Optimizing Unilever’s Capital and Emergency Spare Stock Sizes
By: Kenneth Liang
A thesis submitted in partial fulfilment of the requirements for the degree of
BACHELOR OF APPLIED SCIENCE
Supervisor: Andrew K.S. Jardine
Department of Mechanical and Industrial Engineering
Acknowledgments
I would like to first thank Antanio Santos at Unilever Rexdale who provided me all the
information and guidance that I needed to complete my work. Without his discussions and
insights this thesis would not have been possible. I would like to further thank Professor Andrew
Jardine and Dr. Behzad Ghodrati who both supported by thesis. These individuals gave me
encouragement and the direction I needed on how to complete my thesis. Lastly, I would like to
thank Dr. Dragan Banjevic who gave me a copy of the SMS software which was created by the
group C-MORE at the University of Toronto.
Table of Contents Chapter 1 - Introduction ..............................................................................................................1
1.1 Abstract .................................................................................................................................1 1.2 Statement of objectives .........................................................................................................1 1.3 Background Information ........................................................................................................3
Chapter 2 - Literature Review ......................................................................................................5 2.1 Rethinking Pareto Analysis: maintenance applications of logarithmic scatter plots .............5 2.2 Economic Order Quantity ....................................................................................................13 2.3 An inventory control system for spare parts at a refinery ....................................................15
Chapter 3 - Prioritizing Unilever’s Spare Parts Inventory ......................................................18 3.1 Machine Descriptions ...........................................................................................................18 3.2 Standard Pareto Analysis .....................................................................................................21 3.3 Prioritizing Spare Parts with Jack Knife Diagrams ..............................................................24 3.4 Advantages/Disadvantages Pareto Analysis and Jack Knife Diagrams ...............................27 3.5 Using Jack Knife Diagram Matlab Code .............................................................................28
Chapter 4 - Optimizing Unilever’s Stock Sizes .........................................................................30 4.1 Analysis of Unilever’s Fast Moving Spare Parts .................................................................30 4.2 Analysis of Unilever’s Slow Moving Spare Parts ................................................................35
4.2.1 Machine Descriptions ...................................................................................................35 4.2.2 Data for the Palletizer and Trunkline ............................................................................36 4.2.3 Results of Analysis .......................................................................................................38
Chapter 5 - Conclusions ..............................................................................................................42 5.1 Conclusions and Recommendations for optimal stock sizes ...............................................42 5.2 Future work ..........................................................................................................................43
References .....................................................................................................................................44 Appendix .......................................................................................................................................45
Appendix A–Summary of Pareto Analysis for spare parts other than MPU and Bander ..........45 Appendix B–Raw Data for MPU Pareto Analysis .....................................................................58 Appendix C–Raw Data for Bander Pareto Analysis ..................................................................62 Appendix D–Raw Data for MPU Jack-Knife Diagram .............................................................65 Appendix E–Raw Data for Bander Jack-Knife Diagram ...........................................................67 Appendix F–Matlab program for creating Jack-Knife Diagrams ..............................................70 Appendix G–Data for MPU Pin Blade Fastener ........................................................................72 Appendix H–Jack Knife Diagrams and Summary of Stock Size optimization of spare parts ...73 Appendix I–Matlab program for Fitting Probability Distributions ............................................89
List of Tables and Figures Figure 1 – X-Y dispersion plot of mean repair times versus number of failures ...........................10 Figure 2 – Log Scatter Plot of mean repair times versus number of failures ................................11 Figure 3 – Jack Knife Diagram ......................................................................................................12 Figure 4 – Inventory Levels for the EOQ Model [2] .....................................................................13 Figure 5 – Jack Knife Diagram - MPU ..........................................................................................26 Figure 6 – Jack Knife Diagram – Bander ......................................................................................26 Figure 7 – Probability Density Graph for MPU Pin Blade Fastener .............................................34 Figure 8 – Cumulative Density Graph for MPU Pin Blade Fastener ............................................34 Picture 1 – Picture of Line 7 Margarine Processing Unit (MPU) ..................................................19 Picture 2 – Picture of Line 15 Bander Unit ...................................................................................20 Picture 3 – Matlab Variable Console .............................................................................................29 Picture 4 – Matlab Variable Editor ................................................................................................29 Picture 5 – Matlab Command Window .........................................................................................29 Picture 6 – Matlab Variable Console – Lead Time Demand .........................................................32 Picture 7 – Matlab Variable Editor – Lead Time Demand ............................................................32 Picture 8 – Matlab Command Window – Distribution Function ...................................................32 Picture 9 – KS Test Results ...........................................................................................................33 Picture 10 – EOQ Inputs ................................................................................................................33 Picture 11 – EOQ and Re-Order Point Results ..............................................................................33 Picture 12 – Picture of the Line 1 Palletizer ..................................................................................35 Picture 13 – Picture of the Trunkline .............................................................................................36 Table 1 – Unplanned Downtime for Line 2 equipment ...................................................................6 Graph 1 – Pareto Histogram of unplanned Line 2 downtime (2007) ..............................................7 Graph 2 – Pareto Histogram of unplanned MPU downtime (2008) ..............................................22 Graph 3 – Pareto Histogram of unplanned Bander downtime (2008) ...........................................23 Graph 4 – Pareto Histogram of MPU Part Failure Frequency .......................................................27 Graph 5 – Instantaneous Reliability of Palletizer Motors with 0 or 1 inventory spares and a 4 day lead time .........................................................................................................................................39 Graph 6 – Instantaneous Reliability of Trunkline Gearboxes with 0, 1 or 2 inventory spares and a 11 day lead time .............................................................................................................................40 Graph 7 – Instantaneous Reliability of Trunkline Gearboxes with 0 or 1 inventory spares and variable lead time ...........................................................................................................................41
Chapter 1 - Introduction
1.1 Abstract
In today’s trying economic times company’s world-wide face fierce competition and must do
whatever they can to stay afloat during this recent 2009 recession. With companies like General
Motors nearing bankruptcy, tight credit markets and billion dollar corporate bailout packages it is
even more apparent now that inventory management is an important factor for any company’s
balance sheets and controlling costs. The reasons for inventory management are elegantly
capture by Jeffery Liker in his book “The Toyota Way: 14 Management Principles from the
World’s Greatest Manufacturer”. Liker states the following reasons why companies must control
inventory:
1. Reducing inventory frees up working capital that would be normally tied up in spare
parts inventory
2. The greater the inventory the greater the material handling costs
3. Inventory takes up space and deteriorates causing more scrap/rework
This thesis will compare the Pareto Analysis with Jack Knife Diagrams to determine which
method is superior for prioritizing spare parts. The thesis will further optimize Unilever parts
inventory based on the spare parts that are identified in the superior prioritizing method. Lead
time demand modelling technique introduced by Rommert Dekker will be evaluated using real
data provided by Unilever.
1.2 Statement of objectives
Unilever operates a spare parts store with 6,787 stock keeping units (SKU’s) in order to maintain
all the machinery and assets necessary for margarine production. As of Sept 2008, it currently
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has 1.45 million (CAD) dollars in spare parts inventory. Unilever’s ideal goal is to maximize the
availability of parts so that machine downtime is avoided while minimizing their inventory cost.
There is however an inherent flaw in this goal. Increasing the probability that demand for a spare
part is satisfied at any given time also increases inventory and ties up capital. A more realistic
goal then is to find an optimal balance between maximizing availability of parts and minimizing
cost that Unilever is willing to accept. This is the overall goal that the thesis student will attempt
to achieve with the work and methodologies in this thesis. As mentioned above there are
thousands of parts the thesis student must consider. As such the thesis student cannot provide a
concrete target for cost savings and percentage of availability for spare parts. Sub-goals must be
evaluated for each individual part and must match up with the overall goal. For example,
Unilever maintains parts called Votators which are highly critical to Unilever’s operation.
Downtime of this part is very detrimental and can cost Unilever hundreds of thousands of dollars
in lost production. In this case, one would want to optimize for availability of parts rather than
inventory cost minimization. This goal however may be different when looking at other parts.
Unilever sets a minimum and maximum stock amount for each part. These stock quantities for
parts were initially only based on the frequency of Preventive Maintenance (PM) records and
what parts were needed for that PM. The maximum quantity was set in an ad hoc manner
governed by what has been done in the past. Consequently, the intended objective of this thesis is
twofold. First, prioritize the spare parts to determine which parts in Unilever’s inventory have the
most impact on cost minimization and parts availability. Second, optimization stock sizes for the
spare parts that were identified using valid and proven methodologies for inventory management.
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1.3 Background Information
This section of the thesis will provide the reader with a general overview of Unilever Rexdale’s
spare parts store operation. In order to fully understand how demand for spare parts is generated,
a review of the spare parts store at Unilever Rexdale was completed. This review provided the
thesis student with a basic understanding of how the spare parts store operates, what typical tasks
and activities are done and by whom. The review also exposed important factors that the thesis
student will need to address such as variable number of stock keeping units (SKU) and duplicate
spare parts.
Demand for parts is generated when a work order (WO) is issued to a tradesperson such as a
mechanic or electrician. A WO “is an internal request for maintenance or repair of equipment
and machinery” as defined by Rexdale’s Reliability Coordinator, Andrew Vuong. The WO
describes the type of maintenance work that is to be done by a tradesperson. The WO does not
however explain how the work is to be completed. It is up to the tradesperson to decide what
parts are needed, what tools are needed and thus how to complete the WO. Work orders
themselves are issued for any number of reasons. For instance, they are issued to repair machine
breakdowns, future planning such as a summer maintenance shutdown or to complete preventive
maintenance procedures. Demand for WO’s is important as it is directly related to demand for
spare parts. Also, future planning and regular preventive maintenance divulges information on
seasonal trends in demands for spare parts.
Once a WO has been issued to a tradesperson, they must decide what part(s) they will need to
complete the job and properly obtain it from the parts store. The tradesperson must fill out a parts
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removal form before physically removing the part(s) from the store. This step is to ensure that
accurate inventory levels are maintained in the computerized maintenance management system
(CMMS). Reordering of parts is automatically done through the CMMS once the stock size for a
particular part reaches a certain reorder level.
Management of inventory is a difficult task especially if the number of stock keeping units
(SKU) varies between each month. According to Antonio Santos, Unilever’s store manager,
“There are over 14,000 SKU’s in Unilever’s CMMS. Though, roughly 6,700 are active in any
given month”. There are two reasons why parts can become deactivated. First, parts can become
obsolete and no longer used. Second, similar parts may be obtained at a cheaper price from a
different supplier/vendor. In both cases deactivated parts are physically no longer stocked in the
parts store. A solution to the varying SKU sizes is to simply take a snap shot of Unilever’s
inventory for a given month and optimize only those SKU’s. Any new part SKU’s that are added
in the future should then be considered on a case by case basis only if time permits.
Furthermore, Unilever tracks duplicate parts in their CMMS system. A new part has a different
SKU number than compared to the same part if it is repaired or reconditioned. There are two
reasons why reconditioned parts have different SKU numbers. First, these parts have a different
value (in terms of dollars) than parts that are new. Second, parts can be reconditioned by
different suppliers/vendors. A solution for duplicate parts is to treat them as separate entities
since their dollar value, failure rate and life spans are different.
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Chapter 2 – Literature Review
2.1 “Rethinking Pareto analysis: maintenance applications of logarithmic scatterplots” [1]
2.1.1 Pareto Analysis
A Pareto Analysis is a statistical technique for prioritization spare parts. From a large population
of spare parts it picks a select few that produce a significant overall effect.
“Italian engineer Vilfredo Pareto (1842-1923) constructed histograms of the distribution
of wealth in Italy and concluded that 80 percent of the country’s wealth was owned by 20
percent of the nation’s population. In maintenance engineering Pareto’s 80:20 rule is
commonly used for identifying those failures responsible for the majority of equipment
maintenance cost or downtime.” [1]
There are seven steps to identifying the important causes using Pareto Analysis [1]:
1. Form a table listing the spare parts, their frequency and their downtime as a percentage.
2. Arrange the spare parts in decreasing order of importance, i.e. the highest downtime first.
3. Add a cumulative downtime percentage column to the table.
4. Plot with causes on the x-axis and cumulative percentage on the y-axis.
5. Join the cumulative points to form a curve.
6. Plot (on the same graph) a bar graph with spare parts on the x-axis and percent frequency
on the y-axis.
7. Draw a line (parallel to the x-axis) at 80% on the y-axis until it hits the cumulative curve.
Then drop the line at the point of intersection with the curve to the x-axis. This point on
the x-axis separates the important spare parts on the left and less important ones on the
right.
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Using the methodology from above, Table 1 lists the unplanned downtime for equipment
failures on Unilever’s Line 2 production line. Graph 1 shows the Pareto Histogram for
unplanned downtime of Line 2 in 2007. It is ranked in descending order according to their
downtime contribution. Applying the Pareto’s 80:20 rule to Graph 1, one can see that priority
should be given to the following pieces of equipment: Bander, Sabel, and Elevator/Palletizer.
Table 1: Unplanned Downtime for Line 2 by equipment (2007)
Code Quantity Duration (Min) % Time % Cum
Bander 305 10866 35.506 35.506
Sabel 206 6688 21.854 57.36
Other 62 3213 10.499 67.859
Elevator & Palletizer 117 3105 10.146 78.005
MPU 60 2739 8.9501 86.956
Hamba 41 1456 4.7577 91.713
Trunkline 62 1203 3.931 95.644
Marsh Coder 12 502 1.6404 97.285
Imaje Coder 21 431 1.4084 98.693
Taper 25 400 1.3071 100
Total 911 30603
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36
22
10 109
5 42 1 1
36
57
68
78
8792
96 97 99 100
0
10
20
30
40
50
60
70
80
90
100
5
10
15
20
25
30
35
40
Taper
Percen
tage
Graph 1 ‐ Pareto Histogram of unplanned Line 2 downtime (2007)% Time % Cum
0
Bander Sabel Other Elevator & Palletizer
MPU & Votator
Hamba Trunkline Marsh Coder Imaje Coder
Equipment
Cummulataive percentage
2.1.2 Limitations of Pareto Histograms
Pareto histograms like the example Graph 1 provide a simple technique for identifying which
spare parts contribute the most to inventory costs and machine downtime. However, the
simplistic nature of this analysis also presents several limitations which will be discussed in the
following paragraphs.
Firstly, Pareto histograms for downtime can be prepared in terms of repair cost, equipment
downtime, failure frequency, mean time to repair (MTTR) or any other type of consequence
attributed to part failures. As a result one would need to create a Pareto histogram similar to
Graph 1 for each individual part failure consequence. Each Pareto histogram would then provide
a distinct list of spare part priorities that must be combined in some manner and this is a difficult
task to perform.
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Secondly, Pareto histograms graphed based on different consequences such as the ones listed in
the previous paragraph “cannot determine which factors are dominant in contributing to the
downtime or cost associated with part failures”. [1]
Thirdly, when there is a lot of data to analyze as is the case for this thesis (over 6,000 parts), data
is usually stratified into some functional group. For example, Unilever does not look at
downtime information in terms of components or parts but in terms of pieces of equipment as a
whole. The potential problem that this poses is the following:
“Pareto graphs are only prepared for the significant contributors of system downtime,
failures associated with less significant components or functional failures will not be
explored. It is possible that we may miss identifying a component or failure mode that
offers significant potential for reliability improvement” [1]
As the reader will see in the succeeding sections, Jack-Knife diagrams provide a way of
analyzing and prioritizing spare parts while also addressing the limitations that were just
discussed above. In conclusion, it will be useful for the thesis student to look at Jack-Knife
diagrams as a comparison to the outcomes of the Pareto analysis.
2.1.3 Jack-Knife Diagram Methodology
Before stating the formal methodology of using Jack-Knife diagrams, it will be useful to define
the terminology that will be used.
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For a particular time interval, the total downtime that is caused by a part (i) is represented by the
following equation:
Downtimei = ni x MTTRi [1]
Downtimei is the downtime that is associated with the ith part. MTTRi and ni are respectively the
mean time to repair and number of failures observed for the ith part over a particular time
interval. For Unilever’s case, MTTR may be replaced by the lead time for obtaining a part from a
supplier if the part is not repaired.
Total downtime for all parts in a particular time interval is defined by the following equation:
D = ∑(Downtimei) for all i [1] (1)
Total number of failures is given by:
N = ∑(ni) for all i [1] (2)
The Jack-Knife diagram method starts by graphing some part failure consequence (MTTR, cost,
downtime, etc) on the Y-axis and number of failures on the X-axis. Figure 1 was obtained from
Peter Knights abstract on Jack-Knife diagrams. The hyperbolae curves seen in the graph are
obtained from Downtimei = ni x MTTRi. “A disadvantage of Figure 1 is that the curves can be
difficult to plot” [1]. To mitigate this problem, the logarithmic of the failure consequence and
Page-9
number of failures is obtained instead. In other words the Y-axis and X-axis of Figure 1 is
switched to logarithmic scale to get Figure 2 (page 11). Note that in Figure 2, the hyperbolae
curves become straight lines.
To graphically prioritize the spare parts, Peter Knights uses threshold limits that divide the log
graph into four quadrants as shown in Figure 3 (page 12). These thresholds can be set by
company policy, actual process capabilities or by determining mean values of failure
consequence and failure frequency. Threshold limits to Figure 3 were obtained by the following
equations:
LimitMTTR = ND where D and N are defined in equations (1) and (2) respectively.
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Limitn = QN where N is defined in equation (2) and Q is the number of distinct parts.
A part is categorized as chronic if it fails more frequently than the average of all the parts that
fail in a particular time interval. As seen in Figure 3, Peter Knights identifies a third limit that
divides the chronic quadrant into two parts: Chronic A and Chronic B. The reason why Peter
Knights identifies this third limit is due to situations when there are large sets of downtime data,
in other words there are many spare parts to consider and analyze. The authors “experience with
large sets of downtime data has shown that the priority list simply grows too large” [1]. The third
limit, called the availability limit, is used to further narrow down the spare parts priority list.
Chronic A spare parts have a more significant effect on availability of spare parts and inventory
costs then compared to Chronic B parts. The limit is as follows:
Page-11
( )
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
≥=
<<=
ni
niMTTR
Limitn where QD Limit
Limit n 0 whereLimitMTTR
ty Availabili
i
With the same logic as the chronic parts, a part is considered acute if the failure consequence (in
the case of Figure 3, MTTR) is exceeds the average consequence for all the parts. Peter Knights
then priorities parts based on what quadrant they fall in on the log scatter plot. Acute and chronic
(upper right hand quadrant in Figure 3) parts contribute significantly to the overall downtime
since their mean failure frequency and mean consequence are both above the average for all
parts. These are the parts that should be on the top of any company’s spare parts priority list as
they have the most impact to machine downtime and inventory costs.
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2.2 “Production and Operations Analysis” [2]
2.2.1 Economic Order Quantity (EOQ)
Once the significant spare parts have been identified and prioritized in some manner, it will be
necessary to optimize the stock sizes for these parts. Ford W. Harris developed the EOQ model
in a paper he published in 1915. “EOQ is the most fundamental inventory model and is the basis
for the analysis of more complex inventory systems”. [2]
The underlying assumptions of the inventory model are the following [2]:
1. The demand rate is known and is a constant per unit time.
2. Order lead time is fixed
3. Ordering cost are constant
4. Purchase price of item is fixed, i.e. no discounts or economies of scale
If “Q” is the size of the order, then the EOQ model works in the following manner. Over time
items are consumed or used up from inventory. An order of Q units is placed for a particular item
once the stock size for that item reaches zero. The order from a vendor or supplier requires a
certain amount of lead time to be processed and received at which point the inventory for the part
is Q. Over time the part is again consumed and the process repeats. The stock levels over time
for the EOQ model can be seen in Figure 4.
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2.2.2 Basic EOQ Model
Before stating the formal methodology of the EOQ model, it will be useful to define all the
relevant symbols.
Let:
1. Q be the order quantity of an item
2. Q* be the optimal order quantity of an item
3. K be the Ordering cost for placing an order
4. c be the Price of the item per unit ordered
5. h be the Holding cost per unit held per unit time
6. λ be the demand rate
7. T be the length of time between orders
Using the above symbols, the ordering cost is [2]:
TcQK + (3)
The holding cost to keep items in inventory is [2]:
2hQ (4)
It follows then that the average cost of an item is the addition of the above two cost formulas [2]:
2hQλc
QkλG(Q)
λQTwhere,
2hQ
TcQKG(Q)
++=
=++
=
The goal is to find an optimal reorder quantity that will minimize the costs associated with
inventory. In order to achieve this goal, the first derivative of G(Q) is taken and set equal to zero.
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One then solves for Q which will equivalent to the optimal reorder quantity (also known as
economic order quantity) Q*.
h2KλQ* = [2]
2.3 “An inventory control system for spare parts at a refinery” [3]
2.3.1 Extension of Basic EOQ Model
A severe limitation of the basic EOQ model is the fact that orders of Q are made when the
inventory for a particular part is reaches zero. Waiting until there is no inventory for a part can
pose a serious detriment to a company if there is still demand for that part after the stock size has
been depleted. This is known as a stock out, when demand for spare parts cannot be met by on
hand inventory. The problem of waiting until the stock size is zero to order new spare parts is
further intensified when the lead time to replace or repair a part is quite long. Not having a spare
part available when there is demand for it means that there is a greater chance of having machine
breakdowns/downtime and in the worst case scenario loss of production for a company. In both
cases this could mean thousands of dollars of lost revenue. The following sections of the thesis
will present an extension to the basic EOQ model that removes the above mentioned limitations.
2.3.2 (s, Q) Inventory Model
In order to overcome the limitations of the basic EOQ model, Parras and Dekker propose using a
(s, Q) inventory policy [3]. In their model, ‘s’ is the re-order point and Q is the economic order
quantity Q* mentioned in section 2.2.2. The inventory parameter ‘s’ has the following property
[3]:
s ≥ 0 and s is an integer
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The reason why ‘s’ is not strictly greater than zero is that there is the possibility of having a short
lead time to repair/replace spare parts and a low probability of having demand after stock outs.
Having zero inventory reduces costs, however the trade off as mentioned in the previous
paragraph is an increase risk of having stock outs. If the re-order point is greater than zero, one
can clearly see the added benefits to this extended model since there is a reduced risk of having
stock outs. Ideally one would want find a balance between minimizing risk or minimizing costs.
The EOQ quantity Q* is rounded off in the following manner [3]:
1. Evaluate: ⎣ ⎦*Q where ⎣ ⎦ is floor (rounding down the nearest integer) m =
2. Set
⎪⎪⎩
⎪⎪⎨
⎧
+
⎟⎟⎠
⎞⎜⎜⎝
⎛ +≤≠
=
=
otherwise 1m*Q1m
m*Q and 0m if m
0 m if 1
Q
Difficulty arises in this inventory model when one attempts to evaluate the re-order point ‘s’
from lead time demand (LTD) data of a particular spare part. To clarify, lead time demand data
is the demand that is generated during the time to replace or repair a spare part. Parras and
Dekker model the LTD by fitting the lead time demand data to a particular probability
distribution such as normal or Poisson distributions. As an example, if one assumes that the LTD
data follows a normal distribution and if the average and standard deviation of the observed LTD
data are respectively D and SD. The authors estimate the normal parameters μLTD and σLTD as
follows [3]:
μLTD = LD ⋅
σLTD LSD ⋅=
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The variable L is the lead time of a spare part. The thesis student has made use of the math
software Matlab® and created a Matlab program that evaluates a wider variety of probability
distributions. Including the Normal and Poisson distributions that were discussed by Parras and
Dekker, the program also evaluates Gamma, Weibull, Lognormal, and Exponential distributions.
Further detail of the Matlab program will be discussed in section 4.1 (page 30).
Once the LTD distribution has been obtained, it can be used to determine a re-order point to
achieve fill rate of β as follows [3]:
1. From the cumulative density function, F(x), of the LTD distribution, obtain a list of
possible re-order point values ‘s’ by setting x = s, and also where x are the lead time
demand values
2. Choose ‘s’ that satisfies the following function:
⎟⎟⎠
⎞⎜⎜⎝
⎛−≤
QES(s)1β
∑>
−=sx|x
s)f(x)(xES(s)
1β0 ≤≤
The item fill rate is the ratio of the total number of items shipped divided by the total number of
items ordered [3].
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Chapter 3 – Prioritizing Unilever’s Spare Parts Inventory
3.1 Machine Descriptions
As mentioned in the introduction, Unilever operates a spare parts store with over 6,000 stock
keeping units (SKU’s). Maintaining such a large inventory will be challenging to say the least.
There are many factors that the store manager at Unilever Rexdale, Antonio Santos, must
consider in its daily operation. For example, Mr. Santos must consider two sources of demand
for spare parts. One source comes from machine/equipment breakdowns and another coming
from preventive maintenance which he is also partly responsible for planning. Mr. Santos could
solve this parts availability problem by simply having an extremely large stock size for each part.
However, having a bloated inventory would not be in line with Unilever’s strategic goal of
reducing their inventory from 1.45 to 1.3 million dollars (CAD). This is another issue that the
store manger must always keep in mind. As a result, it will be advantageous for Unilever if they
could effortlessly identify all the spare parts that cause the highest downtime, breakdown the
most, or cause the highest repair costs. The following sections will discuss how the Pareto
analysis was implemented to Unilever’s machinery/equipment in an effort to prioritize all of
Unilever’s spare parts.
Due to the tremendous number of equipment that Unilever requires in order to maintain
margarine production, the thesis student will only discuss about the Margarine Processing Unit
(MPU) and Bander machines in detail. For further detail, a summary of the Pareto analysis has
been compiled for the other pieces of equipment/machinery in Unilever’s inventory and can be
found in Appendix A.
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Before exploring the Pareto analysis in detail for the MPU and Bander machines, it will be
beneficial for the reader to be able to visualize the machines. The following is a brief description
of the purpose and functional workings of each machine. There are eight production lines at
Unilever Rexdale and each production line has a machine called the margarine processing unit
(MPU Picture 1). The MPU is the heart of margarine production and is the machine that creates
margarine from its constituent ingredients. Depending on the production line, each MPU has 2-4
six feet crystallizing tubes called Votators. A jacket of ammonia runs around each Votator and
liquid margarine passes from one end of the Votator to the other. While this is happening the
ammonia cools the liquid margarine. Within the liquid, water crystals start forming and the
substance overall starts to harden. By the time the substance comes out of the other end of the
Votator, margarine has been made. All that is left afterwards is the package the product.
Picture 1 – Line 7 Margarine Processing Unit (MPU)
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The setup of each production line at Unilever is similar and like the MPU, each production line
also has a machine called the Bander Unit (Picture 2). Due too many complaints from customers
about finding foreign objects in their margarine, legitimate or otherwise, Unilever has resorted to
placing plastic tamper evidence seals around the lid of margarine tubs. Unilever is not
responsible for outside tamper of their products, and thus if customers do not find a tamper
evidence seal on their margarine tubs, they advise not to buy the product. The Bander unit cuts
strips of plastic film and heat seals it around the lid of margarine tubs.
Picture 2 – Line 15 Bander Unit
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3.2 Standard Pareto Analysis
Using the Pareto methodology that was presented in section 2.1.1 (page 13) a table was created
listing all the unplanned downtime for the MPU in 2008. This table can be found in Appendix B.
Note 1: The thesis student gathered data for machine downtime caused by part failures using
Megamation, which is Unilever’s computerized maintenance management system. Only data
from 2008 was considered since Megamation is a new system for Unilever and was introduced in
mid 2007.
Note 2: All MPU units can be considered the same as they use the same spare parts. Also, data
presented in Megamation cannot be segregated by line. Thus, downtime information is
accumulated for all MPU units. As a result, the following Pareto analysis is considering all eight
MPU units together.
Using the raw data that was provided by Megamation, the frequency of part failure and the
downtime percentage was capture in the table found in Appendix B. Downtime percentage for a
particular part is obtained by dividing the duration of downtime for that part by the total
downtime experienced by the machine. Take for instance part No. 8 which is a Cherry Burrell O-
Ring for Votators. Total downtime for all eight MPU units was 58,025 min in 2008. Total
downtime attributed to O-Ring failure (all eight MPU’s) was 3,913 min. It follows that 6.7%
( %7.6100580253913
=× ) of MPU downtime was caused by the O-Ring breaking down or failing.
Using all the data presented in Appendix B and following the rest of Pareto Analysis steps from
section 2.1.1, a Pareto histogram was created for the MPU as seen in Graph 2.
Page-21
The goal of a Pareto histogram is to set priority of spare parts by using Pareto’s 80:20 rule. One
can separate the significant parts in the following manner. On the cumulative axis, draw a line
from 80% parallel to the x-axis to the cumulative curve. The next step is to daw another line
from the point on the cumulative curve down to the x-axis. In Graph 2, it can be seen that the
parts with the highest contribution to MPU downtime are the first seventeen parts left of the red
line. (The reader should look at Appendix B to reference the Part Number with its Part Name). If
Unilever wishes to increase the availability of the MPU unit, then management of these
seventeen parts should take priority. If there are stock outs for any of the sixteen parts, this
would simply increase the time to repair the MPU and thus increase its overall downtime.
However, having too much stock for any of these parts would also mean an increase in inventory
costs. Once the significant parts have been identified the next step is to optimize their stock sizes.
Optimizing Unilever’s spare parts inventory will be discussed later in Chapter 4.
Page-22
The same methodology that was applied to the MPU unit will be used to create a Pareto
histogram for the Bander Unit. Appendix C shows the downtime data that as retrieved from
Megamation for the Bander. Again, please be aware that the same two notes on page 21 for the
MPU analysis also apply for the Bander.
It can be seen in Graph 3 that the first twenty two parts left of the red line have the highest
contribution to Bander downtime. Consequently, these parts should be given higher priority
when managing inventory. (The reader should look at Appendix C to reference the Part Number
with its Part Name).
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3.3 Prioritizing Spare Parts with Jack-Knife Diagrams
In order to evaluate the strength of the Pareto Analysis done in section 3.2, Jack-Knife Diagrams
were created for the MPU and Bander Machines as well. The thesis student used the Jack-Knife
diagram technique that was presented in section 2.1.3. The thesis student also created a Matlab
program that is able to generate Jack-Knife Diagrams when provided specific data. The program
will be discussed later on in section 3.5. Appendix D shows information on part downtime,
failure frequency and mean time to repair failed parts for the MPU. This information will be used
to create a Jack-Knife diagram for the MPU.
Please note that the information found in Appendix D is the same as Appendix B except for the
added part failure frequency data and its organization. Thus, the same two notes found in section
3.2 also apply to the data in Appendix D as well.
Using the data in Appendix D, Total downtime for the MPU caused by part failure is:
D = ∑(Downtimei) = 58,025 min, where i is a specific part
Total number of failures for the MPU is:
N = ∑(ni) = 1,455, where i is a specific part
The limits for the Jack-Knife diagram are:
40ND = LimitMTTR = 54
QN = Limitn =
Page-24
The Jack-Knife diagram for the MPU can be seen in Figure 5. As identified in section 2.1.3,
parts that fall within the “Acute & Chronic” quadrant of the graph contribute significantly to the
overall downtime and repair cost. This is due to the fact that their mean failure frequency and
mean consequence (MTTR) are both above the average for all parts. These are the parts that
should be on the top of any company’s spare parts priority list. From Figure 5, the reader can that
the priority list is quite short consisting of only part numbers 8, 12, 23 and 27 (The reader should
look at Appendix D to reference the Part Number with its Part Name). This list is only a fraction
of what was obtained in the Pareto Analysis for the MPU (See Graph 2 pg 22). Graph 2 provided
a spare parts priority list of seventeen parts and part numbers 8, 12, 23 and 27 are also contained
within this list. Part numbers 8 and 23 are also in the top three for Graph 2.
Repeating the Jack-Knife diagram technique for the data in Appendix E, a Jack-Knife diagram
was created for the Bander as seen in Figure 6. From Figure 6, it can be seen that the priority list
consists of only part numbers 17, 31 and 39 (The reader should look at Appendix D to reference
the Part Number with its Part Name). Comparing this list to the one obtain from the Pareto
analysis in Graph 3 (pg 23), we again only have a fraction of the list. Part number 39 is within
the top three of Graph 3.
For further detail, Jack Knife Diagrams have been created for the other pieces of
equipment/machinery in Unilever’s inventory and can be found in Appendix H. The subsequent
section will discuss the advantages and disadvantages of both prioritizing techniques that have
been discussed thus far.
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3.4 Advantages/Disadvantages of Pareto Analysis and Jack-Knife Diagrams
The main advantage of a Pareto analysis is the fact that it is quite simple to make and it does not
require any advance graphing software. The thesis student created his Pareto histograms using
Microsoft Excel. Another advantage is that Pareto histograms are flexible in the type of data that
can be graphed. For a single machine, Pareto histogram can be created for repair costs, duration
of downtime, failure frequency, mean time to repair or any other type of consequence attributed
to part failures. With its flexibility and simplicity come several drawbacks.
Firstly, the flexibility of Pareto histograms is also a disadvantage as well. If a Pareto histogram is
created for each failure consequence, each histogram would provide a distinct list of spare part
priorities. To combine the priority lists in some manner would be a difficult task to perform.
Compare for instance, Graph 2 (pg 22) and Graph 4. Both are Pareto histograms of the MPU
unit. Graph 2 uses downtime duration data whereas Graph 4 uses failure frequency data. Both
graphs provide different priority lists. The question is how would one combine the two?
Page-27
Secondly, if one chooses only a single failure consequence to graph Pareto histograms with, how
can one determine which is the dominant consequence?
The questions posed above are difficult to answer and for that reason Jack-Knife diagrams
remove those limitations by graphing two failure consequences at the same time (one on the x-
axis and one on the y-axis). Another advantage of Jack-Knife diagrams is that actual data is
graph rather than percentages as in Pareto histograms. For instance, in Graph 4 there is no way of
telling exactly how many times part number 19 failed. If one looks at Figure 5, it can be seen that
part 19 failed around 100 times.
The disadvantage of Jack-Knife diagrams is that it is slightly more difficult to graph as the axis’s
are in base 10 log. However, as one can see the advantages of using Jack-Knife diagrams greatly
outweigh its disadvantages. In the following chapter on optimizing Unilever’s spare parts stock
sizes, the thesis student has used the priority list obtained from the Jack-Knife diagrams.
3.5 Using Matlab Jack-Knife Diagram Code
In order to aid the thesis student, the thesis student created a Matlab program that can generate
Jack-Knife diagrams when provided specific data. Please see Appendix F for the Matlab code.
In order to use the code, a variable containing appropriate data must be created in the main
Matlab interface. Please see Picture 3.
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Picture 3 – Matlab Variable Console
Ensure that the variable contains the following information. There should only be four columns
of data. The first column contains data for the part numbers, the second column contains failure
frequency data, the third column contains downtime duration data and finally the fourth column
contains mean time to repair data. Please refer to Picture 4. Finally execute the program in the
command window as in Picture 5.
Picture 4 – Matlab Variable Editor
Picture 5 – Matlab Command Window
Page-29
Chapter 4 – Optimizing Unilever’s Stock Sizes
4.1 Analysis of Unilever’s Fast Moving Spares
Chapter 3 identified all the spare parts that Unilever should concentrate on in an effort to manage
inventory. Section 4.1 will discuss how the thesis student used the principles and concepts
presented in section 2.2 and 2.3 to optimize the stock sizes for parts identified in Chapter 3. The
parts identified in Chapter 3 are known as consumable parts (fast moving spare parts) and they
have a short life span ranging from weeks to several months.
In the EOQ model, K is the Ordering cost and h is the Holding cost for parts. However, exactly
what types of costs are included in each? Ordering cost is defined as “the total of expenses
incurred in placing an order. In the economic order quantity model, this is the costs related to the
clerical work of preparing, releasing, monitoring, and receiving orders as applicable” [4].
“Holding cost, on the other hand, is the cost associated with holding one unit of an item in stock
for one period of time. Incorporating elements to cover: Capital costs for stock; Taxes;
Insurance; Storage; Handling; Administration; Shrinkage; Obsolescence; Deterioration” [4].
At Unilever these costs are difficult to obtain as they are not considered in their inventory
management. However, working with the spare parts store manager, Antonio Santos, estimates
for these costs were determined. The Ordering Cost for Unilever Rexdale was estimated to be
$30.78 (CAD) per order. The annual Holding Cost was estimated to be 30% of the cost of the
part. That is, it costs Unilever 30 cents to maintain a dollars worth of inventory for one year.
Page-30
In Chapter 3, using the Jack-Knife diagram method, it was identified that part numbers 8, 12, 23
and 27 should have the highest priority. Due to the tremendous number of spare parts, the thesis
student will only discuss about the MPU Pin Blade Fastener (part number 27). A summary table
of the optimal re-order points and stock sizes has been compiled for the other spare parts in
Unilever’s inventory. This table can be found in Appendix H.
Appendix G shows information needed to calculate the EOQ for the MPU Pin Blade Fastener.
Using the information in Appendix G and EOQ formula from section 2.2.2 the economic order
quantity is:
parts 619.5467
1.08734)2(30.78)(6
h2KλQ* ===
It is impossible to order fractional parts, thus Q* is rounded to 620 using the technique presented
in section 2.3.2 on page 16. Q* is the optimal re-order quantity that minimizes the costs
associated with maintaining MPU Pin Blade Fasteners. The next step is to determine the optimal
re-order point. This task is quite difficult as it requires the thesis student to fit a probability
distribution to a set of lead time demand data.
In order to match a probability distribution to the lead time demand (LTD) data, the thesis
student created a Matlab program that generates density graphs and performs a Kolmogorov-
Smirnov test (KS test) of several probability distributions. “The KS test is a statistical technique
that tries to determine if two datasets differ significantly from one another” [6]. The thesis
student used this test to determine if the LTD data differed significantly from data obtained
straight from a particular distribution such as a Normal distribution. The Matlab code determines
Page-31
the appropriate lead time demand distribution based on the methodology that was presented in
section 2.3 and can be found in Appendix I.
In order to use the code, a variable containing lead time demand data must be created in the main
Matlab interface. Please see Picture 6. Lead time demand data for the MPU Pin Blade Fasteners
were used and can be found in Appendix G. Ensure that the variable contains lead time demand
data for the spare part in a single column as shown in Picture 7. Finally execute the code as seen
in Picture 8.
Picture 6 – Matlab Variable Console – Lead Time Demand
Picture 7 – Matlab Variable Editor – Lead Time Demand
Picture 8 – Matlab Command Window – Distribution Function
The program will attempt to fit a probability distribution to the lead time demand data that it
receives. The program will generate Figures 7 and 8 (pg 34) which are respectively the LTD
data’s Probability and Cumulative Density graphs for the MPU Pin Blade Fastener. From these
Page-32
graphs it can be determined which probability distribution fits bests with the LTD data. As
mentioned before the program also performs a KS test to aid in the analysis. As seen in Picture 9,
the KS test returns the Gamma distribution as the best fit for the MPU Pin Blade Fasteners. After
determining which distribution is appropriate, the program will ask for the Holding Cost,
Ordering Cost and Yearly demand for the spare part as seen in Picture 10. This data can be found
in Appendix G for the MPU Pin Blade Fasteners. This is all the data the program needs to
determine the optimal inventory policy for re-order quantity and re-order point. Picture 11 shows
that the optimal policy for the MPU Pin Blades is to order 620 units when there are 168 spares
remaining in inventory. This type of analysis was done for all of Unilever’s high priority spare
parts. The summary can be found in Appendix H.
Picture 11 – EOQ and Re-Order Point Results
Picture 10 – EOQ InputsPicture 9 – KS Test Results
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Page-34
4.2 Analysis of Unilever’s Slow Moving Spares
4.2.1 Machine Descriptions
Section 4.2 will continue the analysis of Unilever’s stock sizes but for slow moving spare parts.
These are parts are highly reliable and have a long life span ranging in several years of operation.
For this study, the thesis student will examine the spare parts provisioning decision for
Gearboxes and Motors which are respectively for the Trunkline and Palletizer machines. Each
production line at Unilever has a machine called the Palletizer as seen in Picture 12. The
Palletizer automatically stacks boxes of margarine onto a wood pallet. The number of boxes that
go on the pallet depend on the production line and the product that is currently being made.
However, it ranges from 24 to 48 boxes per pallet. This machine is completely computer
controlled including the pattern of box stacking.
Picture 12 - Line 1 Palletizer
Page-35
After the boxes of margarine have been stacked onto the pallet, it is dropped onto the Trunkline
(see Pictuer 13) which resembles a giant conveyor unit. It is the responsibility of the Trunkline to
move the pallet of margarine from the production area to a waiting tractor trailer in the
shipping/receiving area. The Trunkline is controlled by a series of light sensors that detect the
presence of a pallet. If a pallet is detected, rollers on the Trunkline are activated and the process
of moving the pallet begins.
Picture 13 - Truckline
4.2.2 Data for the Palletizer and Trunkline
The following information was provided to the thesis student by Unilever’s spare parts store
manager, Antonio Santos, and through Unilever’s CMMS system, Megamation.
Page-36
Palletizer
• Cost of the Motor R60DT80N2Z is 591.40
• There are 8 EuroDrive motors currently in service for each of the Palletizers in service
• There is currently 1 motor in on hand inventory
• The motors have been in operation for 5 years since the inception of the Trunkline
• The lead time to get a gearbox from the supplier, SEW-EuroDrive, is 4 days
• According the supplier, the average service life for their motors is 10-20 years
• The gearboxes operate whenever the Palletizer is operational; 2 production shifts at 8 hrs
= 16 hrs, 6 days a week
• Time units are in weeks
Trunline
• Cost of the Gearbox R76DT90L4 is $1107.07
• There are 61 Trunkline sections each with a gearbox, thus there are 61 EuroDrive
Gearboxes currently in service
• There is 1 gearbox in on hand inventory
• The gearboxes have been in operation for 5 years since the inception of the Trunkline
• If the damage to the gearbox is beyond repair, it is replaced. The lead time to get a
gearbox from the supplier, SEW-EuroDrive, is 1.5 weeks
• Depending on severity, gearboxes for the trunkline can be repaired. Repairing gearboxes
in house takes mechanics on average 3 days
• According the supplier, the average service life for their gearboxes is 15-25 years
Page-37
• The gearboxes operate whenever the Trunkline is operational; 2 production shifts at 8 hrs
= 16 hrs, 6 days a week
• Time units are in weeks
4.2.3 Results of Analysis
Given that the above mentioned parts are highly reliable, the decision under analysis is whether
Unilever should stock these spare parts or not. In order to perform the study, the thesis student
used the Spare Management Software (SMS) which was developed by The Centre for
Maintenance Optimization and Reliability Engineering at the University of Toronto. The SMS
software provides the following four optimizing criteria: instantaneous reliability, interval
reliability, cost and availability. The thesis student will only examine the instantaneous reliability
of the stock which is defined as follows:
“Instantaneous Reliability (of stock): this is the probability that a spare is available at any
given moment in time. It is equivalent to the fraction of demand that can be immediately
satisfied from stock at hand” [7].
Using the SMS software and data in section 4.2.2 for the Palletizer, the thesis student was able to
determine the instantaneous reliabilities for 0 and 1 spare Motors. According to the spare part
store manager, Antonio Santos, 95% of the demand for spare parts has to be satisfied by on hand
inventory. In other words, the provisioning criterion is that Unilever has to have an instantaneous
reliability of at least 95%. From Graph 5, it can be observed that the reliability percentage of
stock levels 0 and 1 are very close. The difference in percentage between the two levels is small
ranging from 0.84 to 0.44% when mean time to failure is varied from 10 to 20 years. Also note in
Graph 5 that the instantaneous reliability of 0 spares in inventory is already greater than
Page-38
Unilever’s target of 95%. This is not a surprising result as there is only 8 motors currently in
service and there is a short lead time to replace failed motors (4 days). Based on these findings, it
would be more economical for Unilever if they did not stock any Palletizer motors as the
reliability target can be achieved without spares. Also, Unilever would be able to save on
holdings costs attributed to managing an inventory of motors.
Again using the data from section 4.2.2, the thesis student was able to generate Graph 6 which
depicts the difference in instantaneous reliability for stock levels of 0, 1 and 2 spare Gearboxes.
The lead time to replace a Gearbox from SEW-EuroDrive is 1.5 weeks or 11 days. From Graph
6, one can see that 0 spares would not achieve Unilever’s reliability target of 95% when mean
time before failure changes between 15 to 25 years. This is not a surprising result as there are
many more Gearboxes in service (61 in service) compared to Palletizer Motors (8 in service).
The demand for Gearboxes would be greater and thus the probability of satisfying this demand
with 0 spares in inventory would decrease. On the same graph, stock levels of 1 and 2 achieve an
Page-39
instantaneous reliability that is not only close together but also greater than 99%. As a result, no
further attention will be paid for the case of 0 spare Gearboxes. Due to the fact that the reliability
for 1 and 2 spares are close together, it would be inefficient for Unilever to stock 2 spare
Gearboxes since Unilever’s target can be achieved with fewer inventories.
Furthermore, it was noted in section 4.2.2 that Gearboxes can be repaired in house depending on
the severity of the failure. If repairs can be done in house, then the lead time to repair the part is
3 days. Graph 7 shows instantaneous reliability for stock levels of 1 and 2 spare Gearboxes with
variable lead time. As one would expect, a decrease in lead time to replace or repair a spare part
increases the instantaneous reliability of for that spare. One can see from Graph 7 that the
instantaneous reliability has dramatically increased for the 0 spare scenario when lead time is 3
days. Unilever’s reliability target of 95% is now achievable if the lead time is 3 days. However
this ultimately depends on the severity of the Gearbox failure which is a stochastic variable.
Further analysis is needed to determine how often Gearboxes fail catastrophically requiring the
Page-40
spare part to be replaced and how often failures can be repaired in house for the results in Graph
7 to be of use to Unilever. For example, if the analysis shows that the probability of repairing
Gearboxes in house is high, then Unilever should stock 0 spare Gearboxes based on the findings
in Graph 7. Conversely, Unilever should stock 1 spare Gearbox if the probability of catastrophic
Gearbox failures is high.
Page-41
Chapter 5 – Conclusions
5.1 Conclusions and Recommendations for optimal stock sizes
Due to Unilever’s large population of spare parts it was necessary to be able to pick a select few
that produce a significant overall effect. For this reason, the thesis student compared and
contrasted a simple Pareto Analysis with the prioritizing features of Jack Knife Diagrams. It was
concluded that Jack Knife Diagrams are superior to Pareto Histograms in prioritizing spare parts
by overcoming many of its limitations. For example, Pareto Histograms generate distinct
prioritization lists for each downtime consequence that is graphed. These lists need to be
combined in some manner which is a difficult task. Jack Knife Diagrams overcome this
constraint by graphing two downtime consequences at one time. This eliminates the need to
combined different prioritization lists. A summary of all of Unilever’s significant spare parts is
shown in Appendix A.
In order to optimize Unilever’s stock sizes for fast moving spares, the thesis student turned to the
work of Rommert Dekker who introduced an extension to the basic EOQ model. Dekkers
technique involved modeling a probability distribution for a set of lead time demand data. The
lead time demand distribution along with the EOQ quantity was needed to determine the re-order
point parameter. Dekker’s technique was implemented on all the significant spares that were
identified in the Jack Knife Diagrams as seen in Appendix A. For each spare identified in
Appendix A, the thesis student provides recommendations for optimal stock quantities and re-
order points in Appendix H.
Page-42
Page-43
The last task for the thesis student involved an analysis of two Unilever’s slow moving spares
using the SMS software which was provided by the group C-MORE at the University of
Toronto. Using the SMS software and the data that was provided by Unilever’s spare parts
manager, it was determined that a stock quantity of zero Palletizer Motors gave an instantaneous
reliability greater than Unilever’s target of 95%. Thus it is recommended that Unilever should
not stock Palletizer Motors. On the other hand, the SMS software showed that Unilever should
stock at least one Trunkline Gearbox to achieve Unilever’s target for reliability. This is assuming
that Gearboxes cannot be repaired in house. However, if the Gearbox failure is not catastrophic
in house repair may be possible. In this case the SMS software recommends Unilever to not
stock Trunkline Gearboxes. In spite of this finding, the severity of Gearbox failure is stochastic
in nature. In order words it cannot be predicted for certain and thus a definite recommendation
for Trunkline Gearboxes cannot be made with the current data.
5.2 Future work
Due to time limitations the thesis student was only able to look at a fraction of Unilever’s
inventory using Jack Knife Diagrams to prioritize spare parts. Future work should involve the
optimization of the rest of Unilever’s inventory starting with all the parts that fall in the Acute
quadrant of the Jack Knife diagram. This should be followed by parts that fall in the Chronic
quadrant and then finally the least significant parts that fall in the lower left hand corner of the
Jack Knife Diagram. Also, an in depth study should be done to determine how often Trunkline
Gearboxes can be repaired in-house. This information will be needed to determine if Unilever
should stock 1 or 0 Trunkline Gearboxes.
References [1] Peter F. Knights, “Rethinking Pareto Analysis: Maintenance Applications of Logarithmic
Scatterplots”, Journal of Quality in Maintenance Engineering, Vol. 7 No. 4, 2001, MCB University Press
[2] Steven Nahmias, “Production and Operations Analysis”, Fifth Edition, page 195-223,
McGraw-Hill Irwin [3] Eric Parras, Rommert Dekker, “An inventory control system for spare parts at a refinery”,
European Journal of Operational Research, 2006, Elsevier B.V. [4] M.A. Darwish, “Joint determination of order quantity and reorder point of continuous
review model under quantity and freight rate discounts”, Computers and Operations Research, 2007, Elsevier B.V.
[5] Yu Xia et al, “Market-Based Supply Chain Coordination by Matching Suppliers’ Cost
Structures with Buyers’ Order Profiles”, Management Science, Vol. 54 No. 11, 2008 [6] The MathWorks Inc. (2009), Statistics Toolbox: kstest2. Retrieved: March 11, 2009,
http://www.mathworks.com/access/helpdesk/help/toolbox/stats/index.html?/access/helpdesk/help/toolbox/stats/kstest2.html
[7] Dragan Banjevic et al, “Optimization of Spare Parts Inventories Composed of Repairable
or Non-Repairable Parts”, The Centre for Maintenance Optimization and Reliability Engineering, University of Toronto
[8] Koen Cobbaert et al, “Inventory Models for fast Moving Spare Parts subject to Sudden
Death Obsolescence”, Centre for Industrial Management, 1996, Catholic University of Leuven
[9] Leonard Fortuin, “Stocking Strategy for Service Parts - A Case Study”, Journal of
Quality in Maintenance Engineering, Vol. 20 No. 6, 2000, page 656-674, MCB University Press
[10] Martin Davis et al, “A Decision Support System for Spare Parts Management in a Wafer
Fabrication Facility”, IEEE Transactions on Semiconductor Manufacturing, Vol. 14 No. 1, February 2001
[11] Peter F. Knights, “Downtime Priorities, Jack-Knife Diagrams and the Business Cycle”,
Maintenance & Asset Management Vol. 19 No. 4, page 21-28, 2005
Page-44
Appendix A The following tables are summary lists of all the parts that were deemed significant (Pareto’s 80/20 rule) through a Pareto Analysis of the downtime for particular machine. Pareto Histograms for particular machines/equipment are presented after the tables.
Sabel Case Packer Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
50 90 9533 13.9% 13.9% SPRING, COMPRESSION, IN‐FEED TRIP MEDIUM DUTY, SABEL SPRNC022D8SS56 198 8988 13.1% 27.0% FRAME SUB‐ASSEMBLY, LOAD ELEVATOR ASS'Y, SABLE LINE 1515 135 5488 8.0% 35.0% COUPLING , 13 X RSB BODY (HUB) (SAGA CPLG)27 58 4630 6.8% 41.8% VALVE, VACUUM, 1/4" PORT, 24VDC, MAC VALVE 225B‐111CC20 220 4031 5.9% 47.7% COIL, ELECTRICAL, SOLENOID, 24VDC, CYLINDER CYL‐CHECK, ALLENAIR CYALEA524VDC9 32.5 4026 5.9% 53.5% CHAIN, TENSIONER, ROSTA SE‐18
48 156 4026 5.9% 59.4% WASHER, DISAPPEARING WALL, BRASS, ADA MACHINE3 15 2806 4.1% 63.5% ABSORBER, SHOCK, ENIDINE OEM‐5B
42 75 2806 4.1% 67.6% CONTROL, METER OUTFLOW, 1/4" NPT, SMC NAS2301FN0211S13 25 1657 2.4% 70.0% MODULE, LOGIC MULTI BEAM, 2 WIRE, BANNER 2LM352 195 1595 2.3% 72.3% SCREW, CAP, BUTTON SOCKET HEAD, 1/4"‐28 NF X 1/2", SABLE COVER SCREWS7 7 1304 1.9% 74.2% SCANNER, FIBER OPTICS PAD, BANNER SBFXBT24S
46 54 1304 1.9% 76.1% CONTROL, METER OUTFLOW, 1/4" NPT, SMC VASM 1/4 OUT6 105 1173 1.7% 77.9% BRACKET, FRAMING FITTING, ANCHORING, SABEL, SABLE DESCENDER LINE 5
45 9 1173 1.7% 79.6% METER OUTFLOW CONTROL, 1/8" NPT, SMC VASM 1/8 OUT ; NAS2200‐N01 VALVE24 99 1045 1.5% 81.1% HANDLE, KNOB, 2‐5/16", 18 SS, ADJUSTABLE, ELESA KNOB6801
Palletizer Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
3 144 5790 13.9% 13.9% SPOOL (Steel) for overhead conv. (approx: 2" dia x 2" overall lenght ‐ w/ 2 drilled & tapped 1/4 ‐ 20 set screw holes)
13 187 5573 13.4% 27.4% CAP, BRUSH, CARBON, SABEL, ROTARY SABEL7 103 4640 11.2% 38.5% BUMPER, RUBBER, FB‐2724, MATHEWS PALLITIZERS6 43 3746 9.0% 47.6% HOLDER, PILLOW BLOCK, RAPISTAN 52PB, NTN PP205
11 59 3144 7.6% 55.1% BRUSH, CARBON, SABEL E‐03370, CAROUSEL ROTARY SABEL
Page-45
4 93 3059 7.4% 62.5% JOINT, UNIVERSAL, CONVEYOR SYSTEM, RAPISTAN 04956‐00050
8 152 2492 6.0% 68.5% SHEAVE, IDLER, MATHEWS V42B, PALETIZER INFEED ROLLER (V‐42‐B IDLER PULLEY) (approx: 3" OD x 3/8" ID)
15 146 2360 5.7% 74.2% BRUSH, CASE MAGAZINE, 0.028" X 1" X 2", SABEL 0.028 X 1 X 2
5 110 2272 5.5% 79.7% CLIP, C, NYLON, WHITE INJECTION MOLDED 1256, RAPISTAN CD‐2015‐0001, YC7054 IT.01 ; DO NOT RE‐STOCK
Rollers Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
4 54 5874 12.0% 12.0% IDLER PULLEY ‐ " BEMIS" (150004‐B) / ROLLER, DISC, 2.875" DIA (CROWNED) X 2.7" LONG, SIDE BELT TYPE ASSEMBLY,
16 31 4889 9.9% 21.9% IDLER ROLLER (approx: 1.88" dia x 2.73" long ) with ROLLER BEARING (#6004Z) ON BOTH SIDES AND STUD SHAFT (.75 X 3" LONG)
31 46 4410 9.0% 30.9% ROLLER, CCC‐550‐104, WATER TREATMENT PLANT25 55 4031 8.2% 39.1% ROLLER, 410 MM OAL, INTERROLL 1.154V50C30‐3.75
2 40 4026 8.2% 47.3% ROLLER, GUIDE, 1/2" ID X 2" OD (overall thickness: .88) , PLASTIC, FOR SIDE BELT (for DEKKA Tape)
10 36 3215 6.5% 53.8% HEX AXEL SHAFT FOR ITEM # 674505, 7/16" DIA X 30"LG, 1/4‐20 THRD HOLES AT EACH END
14 74 3090 6.3% 60.1% TRUNKLINE CONVEYOR DRIVE ROLLERS, 2‐1/2" dia X 52‐5/8" LONG (W/ SPROCKETED 5/8" dia., 4.5" long SHAFT ‐ w/ keyway 3/16" x 2‐1/2" long)
33 66 2340 4.8% 64.8% ROLLER, CORAZZA D4000232
12 58 1925 3.9% 68.8%
TRUNKLINE CONVEYOR SPROCKET ROLLERS, 2‐1/2" dia X 56‐1/2" LONG (TWO RS40/22TEETH SPROCKET WELDED 1/2" DISTANCE FROM ONE END; SECOND SPROCKET WELDED 1‐5/8" FROM SAME END)
23 9 1702 3.5% 72.2% ROLLER, COMPRESSION, CERTIPAK 150758, TM 2‐18032 6.5 1285 2.6% 74.8% ROLLER, CORAZZA D4041703
13 10 1185 2.4% 77.3% TRUNKLINE CONVEYOR IDLER ROLLERS, 2‐1/2" dia X 52‐5/8" LONG (W/ SPROCKETED 5/8" dia., 3.75" long SHAFT ‐ w/ keyway 3/16" x 2‐1/2" long)
37 9 1085 2.2% 79.5% Roller (Cam roller) for Doser, # D4000655 (for Corazza Doser rotary valve hold down)
Chains Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
67 85 9840 6.4% 6.4% OFFSET LINK, CHAIN 111046
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92 135 6851 4.5% 10.9% RSD40 LAMBDA RIV CHAIN (SELF‐LUBRICATING CHAIN), TSUBAKI19 641 6544 4.3% 15.1% #40 O/L, SS, OFFSET LINK, STAINLESS STEEL65 235 5850 3.8% 18.9% ROLLER CHAIN, RENOLD 111046, 1352 RL S
60 37 5146 3.3% 22.3%
LINK, CHAIN, TRANSMISSION, CONNECTING, STRAIGHT WITH ATTACHMENT, TSUBAKI C‐2060H A‐2, C2060 B1, 2 HOLE 17/64" BENT LUG ATTACHMENT CURRIE ELEVATOR FLIGHT CHAIN
31 25 4889 3.2% 25.5% #RS08B‐2 METRIC ROLLER CHAIN 68 60 4889 3.2% 28.6% PLASTIC ROLLER CHAIN for sprocket‐25B30 (Line 1 Checkweigher)
95 27 4841 3.2% 31.8% 50 LAMBDA CONNECTING LINK (TO BE USED ONLY WITH THE SELF‐LUBRICATING CHAIN), TSUBAKI
9 55 4410 2.9% 34.7% Stainless Steel Chain, SS16B‐1 RCL, C/W Special WA‐2 Attachments (10mm Holes) Evry 2nd, 4th, 8th, & 10th Repeat (2 link/4link, alternately) (for Line 5 Hamba carrier chain)
46 18 4410 2.9% 37.5% #RF2080‐S O/L, OFFSET LINK WITH HOLLOW PIN83 41 4410 2.9% 40.4% #50‐2 CONNECTING LINK 3 32 4031 2.6% 43.0% #RS50‐2 ROLLER CHAIN
40 49 4031 2.6% 45.6% #25 CONNECTING LINK, TSUBAKI 25 C/L77 67 4031 2.6% 48.3% SPROCKET, 19 HARD TEETH, 1 1/8" BORE, 1/4 KEYWAY, MARTIN, 50BS19HT‐1 1/817 79 4026 2.6% 50.9% #RS60 ROLLER CHAIN54 24 4026 2.6% 53.5% ROLLER CHAIN NO. 40 PROCOAT w/ ATTACHMNETS 3043 , (for BANDERS SPC Chains)91 76 4026 2.6% 56.1% #40‐2 C/L, S.S. CONNECTING LINK
29 68 3090 2.0% 58.1% CHAIN LINK ONLY, TRANSMISSION, CONNECTING, STEEL, LIEFERSCHEIN 034013885 (Connection Joint Straight ‐ Carrier chain Link ONLY, NO attachment for Line 15 Hamba)
66 27 3090 2.0% 60.2% CONNECTING LINK, 111046/26 CHAIN 62 26 2664 1.7% 61.9% #60‐2 O/L, OFFSET LINK56 25 2644 1.7% 63.6% LINK, CHAIN, TRANSMISSION, OFFSET, 1/2" PITCH, 40‐2 CHAIN, SS, DOUBLE, TSUBAKI 40‐211 46 2340 1.5% 65.1% #RS35 S.S. ROLLER CHAIN48 36 2340 1.5% 66.7% #25 OFFSET LINK, TSUBAKI 25 O/L
85 41 2340 1.5% 68.2% LINK, CONNECTING, SPRING CLIP TYPE, ANSI 40‐1, FOR MAIN CARRIER CHAIN,FOR BANDING MACHINES
58 41 2165 1.4% 69.6% #RF2060 C/L, CONNECTING LINK
97 34 1958 1.3% 70.9% 50 LAMBDA OFFSET LINK (TO BE USED ONLY WITH THE SELF‐LUBRICATING CHAIN), TSUBAKI
27 21 1925 1.3% 72.1% #05B C/L, METRIC CHAIN CONNECTING LINK64 10 1925 1.3% 73.4% CHAIN, POWER TRANSMISSION, SINGLE STRAND, BARLOTTI SNC D40346401 57 1702 1.1% 74.5% #RS08B‐1 METRIC ROLLER CHAIN
38 67 1702 1.1% 75.6% #35 OFFSET LINK, TSUBAKI 35 O/L 75 31 1702 1.1% 76.7% #40 B1 2H CONNECTING LINK
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10 52 1285 0.8% 77.5% #RS35 ROLLER CHAIN
47 5 1285 0.8% 78.4% CONNECTING LINK, HOLLOW PIN, TSUBAKI, # C2080HPCL, FOR CHAIN # C2080HP (LINE 5 ‐SABEL DESCENDER)
84 7 1285 0.8% 79.2% #50‐2 OFFSET CONNECTING LINK. 28 43 1185 0.8% 80.0% #05B O/L, METRIC ROLLER CHAIN OFFSET LINK
Certipak Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
1 75 4812 11.1% 11.1% CERTIPAK CARTONER TM12 52.5 4812 11.1% 22.2% PLATE, PUSHER MOUNTING, CERTIPAK 15951‐531‐4223 50 4812 11.1% 33.3% LUG, CERTIPAK 25615‐26, CARTONER 2 38 3725 8.6% 41.9% CHAIN, RH FLIGHT ASSEMBLY, CERTIPAK 25533‐14‐2
13 45 3725 8.6% 50.4% CHAIN GUIDE (LONG), CERTIPAK M/C, 24 45 3725 8.6% 59.0% ASSEMBLY, LUG, CERTIPAK 25236‐27, CARTONER3 28.5 2569 5.9% 64.9% CHAIN, LH FLIGHT ASSEMBLY, CERTIPAK 25533‐14‐3
14 57 2569 5.9% 70.9% CHAIN GUIDE, CERTIPAK M/C , 1/4 x 1‐1/2 x 19‐3/425 28.5 2569 5.9% 76.8% ASSEMBLY, FLIGHT, CERTIPAK 25326‐214 21 1446 3.3% 80.1% LUG, CERTIPAK 25500‐13, CARTONER
Winpak Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
1 11.5 1506 11.8% 11.8% DEPOSITOR VALVE, 6‐LANE , # EK297C007 23 1506 11.8% 23.5% GROMMETS, #CJ288‐A2 21 1250 9.8% 33.3% SLUG, ( to regulate margariine/product weight for Winpak Filler) , # EK307 B00
11 7 1250 9.8% 43.0% CYLINDER , # XY090A , for Tamping Station, Winpak Filler3 42 1130 8.8% 51.9% HEAT SEAL DISCS (heater pad disc) , # DB386‐A (for Winpak Filler)4 21 1130 8.8% 60.7% THERMOCOUPLE, HEAT SEAL5 130 1130 8.8% 69.5% SPRINGS, HEAT SEAL6 84 1130 8.8% 78.3% HEATER CARTRIDGE
Corazza Part No.
Downtime Frequency
Downtime Duration (min) % Time % Cum Part Description
39 237 5909 2.1% 2.1% PIN, CORAZZA D4039285
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54 286 5875 2.1% 4.2% GEAR, SPUR, SPUR, CORAZZA D403443353 73 5846 2.1% 6.2% GEAR, PINION, WITH SPROCKET, CORAZZA D301127785 63 5651 2.0% 8.2% TOOL, CHAIN STRETCHER, CORAZZA D204057145 158 5459 1.9% 10.2% ARM, CORAZZA D308608359 100 5435 1.9% 12.1% LEVER, MOUNTING, CORAZZA D308433226 255 5401 1.9% 14.0% FLANGE, CORAZZA D408433132 95 5264 1.9% 15.8% LOCK, EJECTOR SECTOR, CORAZZA D20915326 11 5239 1.9% 17.7% FINGER, LEFT HAND, CORAZZA D4084777, TAV.7‐7
52 275 5082 1.8% 19.5% PUMP ASSEMBLY , CORAZZA R40000018 115 5071 1.8% 21.3% COUPLING, UNIVERSAL, CORAZZA C1000601, TAV.2‐3 CORAZZA
20 159 5062 1.8% 23.1% FITTING, CURVED, CORAZZA C2000069 ; "SMC" FITTING, # KQ2L06‐01S ‐ ELBOW, TUBE ADAPTER, 6 MM X 1/8" NPT, TUBE X MNPT, 90 DEG
81 273 5059 1.8% 24.9% RECONDITIONED BLADE, BOTTOM, CORAZZA D3005227, FOR LINE 11 CORAZZA FILLER9 138 5003 1.8% 26.6% JOINT, INTRODUCTION, CORAZZA C1001200, CORAZZA CLUTCH
92 73 4984 1.8% 28.4% BRUSH, 2PCS/SET, CORAZZA CR100003, CORAZZA CLUTCH
75 118 4954 1.8% 30.1% CUTTER , LEFT HAND CUTTING, FOR THE DOUGH CUTTER, CORAZZA D2083323, REQUIRED 4
77 159 4860 1.7% 31.8% BLOCK, ASSEMBLY, CORAZZA D3083433, FOR THE SHELL WRAP FORMING63 71 4844 1.7% 33.6% ASSEMBLY, TRANSPORT ROLLER CHAIN, CORAZZA R3001913
80 71 4715 1.7% 35.2% OEM BLADE, BOTTOM, CORAZZA D3005227, FOR LINE 11 CORAZZA FILLER (ORDER WHEN NO MORE 958460R‐RECONDITONED)
74 154 4702 1.7% 36.9% PLATE, SEAL, CORAZZA D4111627 43 168 4621 1.6% 38.5% KNOB, CORAZZA D400084536 86 4327 1.5% 40.0% GEAR, PINION, CORAZZA D3006004 73 173 4318 1.5% 41.6% CUP, VACUUM, NEW STYLE, GEORGE T WHITE VC‐B1521 98 4257 1.5% 43.1% SPROCKET, GEAR, PINION COGGED, CORAZZA D409094015 249 4234 1.5% 44.6% SHAFT, DOSING CELL EJECT END, CORAZZA D40363697 149 4213 1.5% 46.1% FINGER, RIGHT HAND, CORAZZA D4084778, TAV.7‐7
10 139 4202 1.5% 47.5% FOLDER, FIXED, CORAZZA D3084775 14 116 4187 1.5% 49.0% SHAFT, DOSING CELL EJECT, CORAZZA D308660023 178 4173 1.5% 50.5% CUP, SUCTION, RUBBER, BELLI‐ITALIA D4000437, CORAZZA50 210 4149 1.5% 52.0% STOP, RUBBER, PLUG, CORAZZA D400243134 10 4095 1.4% 53.4% PULLEY, COGGED, CORAZZA D3041296 11 153 4083 1.4% 54.9% SHAFT, CORAZZA, (#D3005959), C/W KEYS SHAPE TYPE "B" (#C1002167)46 261 4079 1.4% 56.3% ARM, CORAZZA D308608256 125 3992 1.4% 57.7% PIN, MOUNTING, CORAZZA D4000453
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42 224 3957 1.4% 59.1% PAD, CORAZZA D4000667
51 189 3903 1.4% 60.5% BAR, WEAR, CORAZZA D2084330
40 292 3880 1.4% 61.9% PIN, MODEL #: FB 450, CORAZZA D4000902
62 43 3861 1.4% 63.2% FOLDER, ROTATING, CORAZZA D3084783
83 269 3822 1.4% 64.6% BUSHING, STEEL, CORAZZA C1000173, TYPE BM3
71 147 3733 1.3% 65.9% CARTON SUPPORT FINGERS, RIGHT HAND, ADA MACHINE
30 297 3707 1.3% 67.2% SEGMENT, CORAZZA, (SECTOR) PN# D1084568
78 81 3694 1.3% 68.5% OEM BLADE, TOP, CORAZZA D3005228, FOR LINE 11 CORAZZA FILLER (ORDER WHEN NO MORE 958455R ‐ RECONDITIONED)
18 129 3647 1.3% 69.8% LOCK, CELL SECTOR, SHORTER CURVE, CORAZZA D2084316
65 162 3556 1.3% 71.0% SPRING, CORAZZA D4000349
17 18 3483 1.2% 72.3% LOCK, CELL SECTOR, LONGER CURVED, CORAZZA D2084317
69 178 3382 1.2% 73.5% BRUSH, EPY CURRENT DRIVE, CORAZZA, FOR LINE 11 FILLER CORAZZA
41 178 3351 1.2% 74.7% KNOB, CONTROL, CORAZZA D4053465
25 278 3060 1.1% 75.7% JOINT, UNIVERSAL, DOUBLE, CORAZZA C1001481
44 150 2980 1.1% 76.8% FILTER, OIL, 100 MM DIA X 50 MM LG, CORAZZA C1000791, INSIDE SUMP PUMP
13 278 2888 1.0% 77.8% SHAFT, CELL MOUNTING, CORAZZA D3083328
47 253 2875 1.0% 78.8% SHAFT, ENCODER, 0.5‐12VDC, OMRON E6F‐AB3C‐C2, CORAZZA
58 166 2802 1.0% 79.8% PIN, MOUNTING, CORAZZA D4000452
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Appendix B The following tables show the raw data that was used to create Pareto Histograms for the Margarine Processing Unit (MPU) based on downtime duration and downtime frequency as the consequences. Pareto Histograms for MPU based on both consequences are presented after the tables.
Raw Data for MPU Pareto Analysis (Downtime Duration) Part No.
Downtime Duration (min) % Time % Cum Part Description
8 3913 6.7% 6.7% ITEM E, (5of10) O‐RING, CHERRY BURRELL 700006B23, N70235, FOR VOTATORS
16 3755 6.5% 13.2% ITEM F, (6of10) INSERT, SEAL BODY, GRAPHITE, FOR VOTATORS, CHERRY BURRELL 110892‐A4, CHERRY BURRELL 11089A4
23 3576 6.2% 19.4% BLADE, MUTATOR, CHERRY BURRELL 900099, 112132‐E, FOR MPU 11 , A2 / A321 3562 6.1% 25.5% RING, SUPPORT, FOR WATER CHAMBER, SCHRODER, LINE 15 VOTATORS12 3388 5.8% 31.4% ITEM I, (9of10) HEAD, SEAL, INSERT, VOTATORS
6 3367 5.8% 37.2% ITEM G, (7of10) O‐RING, CHERRY BURRELL 700006A32, N75226, FOR VOTATORS NEW #N75226 FOR BUNA; V‐70226 ‐ FOR VITON; E‐70226 ‐ FOR EPDM
26 3073 5.3% 42.5% PIN, BLADE FASTENER, CHERRY BURRELL 14869, SMALL VOTATOR M123A20 2838 4.9% 47.3% SEAL, SHAFT, CHERRY BURRELL 700030A88, LINE 21 FOR VOTATORS22 2563 4.4% 51.8% BLADE, MUTATOR, CHERRY BURRELL 900129, 121088, FOR MPU 11, A1
27 2533 4.4% 56.1% PIN, BLADE FASTENER, CHERRY BURRELL 14868, LARGE VOTATOR M123A (NOT IN USE ‐ FOR OLD MPU‐01 VOTATOR?
4 2529 4.4% 60.5% NUT, LOCK, CHERRY BURRELL 700004A02 ( approx: 68mm ID x 92mmOD)5 2064 3.6% 64.0% NUT, 3/4", SS, VOTATOR1 1992 3.4% 67.5% BEARING, CHERRY BURRELL 1137497 1962 3.4% 70.9% O‐RING, CHERRY BURRELL 70001A12
15 1918 3.3% 74.2% ITEM D, (4of10) SEAL, U‐CUP BODY, CHERRY BURRELL 7000014A05, FOR VOTATORS (Able O‐ring equivalent: HC187‐02.75ON700 ‐ 2‐3/4" X 3‐1/8" X 3/16")
11 1859 3.2% 77.4% SEAL, PIN DRIVE, CHERRY BURRELL 119036, VOTATOR FOR MPU 518 1703 2.9% 80.3% STUD, COVER, VOTATOR13 1584 2.7% 83.0% NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A 24 1532 2.6% 85.7% PIN, BASE MUTATOR, CHERRY BURRELL 110368‐A, VOTATOR25 1342 2.3% 88.0% PIN, HEAD MUTATOR, CHERRY BURRELL 112004‐A, VOTATOR2 1340 2.3% 90.3% SHAFT, DRIVE, VOTATOR STUD SHAFT FEMALE SPLINE, CHERRY BURRELL 920430, 34438, 801383
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14 1271 2.2% 92.5% FABRICATE (LOCAL ‐ ADA) NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A (do not re‐order ‐more expensive than Orig)
3 1143 2.0% 94.5% ITEM J, (10of10) SEAL, LIPSEAL, CHERRY BURRELL 700030A42, FOR VOTATORS9 994 1.7% 96.2% PIN, BASE, SPECIAL CHAMFER TOPS, VOTATOR
10 891 1.5% 97.7% ITEM B, (2of10) RING, SEAL BACKING, CHERRY BURRELL 110203‐C119 721 1.2% 98.9% ITEM #2, DISK 25 Stainless Steel (approx: 45mm OD x 25 mm ID x 4 mmthick) S14237717 612 1.1% 100.0% STUD, VOTATOR COVER, M24 X 77 , # S101922
58025 1
Raw Data for MPU Pareto Analysis (Downtime Frequency) Part No.
Downtime Frequency
% Frequency % Cum Part Description
19 98 6.7% 6.7% ITEM #2, DISK 25 Stainless Steel (approx: 45mm OD x 25 mm ID x 4 mmthick) S14237724 97 6.7% 13.4% PIN, BASE MUTATOR, CHERRY BURRELL 110368‐A, VOTATOR
6 86 5.9% 19.3% ITEM G, (7of10) O‐RING, CHERRY BURRELL 700006A32, N75226, FOR VOTATORS NEW #N75226 FOR BUNA; V‐70226 ‐ FOR VITON; E‐70226 ‐ FOR EPDM
12 84 5.8% 25.1% ITEM I, (9of10) HEAD, SEAL, INSERT, VOTATORS 25 83 5.7% 30.8% PIN, HEAD MUTATOR, CHERRY BURRELL 112004‐A, VOTATOR7 79 5.4% 36.2% O‐RING, CHERRY BURRELL 70001A12
22 78 5.4% 41.6% BLADE, MUTATOR, CHERRY BURRELL 900129, 121088, FOR MPU 11, A12 77 5.3% 46.9% SHAFT, DRIVE, VOTATOR STUD SHAFT FEMALE SPLINE, CHERRY BURRELL 920430, 34438, 801383
17 73 5.0% 51.9% STUD, VOTATOR COVER, M24 X 77 , # S101922 4 67 4.6% 56.5% NUT, LOCK, CHERRY BURRELL 700004A02 ( approx: 68mm ID x 92mmOD)
18 67 4.6% 61.1% STUD, COVER, VOTATOR23 66 4.5% 65.6% BLADE, MUTATOR, CHERRY BURRELL 900099, 112132‐E, FOR MPU 11 , A2 / A3
15 65 4.5% 70.1% ITEM D, (4of10) SEAL, U‐CUP BODY, CHERRY BURRELL 7000014A05, FOR VOTATORS (Able O‐ring equivalent: HC187‐02.75ON700 ‐ 2‐3/4" X 3‐1/8" X 3/16")
9 65 4.5% 74.6% PIN, BASE, SPECIAL CHAMFER TOPS, VOTATOR
27 57 3.9% 78.5% PIN, BLADE FASTENER, CHERRY BURRELL 14868, LARGE VOTATOR M123A (NOT IN USE ‐ FOR OLD MPU‐01 VOTATOR?
8 55 3.8% 82.3% ITEM E, (5of10) O‐RING, CHERRY BURRELL 700006B23, N70235, FOR VOTATORS
16 45 3.1% 85.4% ITEM F, (6of10) INSERT, SEAL BODY, GRAPHITE, FOR VOTATORS, CHERRY BURRELL 110892‐A4, CHERRY BURRELL 11089A4
13 36 2.5% 87.8% NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A 10 35 2.4% 90.2% ITEM B, (2of10) RING, SEAL BACKING, CHERRY BURRELL 110203‐C120 29 2.0% 92.2% SEAL, SHAFT, CHERRY BURRELL 700030A88, LINE 21 FOR VOTATORS
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26 25 1.7% 94.0% PIN, BLADE FASTENER, CHERRY BURRELL 14869, SMALL VOTATOR M123A
14 23 1.6% 95.5% FABRICATE (LOCAL ‐ ADA) NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A (do not re‐order ‐more expensive than Orig)
5 22 1.5% 97.0% NUT, 3/4", SS, VOTATOR11 18 1.2% 98.3% SEAL, PIN DRIVE, CHERRY BURRELL 119036, VOTATOR FOR MPU 53 15 1.0% 99.3% ITEM J, (10of10) SEAL, LIPSEAL, CHERRY BURRELL 700030A42, FOR VOTATORS
21 5 0.3% 99.7% RING, SUPPORT, FOR WATER CHAMBER, SCHRODER, LINE 15 VOTATORS1 5 0.3% 100.0% BEARING, CHERRY BURRELL 113749
1455 1
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Appendix C The following table shows the raw data that was used to create a Pareto Histogram for the Bander based on downtime duration as the consequences. Pareto Histograms for Bander are presented after the tables.
Raw Data for Bander Pareto Analysis (Downtime Duration) Part No.
Downtime Duration (min)
% Time % Cum Part Description
34 9141 12.3% 12.3% 2" DOUBLE SPLIT STAINLESS COLLARS
10 4889 6.6% 18.9% SMC CYLINDER, PLUNGER ASS'Y, AXON BANDER, 3" STROKE, 5/16" ROD, 1/4‐28 THRD‐MALE , 1/8 NPT PORTS, NO CUSHIONS
39 4889 6.6% 25.4% LABEL OIP OVERLAY FOR HMI DISPLAY MAPLE SYSTEMS (MODEL #: OIT‐3160‐B00) #12012 4646 6.2% 31.7% PERFORATION WHEEL (wheel vertical perf support) , # 5269 (for Bander) (Roller with Bearing # GBC R8RS)
31 4646 6.2% 37.9% FILTER, AIR SUCTION, WITH ONE‐TOUCH FITTINGS, SMC, #ZFB201‐0725 3451 4.6% 42.6% HEATER ELEMENT 220VAC TUBULAR (SIDE)1 3226 4.3% 46.9% BANDER FEED ROLER DRIVE BELT , GATES POWER GRIP 250XL037
30 3226 4.3% 51.3% CONTROL,FLOW, NAS SERIES, SMC, WITH ONE‐TOUCH FITTING, #NAS205IF‐0719 2340 3.1% 54.4% BAR , # 50252‐6.88 ,6.88" Roller Bullet , (subpart for 797459) (‐1 pc rqd)48 2340 3.1% 57.5% SHAFT, 5/8" DIA x 7" LG. ; WITH DRIVE TAB ON ONE END, BANDER SCROLL DRIVE ASS'Y29 2315 3.1% 60.7% CONTROL,FLOW, NAS SERIES, SMC, WITH ONE‐TOUCH FITTING, #NAS200IF‐0717 1702 2.3% 63.0% SHAFT/PIN , # 50251 , 1/8" X 5/8" Roller Bullet , (subpart for 797459) (‐4 pcs rqd)46 1702 2.3% 65.2% BRONZE SPACER WASHERS, 1" X 5/8" X 1/16"3 1649 2.2% 67.5% BRACKET PERF WHEEL MOUNT, # 5270
32 1649 2.2% 69.7% BEARING, BANDER HEAD FILM DRIVE‐ROLLER ASS'Y33 1594 2.1% 71.8% VALVE, SOLENOID, 24VDC, SMC, #VQZ2151‐5YZW FOR BANDING MACHINES18 1285 1.7% 73.5% SUPPORT SHAFT , # 50253 (subpart for 797459) (‐2 pcs rqd) 47 1285 1.7% 75.3% SHAFT, 5/8" DIA X 7" LG. 3/16" KEYWAY ‐ KEYED ALL THE WAY , BANDER SCROLL DRIVE ASS'Y23 1085 1.5% 76.7% ROLLER BULLET ASSEMBLY, 215mm, #6036‐215 (BANDER 1lb)9 984 1.3% 78.1% SMC CYLINDER, #NCGBA20‐0100 (for Bander UPSTREAM film band gripper assy‐ AXON#2407
38 984 1.3% 79.4% DISPLAY, HMI, MAPLE SYSTEMS, WITH 2x20 BACKLIT LCD, MODEL #: OIT‐3160‐B00, #114728 962 1.3% 80.7% DRIVER STEPPER P70360‐SDN , # 17671 ‐ FOR BANDER HEAD FILM FEED5 954 1.3% 82.0% PERFORATION CYLINDER (1/4" Stroke) , # 2047 (for Bander) ("BIMBA" Cylinder # FT‐090.25 ‐3R)4 915 1.2% 83.2% V‐PERFORATION KNIFE (Blade vertical perf wheel) , # 5271 (for Bander) (Gear with Bearing # R8RS)
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15 865 1.2% 84.3% (subpart for 797464): ROLLER BEARING SUPORT SHAFT ASSEMBLY FOR 1 LB BULLET (INCLUDES 4 BEARING #3571; 4 SHAFT#50251 ; 2 SUPPORT SHAFT#50253 & 1 BAR#50252‐6.88) ‐ Assemble in‐house ; parts ordered separately
44 865 1.2% 85.5% LINEAR BEARING SPACER FOR DOWN STREAM GRIPPER ASS'Y
14 821 1.1% 86.6% Gearbox, HP‐2.3, Ratio:20, #SBKHF726L205B7T1 for Bander conveyor (SPC Chain) drive (GEARBOX UNILEVER #301‐G‐040334D)
43 821 1.1% 87.7% THOMSON SHAFT, 3/8 x 12" lg. DOWNSTREAM BAND GRIPPER ASS'Y16 805 1.1% 88.8% BEARING, # 3571 , Bearing Bullet Plate, (subpart for 797459) (‐4 pcs rqd)45 805 1.1% 89.9% KNIFE, CYLINDER (For Bandaid) #2017 (SMC #281770 001 20 , PN:US10437)20 785 1.1% 90.9% BULLET ROD 11" ROLLER BULLET , # 50254‐11‐03 (for Banders)49 785 1.1% 92.0% SHAFT, 5/8" DIA x 4 3/4" LG. ; WITH DRIVE TAB ON ONE END, BANDER SCROLL DRIVE ASS'Y22 615 0.8% 92.8% LOCKNUT WITH NYLON INSERT, #8‐32 UNC X 1/2" LGTH, 18‐8 STAINLESS STEEL51 615 0.8% 93.7% SHOULDER BOLT, S.S., 5/16" X 7/8" LG., BANDER KNIFE ASS'Y24 590 0.8% 94.4% ROLLER BULLET ASSEMBLY, 262mm, #6036‐262 (BANDER 2lb)8 530 0.7% 95.2% SMC CYLINDER, Bander downstream film band gripper assy , # 2406
37 530 0.7% 95.9% COLLAR, SHAFT, QUICK‐CONNECT ONE‐PIECE, 1" BORE SIZE, JERGENS (PN: 101‐040215), #6168K317 440 0.6% 96.5% ROLLER BEARING, # 3150 (for Bander) (#SCE470H)
36 440 0.6% 97.1% NYLON BUSHING SPACER, LINEAR BEARING SPACER FOR DOWNSTREAM BAND GRIPPER ASS'Y, .386" ID x .604 OD x 1.906" LGTH.
6 375 0.5% 97.6% UNWIND CYLINDER (SMC 3") # 2161 (for Bander) 35 375 0.5% 98.1% SMC CYLINDER CLEVIS, DOWNSTREAM BAND GRIPPER CYLINDER11 344 0.5% 98.5% OMRON , CLASS 2 POWER SUPPLY , S8VS‐06024 , INPUT 50/60Hz AC 100‐240V 1.7A , OUTPUT DC24V 2.5A40 344 0.5% 99.0% THOMSON SHAFT, 3/8" DIA, 4 1/16" LG. , UPSTREAM BAND GRIPPER ASS'Y26 203 0.3% 99.3% HEATER ELEMENT 220V TUBULAR TOP21 185 0.2% 99.5% SCREWS.BUTTON HEAD HEX SOCKET CAP, #8‐32 UNC X 1/2" LGTH, 18‐8 STAINLESS STEEL50 185 0.2% 99.8% BRONZE SPACER WASHER, 1" X 5/8" X 1/8" THICK, CHAIN IDLER SPOCKETS ASS'Y ON BANDERS12 50 0.1% 99.8% ETHERNET INTERFACE , AB , CAT # 1761‐NET‐ENI , SER C , FRN 3.01 , FOR CLASS 1 DIVISION 2 41 50 0.1% 99.9% THOMSON SHAFT, 3/8" x 4 5/8" lg.,, KNIFE ASS'Y13 30 0.0% 99.9% ALLEN‐BRADLEY , MICRO LOGIX 1500 , BASE UNIT , CAT # 1764‐28BXB SER # B REV # A , AXON CORP PART # 128842 30 0.0% 100.0% THOMSON SHAFT, 3/8" x 8 1/16" lg., PLUNGER ASS'Y 27 20 0.0% 100.0% STEPPER MOTOR, AXON BANDER, POWERPAC MODEL K31HRLG‐LDK‐NS‐02
74362 1
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Appendix D The following table shows the raw data that was used to create a Jack Knife Diagram for the MPU. A Jack Knife Diagram for the MPU is presented after the table.
Raw Data for MPU Jack Knife Diagram Part No.
Downtime Frequency
Downtime Duration (min) MTTR Part Description
1 5 1992 398.4 BEARING, CHERRY BURRELL 1137492 77 1340 17.4025974 SHAFT, DRIVE, VOTATOR STUD SHAFT FEMALE SPLINE, CHERRY BURRELL 920430, 34438, 8013833 15 1143 76.2 ITEM J, (10of10) SEAL, LIPSEAL, CHERRY BURRELL 700030A42, FOR VOTATORS4 67 2529 37.7462687 NUT, LOCK, CHERRY BURRELL 700004A02 ( approx: 68mm ID x 92mmOD)5 22 2064 93.8181818 NUT, 3/4", SS, VOTATOR
6 86 3367 39.1511628 ITEM G, (7of10) O‐RING, CHERRY BURRELL 700006A32, N75226, FOR VOTATORS NEW #N75226 FOR BUNA; V‐70226 ‐ FOR VITON; E‐70226 ‐ FOR EPDM
7 79 1962 24.835443 O‐RING, CHERRY BURRELL 70001A128 55 3913 71.1454545 ITEM E, (5of10) O‐RING, CHERRY BURRELL 700006B23, N70235, FOR VOTATORS9 65 994 15.2923077 PIN, BASE, SPECIAL CHAMFER TOPS, VOTATOR
10 35 891 25.4571429 ITEM B, (2of10) RING, SEAL BACKING, CHERRY BURRELL 110203‐C111 18 1859 103.277778 SEAL, PIN DRIVE, CHERRY BURRELL 119036, VOTATOR FOR MPU 512 84 3388 40.3333333 ITEM I, (9of10) HEAD, SEAL, INSERT, VOTATORS 13 36 1584 44 NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A
14 23 1271 55.2608696 FABRICATE (LOCAL ‐ ADA) NUT, LOCK, SHAFT, CHERRY BURRELL 119275‐A (do not re‐order ‐more expensive than Orig)
15 65 1918 29.5076923 ITEM D, (4of10) SEAL, U‐CUP BODY, CHERRY BURRELL 7000014A05, FOR VOTATORS (Able O‐ring equivalent: HC187‐02.75ON700 ‐ 2‐3/4" X 3‐1/8" X 3/16")
16 45 3755 83.4444444 ITEM F, (6of10) INSERT, SEAL BODY, GRAPHITE, FOR VOTATORS, CHERRY BURRELL 110892‐A4, CHERRY BURRELL 11089A4
17 73 612 8.38356164 STUD, VOTATOR COVER, M24 X 77 , # S101922 18 67 1703 25.4179104 STUD, COVER, VOTATOR19 98 721 7.35714286 ITEM #2, DISK 25 Stainless Steel (approx: 45mm OD x 25 mm ID x 4 mmthick) S14237720 29 2838 97.862069 SEAL, SHAFT, CHERRY BURRELL 700030A88, LINE 21 FOR VOTATORS21 5 3562 712.4 RING, SUPPORT, FOR WATER CHAMBER, SCHRODER, LINE 15 VOTATORS22 78 2563 32.8589744 BLADE, MUTATOR, CHERRY BURRELL 900129, 121088, FOR MPU 11, A1
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23 66 3576 54.1818182 BLADE, MUTATOR, CHERRY BURRELL 900099, 112132‐E, FOR MPU 11 , A2 / A324 97 1532 15.7938144 PIN, BASE MUTATOR, CHERRY BURRELL 110368‐A, VOTATOR25 83 1342 16.1686747 PIN, HEAD MUTATOR, CHERRY BURRELL 112004‐A, VOTATOR26 25 3073 122.92 PIN, BLADE FASTENER, CHERRY BURRELL 14869, SMALL VOTATOR M123A
27 57 2533 44.4385965 PIN, BLADE FASTENER, CHERRY BURRELL 14868, LARGE VOTATOR M123A (NOT IN USE ‐ FOR OLD MPU‐01 VOTATOR?
1455 58025 2293.05524
100 101 102100
101
102
103Figure 5: Jack Knife Diagram - MPU (2008)
Frequency of Failure
Mea
n Ti
me
to R
epai
r (m
in) 1
2 2425
Acute
Chronic A
Chronic B
Acute &Chronic
3
4
5
6
7
8
9
10
11
121314
15
16
17
18
19
20
21
22
23
26
27
54
40
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Appendix E The following table shows the raw data that was used to create a Jack Knife Diagram for the Bander. A Jack Knife Diagram for the Bander is presented after the table.
Raw Data for Bander Jack Knife Diagram Part No.
Downtime Frequency
Downtime Duration (min) MTTR Part Description
1 216 3226 14.9351852 BANDER FEED ROLER DRIVE BELT , GATES POWER GRIP 250XL0372 27 4646 172.074074 PERFORATION WHEEL (wheel vertical perf support) , # 5269 (for Bander) (Roller with Bearing # GBC R8RS)3 188 1649 8.7712766 BRACKET PERF WHEEL MOUNT, # 52704 14 915 65.3571429 V‐PERFORATION KNIFE (Blade vertical perf wheel) , # 5271 (for Bander) (Gear with Bearing # R8RS)5 33 954 28.9090909 PERFORATION CYLINDER (1/4" Stroke) , # 2047 (for Bander) ("BIMBA" Cylinder # FT‐090.25 ‐3R)6 4 375 93.75 UNWIND CYLINDER (SMC 3") # 2161 (for Bander) 7 37 440 11.8918919 ROLLER BEARING, # 3150 (for Bander) (#SCE470H) 8 3 530 176.666667 SMC CYLINDER, Bander downstream film band gripper assy , # 24069 120 984 8.2 SMC CYLINDER, #NCGBA20‐0100 (for Bander UPSTREAM film band gripper assy‐ AXON#2407
10 11 4889 444.454545 SMC CYLINDER, PLUNGER ASS'Y, AXON BANDER, 3" STROKE, 5/16" ROD, 1/4‐28 THRD‐MALE , 1/8 NPT PORTS, NO CUSHIONS
11 14 344 24.5714286 OMRON , CLASS 2 POWER SUPPLY , S8VS‐06024 , INPUT 50/60Hz AC 100‐240V 1.7A , OUTPUT DC24V 2.5A12 1 50 50 ETHERNET INTERFACE , AB , CAT # 1761‐NET‐ENI , SER C , FRN 3.01 , FOR CLASS 1 DIVISION 2
13 2 30 15 ALLEN‐BRADLEY , MICRO LOGIX 1500 , BASE UNIT , CAT # 1764‐28BXB SER # B REV # A , AXON CORP PART # 1288
14 41 821 20.0243902 Gearbox, HP‐2.3, Ratio:20, #SBKHF726L205B7T1 for Bander conveyor (SPC Chain) drive (GEARBOX UNILEVER #301‐G‐040334D)
15 36 865 24.0277778
(subpart for 797464): ROLLER BEARING SUPORT SHAFT ASSEMBLY FOR 1 LB BULLET (INCLUDES 4 BEARING #3571; 4 SHAFT#50251 ; 2 SUPPORT SHAFT#50253 & 1 BAR#50252‐6.88) ‐ Assemble in‐house ; parts ordered separately
16 16 805 50.3125 BEARING, # 3571 , Bearing Bullet Plate, (subpart for 797459) (‐4 pcs rqd)17 83 1702 20.5060241 SHAFT/PIN , # 50251 , 1/8" X 5/8" Roller Bullet , (subpart for 797459) (‐4 pcs rqd)18 6 1285 214.166667 SUPPORT SHAFT , # 50253 (subpart for 797459) (‐2 pcs rqd)19 252 2340 9.28571429 BAR , # 50252‐6.88 ,6.88" Roller Bullet , (subpart for 797459) (‐1 pc rqd)20 3 785 261.666667 BULLET ROD 11" ROLLER BULLET , # 50254‐11‐03 (for Banders)
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21 96 185 1.92708333 SCREWS.BUTTON HEAD HEX SOCKET CAP, #8‐32 UNC X 1/2" LGTH, 18‐8 STAINLESS STEEL22 6 615 102.5 LOCKNUT WITH NYLON INSERT, #8‐32 UNC X 1/2" LGTH, 18‐8 STAINLESS STEEL23 70 1085 15.5 ROLLER BULLET ASSEMBLY, 215mm, #6036‐215 (BANDER 1lb)24 11 590 53.6363636 ROLLER BULLET ASSEMBLY, 262mm, #6036‐262 (BANDER 2lb)25 236 3451 14.6228814 HEATER ELEMENT 220VAC TUBULAR (SIDE)26 6 203 33.8333333 HEATER ELEMENT 220V TUBULAR TOP27 3 20 6.66666667 STEPPER MOTOR, AXON BANDER, POWERPAC MODEL K31HRLG‐LDK‐NS‐0228 31 962 31.0322581 DRIVER STEPPER P70360‐SDN , # 17671 ‐ FOR BANDER HEAD FILM FEED29 352 2315 6.57670455 CONTROL,FLOW, NAS SERIES, SMC, WITH ONE‐TOUCH FITTING, #NAS200IF‐0730 5 3226 645.2 CONTROL,FLOW, NAS SERIES, SMC, WITH ONE‐TOUCH FITTING, #NAS205IF‐0731 139 4646 33.4244604 FILTER, AIR SUCTION, WITH ONE‐TOUCH FITTINGS, SMC, #ZFB201‐0732 99 1649 16.6565657 BEARING, BANDER HEAD FILM DRIVE‐ROLLER ASS'Y 33 87 1594 18.3218391 VALVE, SOLENOID, 24VDC, SMC, #VQZ2151‐5YZW FOR BANDING MACHINES34 58 9141 157.603448 2" DOUBLE SPLIT STAINLESS COLLARS35 48 375 7.8125 SMC CYLINDER CLEVIS, DOWNSTREAM BAND GRIPPER CYLINDER
36 11 440 40 NYLON BUSHING SPACER, LINEAR BEARING SPACER FOR DOWNSTREAM BAND GRIPPER ASS'Y, .386" ID x .604 OD x 1.906" LGTH.
37 450 530 1.17777778 COLLAR, SHAFT, QUICK‐CONNECT ONE‐PIECE, 1" BORE SIZE, JERGENS (PN: 101‐040215), #6168K3138 15 984 65.6 DISPLAY, HMI, MAPLE SYSTEMS, WITH 2x20 BACKLIT LCD, MODEL #: OIT‐3160‐B00, #114739 94 4889 52.0106383 LABEL OIP OVERLAY FOR HMI DISPLAY MAPLE SYSTEMS (MODEL #: OIT‐3160‐B00) #120140 7 344 49.1428571 THOMSON SHAFT, 3/8" DIA, 4 1/16" LG. , UPSTREAM BAND GRIPPER ASS'Y41 42 50 1.19047619 THOMSON SHAFT, 3/8" x 4 5/8" lg.,, KNIFE ASS'Y 42 3 30 10 THOMSON SHAFT, 3/8" x 8 1/16" lg., PLUNGER ASS'Y 43 82 821 10.0121951 THOMSON SHAFT, 3/8 x 12" lg. DOWNSTREAM BAND GRIPPER ASS'Y44 19 865 45.5263158 LINEAR BEARING SPACER FOR DOWN STREAM GRIPPER ASS'Y45 74 805 10.8783784 KNIFE, CYLINDER (For Bandaid) #2017 (SMC #281770 001 20 , PN:US10437)46 7 1702 243.142857 BRONZE SPACER WASHERS, 1" X 5/8" X 1/16" 47 130 1285 9.88461538 SHAFT, 5/8" DIA X 7" LG. 3/16" KEYWAY ‐ KEYED ALL THE WAY , BANDER SCROLL DRIVE ASS'Y48 32 2340 73.125 SHAFT, 5/8" DIA x 7" LG. ; WITH DRIVE TAB ON ONE END, BANDER SCROLL DRIVE ASS'Y49 176 785 4.46022727 SHAFT, 5/8" DIA x 4 3/4" LG. ; WITH DRIVE TAB ON ONE END, BANDER SCROLL DRIVE ASS'Y50 3 185 61.6666667 BRONZE SPACER WASHER, 1" X 5/8" X 1/8" THICK, CHAIN IDLER SPOCKETS ASS'Y ON BANDERS51 180 615 3.41666667 SHOULDER BOLT, S.S., 5/16" X 7/8" LG., BANDER KNIFE ASS'Y
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100 101 102 103100
101
102
103Figure 6: Jack Knife Diagram - Bander (2008)
Frequency of Failure
Mea
n Ti
me
to R
epai
r (m
in)
1
2
3
4
5
6
7
8
9
10
11
12
1314
15
16
17
18
19
20
37
Acute
Chronic A
Chronic B
Acute & Chronic
21
22
23
24
25
26
27
28
29
30
31
3233
34
35
36
383940
41
42 43
44
45
46
47
48
49
50
51
72
20
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Appendix F The following is the Matlab code that the thesis student created to generate Jack Knife Diagrams %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Matlab Jack Knife Digram Function % Function written by Kenneth Liang 993101905 % NOTE: This program requires a .mat file containing parts information. % This file should include a parts description, frequency of % downtime, duration of downtime for part, and consequence (MTTR). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function JackKnifeDiagram(data) %Data file should contain four columns representing part description, %frequency of part failure, duration of downtime and consequnce (MTTR) Type = data(:,1); %cell2mat converts cell array to a matrix array Frequency = data(:,2); Duration = data(:,3); MTTR = data(:,4); Q = length(Type); %Total number of parts in a particular category N = sum(Frequency); %Total number of times parts failed D = sum(Duration); %Total duration of downtime caused by all parts LimitX = N/Q; %X axis limit LimitY = D/N; %Y axis limit %Creating Jack Knife Diagram loglog(Frequency,MTTR,'.');grid; %loglog(row, col) hold on; %Labelling Graph Title and Axis title('\bfJack Knife Diagram - Packaging Spare Parts','FontSize',16); xlabel('\bfFrequency of Failure','FontSize',16); ylabel('\bfMTTR (min)','FontSize',16); %Labelling points (i.e. the part description) text(Frequency + 0.3, MTTR + 0.3, int2str(Type),'FontSize',8); %Quadrant Labels text(100, 150, '\bfAcute','FontSize',12,'Color',[1,0,0]); text(600, 12, '\bfChronic A','FontSize',12,'Color',[1,0,0]); text(600, 5, '\bfChronic B','FontSize',12,'Color',[1,0,0]); text(300, 50, '\bfAcute & Chronic','FontSize',12,'Color',[1,0,0]); %Limit lines for frequency and consequence (i.e. MTTR) %Need to specify the end points of line (i.e. [x1;x2],[y1;y2]) line([LimitX;LimitX],[1;10000],'LineWidth',1.5); line([1;1000],[LimitY;LimitY],'LineWidth',1.5); %Limit line for Chronic A and B line([LimitX;1000],[LimitY;log(D/Q)],'LineWidth',1.5);
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display(log(D/Q)); %Limit Labels text(LimitX, 1, num2str(round(LimitX)),'FontSize',10,'Color',[1,0,0]); text(1, LimitY+1.5, num2str(round(LimitY)),'FontSize',10,'Color',[1,0,0]); hold off; end
Appendix G The following table shows the raw data that was used to optimize MPU Pin Blade Fastener part.
Part No. SKU # Description
Mfg. Name Class OHQ
Cost Per Unit
27 596915 PIN, BLADE FASTENER, CHERRY BURRELL 14868, LARGE VOTATOR M123A (NOT IN USE - FOR OLD MPU-01 VOTATOR?
CHERRY BURRELL
MUTATOR-BLADES 172.00 3.5900
Distribution Reorder Quantity
Reorder point
Holding Cost
Ordering Cost
Yearly Demand
Gamma 620 168 1.077 30.78 6734 Demand for Blade Fasteners (# of parts) during Lead Time (1 Week) (2008 Data)
Week 1 147 Week 14 94 Week 27 136 Week 40 121
Week 2 110 Week 15 95 Week 28 91 Week 41 111
Week 3 149 Week 16 90 Week 29 137 Week 42 148
Week 4 109 Week 17 119 Week 30 145 Week 43 102
Week 5 127 Week 18 137 Week 31 159 Week 44 147
Week 6 167 Week 19 163 Week 32 160 Week 45 168
Week 7 98 Week 20 169 Week 33 157 Week 46 111
Week 8 102 Week 21 115 Week 34 165 Week 47 109
Week 9 163 Week 22 158 Week 35 121 Week 48 106
Week 10 130 Week 23 172 Week 36 172 Week 49 133
Week 11 98 Week 24 91 Week 37 133 Week 50 172
Week 12 122 Week 25 128 Week 38 114 Week 51 123
Week 13 100 Week 26 112 Week 39 104 Week 52 124
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Appendix H The following tables are summary lists showing the optimal re-order point and re-order quantity for all the parts that were deemed significant by the Jack Knife Diagrams. These parts are found in the Acute and Chronic quadrant of the Jack Knife Diagram. Jack Knife Diagrams for each machine/equipment is also presented after each table.
Optimal Inventory Parameters for Corazza Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
11 SHAFT, CORAZZA, (#D3005959), C/W KEYS SHAPE TYPE "B" (#C1002167) Normal 13 1
20 FITTING, CURVED, CORAZZA C2000069 ; "SMC" FITTING, # KQ2L06‐01S ‐ ELBOW, TUBE ADAPTER, 6 MM X 1/8" NPT, TUBE X MNPT, 90 DEG Weibull 164 0
23 CUP, SUCTION, RUBBER, BELLI‐ITALIA D4000437, CORAZZA Gamma 1421 139 26 FLANGE, CORAZZA D4084331 Normal 8 2 39 PIN, CORAZZA D4039285 Weibull 24 1 43 KNOB, CORAZZA D4000845 Normal 42 0 45 ARM, CORAZZA D3086083 Normal 29 2 51 BAR, WEAR, CORAZZA D2084330 Normal 9 1 54 GEAR, SPUR, SPUR, CORAZZA D4034433 Gamma 19 2 65 SPRING, CORAZZA D4000349 Weibull 71 0 73 CUP, VACUUM, NEW STYLE, GEORGE T WHITE VC‐B15 Gamma 548 111 74 PLATE, SEAL, CORAZZA D4111627 Normal 25 0 77 BLOCK, ASSEMBLY, CORAZZA D3083433, FOR THE SHELL WRAP FORMING Weibull 29 0
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Optimal Inventory Parameters for Certipak Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
1 CERTIPAK CARTONER TM Gamma 34 6 2 CHAIN, RH FLIGHT ASSEMBLY, CERTIPAK 25533‐14‐2 Lognormal 11 1 3 CHAIN, LH FLIGHT ASSEMBLY, CERTIPAK 25533‐14‐3 Lognormal 11 1
12 PLATE, PUSHER MOUNTING, CERTIPAK 15951‐531‐42 Normal 16 0 13 CHAIN GUIDE (LONG), CERTIPAK M/C, Lognormal 15 0 23 LUG, CERTIPAK 25615‐26, CARTONER Weibull 44 1 24 ASSEMBLY, LUG, CERTIPAK 25236‐27, CARTONER Normal 33 0 25 ASSEMBLY, FLIGHT, CERTIPAK 25326‐21 Lognormal 27 0
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Optimal Inventory Parameters for Palletizer Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
3 SPOOL (Steel) for overhead conv. (approx: 2" dia x 2" overall lenght ‐ w/ 2 drilled & tapped 1/4 ‐ 20 set screw holes) Weibull 50 2
13 CAP, BRUSH, CARBON, SABEL, ROTARY SABEL Normal 28 0
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Optimal Inventory Parameters for Chains Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
9
Stainless Steel Chain, SS16B‐1 RCL, C/W Special WA‐2 Attachments (10mm Holes) Evry 2nd, 4th, 8th, & 10th Repeat (2 link/4link, alternately) (for Line 5 Hamba carrier chain) Normal 22 0
17 #RS60 ROLLER CHAIN Gamma 267 53
29
CHAIN LINK ONLY, TRANSMISSION, CONNECTING, STEEL, LIEFERSCHEIN 034013885 (Connection Joint Straight ‐ Carrier chain Link ONLY, NO attachment for Line 15 Hamba) Weibull 237 11
40 #25 CONNECTING LINK, TSUBAKI 25 C/L Gamma 349 8 67 OFFSET LINK, CHAIN 111046 Normal 63 0 68 PLASTIC ROLLER CHAIN for sprocket‐25B30 (Line 1 Checkweigher) Gamma 58 9
77 SPROCKET, 19 HARD TEETH, 1 1/8" BORE, 1/4 KEYWAY, MARTIN, 50BS19HT‐1 1/8 Normal 28 0
91 #40‐2 C/L, S.S. CONNECTING LINK Normal 190 21 92 RSD40 LAMBDA RIV CHAIN (SELF‐LUBRICATING CHAIN), TSUBAKI Weibull 179 61
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Optimal Inventory Parameters for Rollers Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
2 ROLLER, GUIDE, 1/2" ID X 2" OD (overall thickness: .88) , PLASTIC, FOR SIDE BELT (for DEKKA Tape) Lognormal 93 12
4 IDLER PULLEY ‐ " BEMIS" (150004‐B) / ROLLER, DISC, 2.875" DIA (CROWNED) X 2.7" LONG, SIDE BELT TYPE ASSEMBLY, Normal 15 4
10 HEX AXEL SHAFT FOR ITEM # 674505, 7/16" DIA X 30"LG, 1/4‐20 THRD HOLES AT EACH END Gamma 48 30
16 IDLER ROLLER (approx: 1.88" dia x 2.73" long ) with ROLLER BEARING (#6004Z) ON BOTH SIDES AND STUD SHAFT (.75 X 3" LONG) Normal 15 2
25 ROLLER, 410 MM OAL, INTERROLL 1.154V50C30‐3.75 Normal 36 0 31 ROLLER, CCC‐550‐104, WATER TREATMENT PLANT Lognormal 25 2
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Optimal Inventory Parameters for Belts Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
9 BELT, CONVEYOR, 15" WD X 12' LG, UPPER CASE, FEED TO PALLETIZER ON THE BULK LINE, CONNECT BELTING TR‐15NF‐CB15X12' Normal 5 1
17 BELT, V, 400J16, 40.5000" OC, 1.5000" WD, 0.1560" THK, POLY‐V 16 RIB, JASON Normal 75 9
29 BELT, V, A62, 64.3000" OC, 0.5000" WD, 0.3440" THK, GATES Weibull 61 4 40 BELT, TIMING, 2450‐14M‐40, 2450 MM, 14 MM, 40 MM, GATES Gamma 73 4 67 BELT, V, 3L240, 24.0000" OC, 0.3750" WD, 0.2190" THK, GATES, TRUFLEX Gamma 94 4 68 BELT, V, 3L250, 25.0000" OC, 0.3750" WD, 0.2190" THK, GATES Normal 100 0 77 BELT, V, 3V630, 63.0000" OC, 0.3750" WD, 0.3130" THK, GATES, TRUFLEX Weibull 58 0 91 BELT, V, 4L320, 32.0000" OC, 0.5000" WD, 0.2810" THK, GATES, TRUFLEX Gamma 106 4 92 BELT, V, 4L330, 33.0000" OC, 0.5000" WD, 0.2810" THK, GATES, TRUFLEX Weibull 109 0
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Optimal Inventory Parameters for Sabel Case Packer Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
15 COUPLING , 13 X RSB BODY (HUB) (SAGA CPLG) Gamma 19 2 27 VALVE, VACUUM, 1/4" PORT, 24VDC, MAC VALVE 225B‐111CC Lognormal 16 0 42 CONTROL, METER OUTFLOW, 1/4" NPT, SMC NAS2301FN0211S Lognormal 34 0 50 SPRING, COMPRESSION, IN‐FEED TRIP MEDIUM DUTY, SABEL SPRNC022D8SS Gamma 666 80 56 FRAME SUB‐ASSEMBLY, LOAD ELEVATOR ASS'Y, SABLE LINE 15 Normal 14 2
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Optimal Inventory Parameters for Hamba Filler Part No. Part Description
Probability Distribution
Optimal Reorder Quantity
Optimal Reorder Point
15 SENSOR, UNIT‐OPTIC, HAMBA AMMS‐10‐1, 4002/6003 Normal 11 1
24 13MM, STAINLESS STEEL HEAVY DUTY WASHERS, 25MM OD X 13MM ID X 4MM THICK Gamma 127 31
35 8 MM SHOULDER BOLTS AND SPACERS, HAMBA LIDDER, L‐ 5 , L‐ 15, (M8 X 12 Socket Shoulder Screw A2 SS) Gamma 269 75
52 CONTACTOR, ALLEN‐BRADLEY 100‐C23UZJ01 Normal 22 1
82 PACKING, FLAT, 70.0 MM X 51.50 MM X 2.0 MM, FILLER HEAD VALVE ROD ASSEMBLY, HAMBA 34031122, 234 Weibull 108 11
84 FLAT PACKING, 50.5 MM X 70 MM X 2 MM, HAMBA 155‐01‐200‐016‐0 (previous ref# 130 00 006 038 1)(for AP Weibull 104 10
90 BUSHING, HAMBA 34100169, HAMBA 234 DOSING CAM FOLLOWER ASSEMBLY Weibull 59 0
105 STARTER, ELECTRIC MOTOR, MANUAL PROTECTOR, 600V 4.4A 3PH 50/60HZ 3P, ALLEN‐BRADLEY 140‐MN‐0040‐C Gamma 76 24
112 SWITCH, PUSHBUTTON, 1NO, BLACK, BOOTLESS FLUSH HEAD MOMENTARY NON‐ILLUMINATED, ALLEN‐BRADLEY 800H‐AR Normal 45 0
127 RELAY, CONTROL MINIATURE SQUARE BASE, 24VDC, 3A, 4PDT, 14 BLADE, ALLEN‐BRADLEY 700‐HC14Z24 Lognormal 38 0
144 POS. 08 ‐ GASKET, FLAT PACKING, HAMBA 657‐00‐245‐153‐0 (FPM) 60.5 X 80.0 X 2.00 Normal 17 0
174 CAM, 1 LB. LINE 5, HAMBA, KOL BEN, 598 715, 34224425, 65700207840, LR .454 Normal 23 0
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Appendix I The following is the Matlab code that the thesis student created to determine the optimal re-order point and re-order quantity. function distribution_function(x) %DISTRIBUTION_FUNCTION Create plot of datasets and fits % % Created By: Kenneth Liang % Student Number: 993101905 % Thesis: Optimizing Unilever's Captical/Emergency Spare Parts Inventory % % Purpose: This Matlab code fits a particular distribution to a set of % data supplied by the user. The main purpose is to identify the Lead % Time Demand Distribution (LTD) which is necessary to identify the % reorder point for inventory spare parts. % % Number of datasets: 1 % Number of fits: 5 (Normal, Weibull, Log Normal, Exponential, Gamma) % Force all inputs to be column vectors x = x(:); % Set up figure to receive datasets and fits f_ = clf; figure(f_); set(f_,'Units','Pixels','Position',[1 61 1440 709.45]); legh_ = []; legt_ = {}; % handles and text for legend ax_ = newplot; set(ax_,'Box','on'); hold on; % --- Plot data originally in dataset "My Data" t_ = ~isnan(x); Data_ = x(t_); [F_,X_] = ecdf(Data_,'Function','cdf'... ); % compute empirical cdf Bin_.rule = 1; [C_,E_] = dfswitchyard('dfhistbins',Data_,[],[],Bin_,F_,X_); [N_,C_] = ecdfhist(F_,X_,'edges',E_); % empirical pdf from cdf h_ = bar(C_,N_,'hist'); set(h_,'FaceColor','none','EdgeColor',[0.333333 0 0.666667],... 'LineStyle','-', 'LineWidth',1); title('\bf Probabiliy Density Graph','FontSize',16); xlabel('Lead Time Demand Data','FontSize',16); ylabel('Probability Density (PDF)','FontSize',16) legh_(end+1) = h_; legt_{end+1} = 'Lead Time Demand Data'; % Nudge axis limits beyond data limits xlim_ = get(ax_,'XLim'); if all(isfinite(xlim_)) xlim_ = xlim_ + [-1 1] * 0.01 * diff(xlim_); set(ax_,'XLim',xlim_)
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end x_ = linspace(xlim_(1),xlim_(2),100); % --- Create fit "Normal" % Fit this distribution to get parameter values t_ = ~isnan(x); Data_ = x(t_); % To use parameter estimates from the original fit: pargs_ = cell(1,2); [pargs_{:}] = normfit(Data_, 0.05); p_ = [pargs_{:}]; y_ = normpdf(x_,p_(1), p_(2)); h_ = plot(x_,y_,'Color',[1 0 0],... 'LineStyle','-', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_; legt_{end+1} = 'Normal'; % --- Create fit "Weibull" % Fit this distribution to get parameter values t_ = ~isnan(x); Data_ = x(t_); % To use parameter estimates from the original fit: p_ = wblfit(Data_, 0.05); y_ = wblpdf(x_,p_(1), p_(2)); h_ = plot(x_,y_,'Color',[0 0 1],... 'LineStyle','-', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_; legt_{end+1} = 'Weibull'; % --- Create fit "Lognormal" % Fit this distribution to get parameter values t_ = ~isnan(x); Data_ = x(t_); % To use parameter estimates from the original fit: p_ = lognfit(Data_, 0.05); y_ = lognpdf(x_,p_(1), p_(2)); h_ = plot(x_,y_,'Color',[0.666667 0.333333 0],... 'LineStyle','-', 'LineWidth',2,... 'Marker' none', 'MarkerSize',6); ,'legh_(end+1) = h_; legt_{end+1} = 'Lognormal'; % --- Create fit "Exponential" % Fit this distribution to get parameter values t_ = ~isnan(x); Data_ = x(t_); % To use parameter estimates from the original fit: p_ = expfit(Data_, 0.05);
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y_ = exppdf(x_,p_(1)); h_ = plot(x_,y_,'Color',[0.333333 0.333333 0.333333],... 'LineStyle','-', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_; legt_{end+1} = 'Exponential'; % --- Create fit "Gamma" % Fit this distribution to get parameter values t_ = ~isnan(x); Data_ = x(t_); % To use parameter estimates from the original fit: p_ = gamfit(Data_, 0.05); y_ = gampdf(x_,p_(1), p_(2)); h_ = plot(x_,y_,'Color',[1 0 1],... 'LineStyle','-', 'LineWidth',2,... 'Marker','none', 'MarkerSize',6); legh_(end+1) = h_; legt_{end+1} = 'Gamma'; hold off; leginfo_ = {'Orientation', 'vertical', 'Location', 'NorthEast'}; h_ = legend(ax_,legh_,legt_,leginfo_{:}); % create legend set(h_,'Interpreter','none'); %Generate random numbers that are obtained straight from a particular %distribution such as Normal rndNorm_Data = round(normrnd(Normal_mu,Normal_sigma,200,1)); rndWeibull_Data = round(wblrnd(Weibull_scale,Weibull_shape,200,1)); rndLogNorm_Data = round(lognrnd(LogNorm_mu,LogNorm_sigma,200,1)); rndExponential_Data = round(exprnd(Exponential_Rate,200,1)); rndGamma_Data = round(gamrnd(Gamma_shape,Gamma_scale,200,1)); %Using a KS statistical test to determined whether the lead time demand %data matches with numbers obtained from a particular distribution. If they %match, then the actual lead time demand data must come from that %probability distribution. a = kstest2(x,rndNorm_Data); b = kstest2(x,rndWeibull_Data); c = kstest2(x,rndLogNorm_Data); d = kstest2(x,rndExponential_Data); e = kstest2(x,rndGamma_Data); %KS test works as follows. If the KS test returns zero, then the lead time %demand data comes from that particular probability distribution. If the KS %test returns one, then it DOES NOT come from that probability %distribution. if (e == 0) Output = 'Lead Time Demand Data for Spare Part fits a Gamma Distribution'; elseif (e == 1) Output = 'Lead Time Demand Data for Spare Part does not fit a Gamma Distribution'; end
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if (a == 1) Output1 = [Output, sprintf('\nLead Time Demand Data for Spare Part does not fit a Normal Distribution')]; elseif (a == 0) Output1 = [Output, sprintf('\nLead Time Demand Data for Spare Part fits a Normal Distribution')]; end %Output KS test message msgbox(Output4,'Which Distribution Fits Data best'); %Ask the user for Economic Order Quantity Data prompt = {'Enter Distribution you think fits best:','Enter the Holding Cost for Spare Part:','Enter the Average Ordering Cost:','Enter the Yearly Demand for Spare Part:'}; dlg_title = 'Inputs for EOQ and Reorder Point Calculation'; num_lines = 1; answer = inputdlg(prompt,dlg_title,num_lines); %Error Checking to see if the user entered the correct data in order to %determine the EOQ quantity. errorCheck =0; while (errorCheck ~=1) %Tests to see if the user entered a distribution if (strcmpi(answer(1),'normal')==1 || strcmpi(answer(1),'weibull')==1 || strcmpi(answer(1),'exponential')==1 || strcmpi(answer(1),'lognormal')==1 || strcmpi(answer(1),'gamma')==1)&& isempty(answer(1))~=1; %Tests to see if the user entered an appropriate holding cost if(isnumeric(str2double(answer(2)))==1 && isempty(answer(2))~=1 && str2double(answer(2))>=0) %Tests to see if the user entered an appropriate ordering cost if(isnumeric(str2double(answer(3)))==1 && isempty(answer(3))~=1 && str2double(answer(3))>=0) %Tests to see if the user entered an appropriate yearly %demand if(isnumeric(str2double(answer(4)))==1 && isempty(answer(4))~=1 && str2double(answer(4))>=0) errorCheck=1; else answer = inputdlg(prompt,dlg_title,num_lines); end else answer = inputdlg(prompt,dlg_title,num_lines); end else answer = inputdlg(prompt,dlg_title,num_lines); end
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else answer = inputdlg(prompt,dlg_title,num_lines); end end %EOQ quantity Q = sqrt((2*str2double(answer(3))*str2double(answer(4)))/str2double(answer(2))); %Dekker's Rounding technique FloorQ = floor(Q); if FloorQ == 0 Q = 1; elseif FloorQ ~= 0 && ((Q/FloorQ) <= ((FloorQ+1)/Q)) Q = FloorQ; else Q = FloorQ + 1; end %Determine the re-order point using Dekker's technique if strcmpi(answer(1),'normal')==1 k=0; %k = the variable s (list of possible reorder points) in the formula while(normcdf(k,Normal_mu,Normal_sigma)~=1) k = k + 1; end l=0; %l = the variable x in the formula while(normpdf(l,Normal_mu,Normal_sigma)>0) l = l + 1; end Sum=0; for m=0:1:k for n=m:1:l Sum = Sum + (n-m) * normpdf(n,Normal_mu,Normal_sigma); end if ((1 - Sum/Q) > 0.90) %Fill Rate is 90% according to Antonio Santos break end Sum=0; end %End Normal end display(['You should put in a new order for ' num2str(Q) ' part(s) when there is ' num2str(m) ' spare(s) remaining in inventory']);
