# AACC Ancient Roman Mills Problem Analysis Pareto Positioning Error Excel Worksheet Using the provided pareto Excel template, create 8 technical problem are

AACC Ancient Roman Mills Problem Analysis Pareto Positioning Error Excel Worksheet Using the provided pareto Excel template, create 8 technical problem areas for your project, inventing the number of their associated occurrences, evaluating those areas that warrant attention. Problem areas can include maintenance and support areas. Total production time (up time + down time)
Total down time
Number of breakdowns
MTBF and MTTR – calculator
Value
250
40
16
Unit
Hours
Hours
Hours
Result from Calculation
Mean Time Between Failures (MTBF)
Mean Time To Repair (MTTR)
Value
13,1
2,5
Unit
Hours
Hours
System Availability
Operational Availability
0,84
0,84
©2011 Oskar Olofsson
World Class Manufacturing
Mean Time Between Failures (MTBF) and Mean Time To Repair (MTTR) are two important
KPI’s in plant maintenance.
MTBF = (Total up time) / (number of brekdowns)
MTTR = (Total down time) / (number of breakdowns)
Mean Time Between Failures & Mean Time To Repair – What do these mean?
Mean Time means, statistically, the average time.
Mean Time Between Failures (MTBF) is literally the average time elapsed from one failure to
the next. Usually people think of it as the average time that something works until it fails and
needs to be repaired (again).
Mean Time To Repair (MTTR) is the average time that it takes to repair something after a
failure.
For something that cannot be repaired, the correct term is Mean Time To Failure (MTTF).
Some would define MTBF  for repair-able devices  as the sum of MTTF plus MTTR. (MTBF
= MTTF + MTTR). In other words, the mean time between failures is the time from one failure
to another. This distinction is important if the repair time (MTTR) is a significant fraction of
MTTF.
Here is an example. A light bulb in a chandelier is not repairable, so MTTF is most
appropriate. (The light bulb will be replaced). The MTTF might be 10,000 hours.
On the other hand, without oil changes, an automobiles engine may fail after 150 hours of
highway driving  that is the MTTF. Assuming 6 hours to remove and replace the engine
(MTTR), MTBF is 150 + 6 = 156 hours.
Like automobiles, most manufacturing equipment will be repaired, rather than replaced after a
failure, so MTBF is the more appropriate measurement.
What is a Failure?
Failure can have multiple meanings. Let us briefly examine one devices failures:
An Uninterruptible Power Source (UPS) may have five functions under two conditions:
While the main power is available:
Allow power to flow from the main source to the machine being protected
Condition the power by limiting surges or brownouts
Store power in a battery, up to the batterys full charge
Store power in a battery, up to the batterys full charge
When the main power is interrupted:
Supply continuous power to the machine being protected
Emit a signal to indicate that the main power is off
There is no question that the UPS has failed if it prevents main power from flowing to the
machine being protected (function 1). Failures for functions 2, 3 or 5 may not be obvious,
because the protected machine is still running on main power or on the battery supply. Even
if noticed, these failures may not trigger immediate corrective measures because the
protected machine is still running and it may be more important to keep it running than to
repair or replace the UPS.
What is Availability?
The availability of a device is, mathematically, MTBF / (MTBF + MTTR) for scheduled
working time.
The automobile in the earlier example is available for 150/156 = 96.2% of the time. The repair
is unscheduled down time.
With an unscheduled half-hour oil change every 50 hours  when a dashboard indicator alerts
the driver  availability would increase to 50/50.5 = 99%.
If oil changes were properly scheduled as a maintenance activity, then availability would be
100%.
Why are these important?
Availability is a key performance indicator in manufacturing; it is part of the Overall
Equipment Effectiveness (OEE) metric.
A production schedule that includes down time for preventative maintenance can accurately
predict total production. Schedules that ignore MTBF and MTTR are simply future disasters
awaiting remediation.
How to calculate actual MTBF
Actual or historic MTBF is calculated using observations in the real world. (There is a
separate discipline for equipment designers to predict MTBF, based on the components and
anticipated workload).
Calculating actual MTBF requires a set of observations; each observation is:
Uptime_moment: the moment at which a machine began operating (initially or after a repair)
Downtime_moment: the moment at which a machine failed after operating since the previous
uptime-moment
So each Time Between Failure (TBF) is the difference between one Uptime_moment
observation and the subsequent Downtime_moment.
Three quantities are required:
n = Number of observations.
ui = This is the ith Uptime_moment
di = This is the ith Downtime_moment following the ith Uptime_moment
So MTBF = Sum (di  ui)/ n , for all i = 1 through n observations. More simply, it is the total
working time divided by the number of failures.
Oskar Olofsson, 2010
Class 7
Testing and Reliability
Reading
Simulation is the process of designing and utilizing an
operational model of a system to conduct experiments for
the purpose of either understanding the behavior of the
system or evaluating alternative strategies and/or system
design configurations.
Simulation methods can be applied in the development of
three-dimensional computer-aided design (CAD) models
Design engineers can visually see the system
configuration, as an entity, during the early stages of
preliminary design. This will, of course, enable the
designer to evaluate different alternatives
Section 4.4.
Simulation
Availability

Availability represents the probability that the system is capable of conducting its required
function when it is called upon

Availability is a function of reliability, but it is also a function of maintainability

Inherent availability is the steady state availability when considering only the corrective
maintenance (CM) downtime of the system. This classification is what is sometimes referred
to as the availability as seen by maintenance personnel.
? MTBF  Mean Time Between Failure = Uptime/Number of System Failures
? MTTR  Mean Time to Repair = Corrective Maintenance Downtime/Number of System Failures
? AI = MTBF/(MTBF + MTTR)

For a single component, the inherent availability can be computed by:
? Operational availability is a measure of the “real” average availability over a period of time and
includes all experienced sources of downtime, such as administrative downtime, logistic downtime,
etc.

Operational availability is the ratio of the system uptime to total time.
Reliability,
availability and
maintainability
(RAM)
Reliability, in itself, does not account for any repair actions
that may take place. Reliability accounts for the time that it
will take the component, part or system to fail while it is
operating. It does not reflect how long it will take to get the
unit under repair back into working condition.
As the time to repair increases, the availability decreases.
Even a system with a low reliability could have a high
availability if the time to repair is short.
http://www.weibull.com/hotwire/issue26/relbasics26.htm
Reliability represents the probability of components, parts
and systems to perform their required functions for a
desired period of time without failure in specified
environments with a desired confidence.
Reliability Testing can be performed at the
component, subsystem, and system level
throughout the product or system lifecycle

Reliability testing provides the most detailed
form of reliability data

A properly designed series of tests, can
generate data that would be useful in the
implementation of a reliability growth tracking
program.

This will provide information that will be
helpful in making management decisions
regarding scheduling, development cost
projections and so forth.

This information will also be useful in planning
the development cycle of future products.
Reliability testing
http://www.weibull.com/hotwire/issue41/hottopics41.htm

Types of
reliability
tests
Reliability growth testing is part of a reliability growth program in which
items are tested throughout the development with the intent of assessing
reliability increases due to improvements in the manufacturing process (for
hardware) or software quality (for software).
Maintainability Testing assesses the system diagnostics capabilities,
physical accessibility, and maintainer training by simulating hardware or
software failures that require maintainer action for restoration
etc
https://www.sebokwiki.org/wiki/Reliability,_Availability,_and_Ma
intainability
Accelerated life testing is performed by subjecting the items under test to
increased environmental conditions well above the expecting operating
range and extrapolating results
http://www.weibull.com/hotwire/issue41/hottopics41.htm
Reliability life tests are used to empirically assess the time to failure for
non-repairable products and systems and the times between failure for
repairable or restorable systems.
Failure modes and effects and criticality
analysis (FMECA)

Methodologies designed to identify potential failure modes for a product or process, to
assess the risk associated with those failure modes, to rank the issues in terms of
importance and to identify and carry out corrective actions to address the most serious
concerns.

FMECA incorporates some method to evaluate the risk associated with the potential
problems identified through the analysis

It can contribute to improved designs for products and processes, resulting in higher
reliability, better quality, increased safety, enhanced customer satisfaction and reduced
costs. The tool can also be used to establish and optimize maintenance plans for
repairable systems and/or contribute to control plans and other quality assurance
procedures.
The Pareto principle also known as the 80-20 rule states that 80% of the
effects are coming from 20% of the causes.
As a tool in Six Sigma, Pareto is part of the quality control tools that are
derived from historical data in order to come up with efficient and most
appropriate actions to address most common and impacting failures.
With the use of Pareto, scarce resources are efficiently allocated.
6.2
To communicate data
B.1
Used to figure out what the most significant problem is

Pareto Chart and Analysis

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Pareto
principle

20% of criminals commit 80% of crimes

20% of drivers cause 80% of all traffic accidents

80% of pollution originates from 20% of all factories

20% of a companys products represent 80% of sales

20% of employees are responsible for 80% of the results

20% of students have grades 80% or higher

Pareto 80 20 rule examples: Be more efficient and productive

Pareto applies to a variety of situations
B.1
For a continuous process improvement
program, an analyst may wish to rank the
problem areas on the basis of relative
importance, the higher-ranked problems
requiring immediate attention.
6.2
Pareto
analysis
A Pareto analysis approach might be
beneficial in creating visibility pertaining
to degrees of importance. The highestranked items need the most
management attention.
1.
Create a vertical bar chart with causes on the xaxis and count (number of occurrences) on the yaxis.
2.
Arrange the bar chart in descending order of
cause importance that is, the cause with the
highest count first.
3.
Calculate the cumulative count percentage for
each cause in descending order. Percentage
calculation: {Individual Cause Count} / {Total
Causes Count}*100
4.
Plot the cumulative count percentage of each
cause on the x-axis
5.
Draw a line at 80% on the y-axis
6.
This point on the x-axis separates the important
causes on the left (vital few) from the less
important causes on the right
https://www.projectsmart.co.uk/pareto-analysis-step-by-step.php
Pareto analysis
Creating a pareto
chart in excel
Theres a template provided for the
Assignment, but this is a more primitive
example
1.
Set up your data and sort from
largest to smallest. Use =SUM( ) to
sum values
Example step 2
Create a Cumulative Amount column.
Start with the first amount, 67 or B3.
Each amount builds on the one before it.
In C4, type =C3+B4 then press Enter.
Step 3
Next, create a Cumulative Percent
column. You can use the amount total
and each cumulative amount to build this
column. In the function bar for D3, type
=C3/\$B\$9 and Enter. The \$ figures
create an absolute reference so that the
Amount total (B9) does not change when
you drag the formula down.
Step 4
Highlight your data (from B2 to D10 in
this example).
Step 5

Right click in the Chart Area and
select Select Data. The Select Data
Source dialog box appears.
Select Cumulative Amount and
choose Remove. Then choose OK
Step 6

Click in the chart and use your
keyboards arrow keys to toggle
between areas on your chart. When
Cumulative % is highlighted on the xaxis, hover and right click Change Chart
Series Type. Its hard to see right now
but you should see it along the x-axis.
Step 7

You now have a bar chart with a flat
line graph along the x-axis. In order to
get a curve to our Cumulative % line,
we need the other vertical axis.

Right click on the Cumulative % line
and choose Format Data Series.
The Format Data Series dialog box
appears.

Choose Secondary Axis under Series
Options then click Close.
Using the provided pareto Excel template, create
8 technical problem areas for your project,
inventing the number of their associated
occurrences, evaluating those areas that warrant
attention. You do not need to perform RAM and
FMECA calculations. Problem areas can include
maintenance and support areas.
Post your Assignment 4 in the Discussion
Board. Everyone should review each other’s
submissions in order to learn from each
other. Post comments, questions, suggestions to
each other as part of your class participation.
Assignment 4
Next class Lesson 8 July 6

Prior to Lesson 8 Review Sections 1.4, B.1 and provided Six Sigma Continuous
Improvement
PROBLEM ANALYSIS – PARETO
PROBLEM AREAS
40
100%
90%
35
80%
30
70%
25
60%
20
50%
40%
15
30%
10
20%
5
10%
0
0%
problem 1 problem 2 problem 3 problem 4 problem 5 problem 6 problem 7 problem 8 problem 9 problem problem
10
11
OCCURRENCES
CUMULATIVE PERCENT
Pareto Chart for Cumulative Percent of number of Occurrences of all Problem Areas is in this cell.
PROBLEM DATA
PROBLEM AREA
OCCURRENCES
PERCENT OF TOTAL
CUMULATIVE PERCENT
problem 1
4
2,30%
2,30%
problem 2
10
5,75%
8,05%
problem 3
2
1,15%
9,20%
problem 4
25
14,37%
23,56%
problem 5
13
7,47%
31,03%
problem 6
8
4,60%
35,63%
problem 7
28
16,09%
51,72%
problem 8
32
18,39%
70,11%
PROBLEM AREA
OCCURRENCES
PERCENT OF TOTAL
CUMULATIVE PERCENT
problem 9
11
6,32%
76,44%
problem 10
6
3,45%
79,89%
problem 11
35
20,11%
100,00%
Page 2 of 2

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