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

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Production and Operations ManagementMGT613

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%

Production and Operations ManagementMGT613

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

.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.

Production and Operations ManagementMGT613

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

.90+.90(1--

.95+.92(1-

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.

Production and Operations ManagementMGT613

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

Production and Operations ManagementMGT613

Reliability = e -T/MTBF

1- e -T/MTBF

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

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

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

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.

Production and Operations ManagementMGT613

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

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

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)

Production and Operations ManagementMGT613

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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