defined as
probabilitythat at least one of the events willoccur, then the
probability of either one plus 1.00 minus that probability
multiplied by the other probability
Lamp 2 is an example of redundancy here, as it being backup
Lampincreases the reliability of the system from 0.9 to 0.98
.80
Lamp 2 (backup)
.90 + (1-.90)*.80 = .98
.90
Lamp 1
RULE 3
·If three events are involved andsuccess is defined as the probabilitythat at least one of them occurs,
the probability of success is equal to the probability of the first one ( any of the events), plus the product
1.00 minus that probability and the probability of the second event ( any of the remaining events), plus
the product of 1.00 minus each of the two probabilities and the probability of third event and so on.This
rulecan be extended to cover more than three events.
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Production and Operations Management­MGT613
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Lamp 3 (backup for Lamp 2)
.70
Lamp 2 (backup for Lamp1)
.80
1 ­ P(all fail)
.90
1-[(1-.90)*(1-.80)*(1-.70)] = .994
Lamp 1
Rule 3
Example S-1 Reliability
Determinethe reliability of thesystem shown
.92
.90
.98
.90
.95
Example S-1 Solution
Thesystem can be reduced to a series of three
components
.9
.90+.90(1--
.95+.92(1-
8
0.9)
.95)
.98 x .99 x .996 =
.966
2. Time based Reliability"Failure Rate"
Thesecond measurement of reliability is carried out in terms of the time. We all know that component,
products or even services have limited lives.They function or fulfilltheir expected work in some
normaloperating conditions. A product or service's working life whenexhausted or endingprematurely
is often referred to as Failure rate.
Let us go back to the first statement of the lecture, when we made a comment that this bulb is less
reliable, if we are investigate further, we can take up the example in a more detail manner. Say if 1000
bulbsare being manufactured at a facility in Karachi, these bulbs once manufactured are not sent to the
customerswithout quality checks. Theyare made to go throughstringent testing, afterconducting
statistical analysis. The manufacturers can identify the time based reliability or failure of the bulb.This
is quite simple as well as a standard procedure in determining the expected life of any product. In fact
thishas been a part of manufacturing industry foryears now. Some of the bulbswould fail in testing and
wouldnot be shipped. As a part of processcontrol, we can plot the testing of bulbs.
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Production and Operations Management­MGT613
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Infant
Failures
Few(random)
due
mortality
to wear-out
Time,
Thefigure above shows a bathtubshape and thus rightly is referred to as the Bathtub curve. On the Y
axis we represent the Failure rate and on the X axis we represent the Time. A careful look at the graph
wouldhelp us to identify the three phases
Phase I near the origin is calledInfant Mortality.
Phase II in the middle refers to few random failures.
Phase III at the far end from the originrepresent failures due to wear out.
Whatcan we observe in the BathTub Curve?
In Phase I : One can easilysee that quite a few of the products fail shortly putinto service, notbecause
they wear out but they aredefective to beginwith.
In Phase II: The rate of failuredecreases rapidly once the truly defective items areWEEDED OUT
(Eliminatinginferior products/Services). During phase II, there are fewer failuresbecause the
inferior/defectivehas already been eliminated.This phase is free of wornout items and as seen is the
LONGESTPERIOD here.
In Phase III: In the third phase,failure occurs because the products have completed the normal life of
their service life and thus wornout. As we can see the graphs steeps up in thisphase indicating an
increase in the failure rate.
Thequestion now is how can we collect information on the distribution,length of each phase? We
knowthat all this requires collection and analysis of data. we are interested in calculating mean time
between failure for eachphase.
If we analyze phases I and III separately and observe them in exploded or enlarged views we may be
able to trace the presence of exponential curve in both the phases. Its clear that in Phase I we observe a
clear exponential decrease in the time expected of a products life.
ExponentialDistribution FOR INFANT MORTALITY STAGE
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Reliability = e -T/MTBF
1- e -T/MTBF
T
Time
EXPONENTIALDISTRIBUTION
Equipmentfailures as well as productfailures may occur in thispattern. In such a case the exponential
distribution,such as depicted on the graph. We can identify two phasesPhase I and Phase II. Phase I
indicates the probability that equipment or product put into service at time 0 will fail beforespecified T
is ability that a product will last until Time T and is represented by area under the curve between O and
T.
Phase II indicates that the curve to the right of Point T increases in Timebut reduces in reliability. We
can calculate the reliability or probability values using a table of exponential values. An exponential
distribution is completely described using the distribution mean, whichreliability engineers call it the
MEAN TIME BETWEEN FAILURES. Using T to represent the length of service, we can calculate P
beforefailure as P ( No failure beforeT)= e-T/MBTF.
NORMALDISTRIBUTION
Reliability
0
z
Product failure due to wear out can be determined by using normaldistribution. From ourknowledge of
statistics we already know that the statistic table for a standardized variable Z represents the areaunder
the normal curve fromessentially from the left end of the curve to a specified point z, where z is a
standardized value computing use
z=
T-Mean wear out time
Std Deviation of Wear outTime
Thus we must know the mean and the standard deviation of the distribution.Again for the sake of easy
reference we can use the statisticaltable available to us wouldalways show the area thatlies to the left
of Z.
To obtain a probability that service life will not exceed,some value T, compute Z andrefer to the table.
To find the reliability forsome T, subtract thisprobability from 100 percent.
To obtain the value of T thatwill provide a givenprobability, locate the nearestprobability under the
curve to the left in the statisticaltable.
Then the corresponding z in the precedingformula and determine T.
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z=
T-Mean wear out time
Std Deviation of Wear outTime
Example
Themean life of a certain steamturbine can be modeled using a normal distribution with a mean life of
sixyears, and a standard deviation of one year. Determine each of the following:
Theprobability that a stemturbine will wear out beforeseven years of service.
To probability that a steamturbine will wear out afterseven years of service ( i.e.find its reliability)
The service life will provide a wear-out probability of 10 percent.
·Wearout life mean= 6 years.
·Wearout life standard deviation = 1 year
·Wear out life is normallydistributed.
ForNormal Distribution, we can compute Z and use it to obtain the probability directly from a statistical
table
z=
T-Mean wear out time
Std Deviation of Wear outTime
= 7-6/1= +1.00
Since P (T<7) =0.8413
Also,subtract the probability (reliability)determined in part a from100 percent
1.00-0.8413
= 0.1587
Reliability=0.1587
0
z
We can see that on the Z scale,both a and b gives1.00
·Use the normal table and find the value of z that corresponds to an area under the cure of 10%
We are focusing on 10 % of the areaunder the curve and checkonly the left hand side
Z=-1.28=(T-6)/1
Thus T =6-1.28=4.72
We calculate and find value of T is 4.72
AVAILABILITY
Thefraction of time a piece of equipment is expected to be available foroperation.
Mathematically, If we represent mean time between failures by MTBF and meantime to repair by
MTR then
Availability = (MTBF)/(MTBF + MTR)
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ImprovingReliability
We should develop the ability to understand the importance of reliability and at the same time identify
the ways in which Reliability can be improved in the following generic ways.
1. Component design : Parts of a car
2. Production/assembly techniques: No reworks alsofool proof assembly.
3. Testing :for trouble freefinal product
4. Redundancy/backups: not possible all the time but common remedy.
5. Preventive maintenance procedures
6. User education( operating manuals)
7. System design ( we will discuss in later chapters, a senior managementissue, but indicativethat
reliability is always considered VIP)
8.  Research & Development (R&D) : Organized efforts to increase scientificknowledge or
productinnovation & mayinvolve:
Basic Research advances knowledgeabout a subject without near-term expectations of commercial
applications.
·AppliedResearch achieves commercial applications.
·Development converts results of applied researchinto commercialapplications.
CONCLUSION
It is important to understand the concept of reliability in terms of normaloperating conditions as well as
safe operations. Services in general andProducts in particular are designed to provide thisopportunity
to the fullest. It is recommended to invest more in R &D, with regards to increase in Reliability.Quality
checksshould be incorporated at suitableplaces to enhance product and services reliability.
It is also suggested thatemphasis should be shiftedaway from short term performance to both short as
well as long term Performance improvementwhile formulating a reliabilitybased operations strategy.
Operations Manager should work towards continual and gradual improvements instead of big bang
approach. They should work to shorten the product life cycle (not the products life) as it increases
products safety as well as reliability. Operations side should be encouraged to potfor component
commonalitycontinual improvement and shorten time to market.
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Table of Contents:
  1. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT
  2. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Decision Making
  3. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Strategy
  4. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Service Delivery System
  5. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Productivity
  6. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:The Decision Process
  7. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Demand Management
  8. Roadmap to the Lecture:Fundamental Types of Forecasts, Finer Classification of Forecasts
  9. Time Series Forecasts:Techniques for Averaging, Simple Moving Average Solution
  10. The formula for the moving average is:Exponential Smoothing Model, Common Nonlinear Trends
  11. The formula for the moving average is:Major factors in design strategy
  12. The formula for the moving average is:Standardization, Mass Customization
  13. The formula for the moving average is:DESIGN STRATEGIES
  14. The formula for the moving average is:Measuring Reliability, AVAILABILITY
  15. The formula for the moving average is:Learning Objectives, Capacity Planning
  16. The formula for the moving average is:Efficiency and Utilization, Evaluating Alternatives
  17. The formula for the moving average is:Evaluating Alternatives, Financial Analysis
  18. PROCESS SELECTION:Types of Operation, Intermittent Processing
  19. PROCESS SELECTION:Basic Layout Types, Advantages of Product Layout
  20. PROCESS SELECTION:Cellular Layouts, Facilities Layouts, Importance of Layout Decisions
  21. DESIGN OF WORK SYSTEMS:Job Design, Specialization, Methods Analysis
  22. LOCATION PLANNING AND ANALYSIS:MANAGING GLOBAL OPERATIONS, Regional Factors
  23. MANAGEMENT OF QUALITY:Dimensions of Quality, Examples of Service Quality
  24. SERVICE QUALITY:Moments of Truth, Perceived Service Quality, Service Gap Analysis
  25. TOTAL QUALITY MANAGEMENT:Determinants of Quality, Responsibility for Quality
  26. TQM QUALITY:Six Sigma Team, PROCESS IMPROVEMENT
  27. QUALITY CONTROL & QUALITY ASSURANCE:INSPECTION, Control Chart
  28. ACCEPTANCE SAMPLING:CHOOSING A PLAN, CONSUMER’S AND PRODUCER’S RISK
  29. AGGREGATE PLANNING:Demand and Capacity Options
  30. AGGREGATE PLANNING:Aggregate Planning Relationships, Master Scheduling
  31. INVENTORY MANAGEMENT:Objective of Inventory Control, Inventory Counting Systems
  32. INVENTORY MANAGEMENT:ABC Classification System, Cycle Counting
  33. INVENTORY MANAGEMENT:Economic Production Quantity Assumptions
  34. INVENTORY MANAGEMENT:Independent and Dependent Demand
  35. INVENTORY MANAGEMENT:Capacity Planning, Manufacturing Resource Planning
  36. JUST IN TIME PRODUCTION SYSTEMS:Organizational and Operational Strategies
  37. JUST IN TIME PRODUCTION SYSTEMS:Operational Benefits, Kanban Formula
  38. JUST IN TIME PRODUCTION SYSTEMS:Secondary Goals, Tiered Supplier Network
  39. SUPPLY CHAIN MANAGEMENT:Logistics, Distribution Requirements Planning
  40. SUPPLY CHAIN MANAGEMENT:Supply Chain Benefits and Drawbacks
  41. SCHEDULING:High-Volume Systems, Load Chart, Hungarian Method
  42. SEQUENCING:Assumptions to Priority Rules, Scheduling Service Operations
  43. PROJECT MANAGEMENT:Project Life Cycle, Work Breakdown Structure
  44. PROJECT MANAGEMENT:Computing Algorithm, Project Crashing, Risk Management
  45. Waiting Lines:Queuing Analysis, System Characteristics, Priority Model