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Equipment Availability AnalysisFred Schenkelberg, Ops A La Carte, LLCAngela Lo, Kaiser PermanenteKey Words: Availability, ...
that the design team could explore the differences in              2.1 MTBFequipment availability over time. For example, ...
run with fewer failures. Furthermore, this supports the use of     Thus, for small bottles and this particular filler, the...
beta less than one indicate a system that has a decreasing                                                                ...
5.1 Analysis                                                                   Minutes              120       240      480...
comparison of the current short run performance to thepotential performance provides a basis for the potential            ...
1.   Mettas, A. and Z. Wenbiao (2005). Modeling and                currently the Chair of the American Society of Quality ...
1.   Mettas, A. and Z. Wenbiao (2005). Modeling and                currently the Chair of the American Society of Quality ...
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Equipment Availability Analysis

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A case study paper on equipment availability data analysis.


Tracking bottling equipment line uptime and downtime is a common metric for bottling production lines. The runtime and downtime along with reasons for being down are routinely and semi-automatically recorded. The data is often summarized using the exponential distribution and reported as MTBF and MTTR.
During the design of a new bottling line, the design team used the recorded data from existing lines and equipment to estimate the proposed line availability. If the new line could shorten the run time to accommodate a high mix of products and improve the line availability and thus throughput, the new line would permit significant warehouse savings.
The experienced operator, maintenance and engineering teams knew that the line availability improved as the run duration increased. After the initial setup, the line operator and maintenance crew continued to adjust and improve the operation of the bottling line, thus, overtime improving the line availability. It was not a constant value independent of the run duration. And, the existing calculations based on MTBF and MTTR did not reflect this behavior.
This paper examines the use of expected values of the fitted distributions for uptime and downtime, rather than using MTBF and MTTR. The expected values permit the analysis to study the changes in availability as the run duration changes. The result was the design team’s analysis could tradeoff the run duration and associated throughput with the expected warehouse requirements and cost savings for an optimal bottling line design. This paper primarily explores the equipment analysis and availability calculations.

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Equipment Availability Analysis

  1. 1. Equipment Availability AnalysisFred Schenkelberg, Ops A La Carte, LLCAngela Lo, Kaiser PermanenteKey Words: Availability, Data Analysis, Repairable System SUMMARY & CONCLUSIONS require 2 to 4 hours to reset the bottle alignment guides, chutes and other equipment and supplies. Tracking bottling equipment line uptime and downtime is A scheduling team worked out the production schedulea common metric for bottling production lines. The runtime well in advance with the intent to maximize the line uptime byand downtime along with reasons for being down are routinely avoiding bottle size changes. Yet, the bottling line design teamand semi-automatically recorded. The data is often was asked to explore the increase in throughput by increasingsummarized using the exponential distribution and reported as the availability of the overall line with both engineering andMTBF and MTTR. layout changes. For example, one consideration was if During the design of a new bottling line, the design team purchasing dedicated equipment for each bottle size increasedused the recorded data from existing lines and equipment to throughput sufficiently to offset the cost of the additional (andestimate the proposed line availability. If the new line could often idle) equipment. Another consideration was the use ofshorten the run time to accommodate a high mix of products redundant pieces of equipment, especially those prone toand improve the line availability and thus throughput, the new extended downtime due to a major repair.line would permit significant warehouse savings. While exploring the effectiveness in increasing The experienced operator, maintenance and engineering throughput by improving the overall line availability, we alsoteams knew that the line availability improved as the run need to consider the tradeoff between throughput andduration increased. After the initial setup, the line operator and inventory costs. For example, in order to increase the linemaintenance crew continued to adjust and improve the availability and hence the throughput, we should prioritize inoperation of the bottling line, thus, overtime improving the minimizing bottlenecks during the process. Therefore theline availability. It was not a constant value independent of the focus on this paper is on the ‘filler’ equipment as it is the linerun duration. And, the existing calculations based on MTBF bottleneck. Increasing the throughput of the filler will permitand MTTR did not reflect this behavior. the line to produce that same quantity in less time. This frees This paper examines the use of expected values of the up the line for other production and reduces quantity offitted distributions for uptime and downtime, rather than using finished goods inventory required.MTBF and MTTR. The expected values permit the analysis to The design team had a line throughput modeling softwarestudy the changes in availability as the run duration changes. package, which included buffer sizing, permitted dwell timesThe result was the design team’s analysis could tradeoff the for the contents at specific temperatures or between bottlingrun duration and associated throughput with the expected and sterilization equipment. They also knew from experiencewarehouse requirements and cost savings for an optimal and simple data analysis that the longer duration runs with abottling line design. This paper primarily explores the single bottle size tended to have better throughput (equipmentequipment analysis and availability calculations. availability) performance during the later stages of the run. Anecdotally they knew that the first 12 hours of a run includes 1 INTRODUCTION a significant number of adjustments, which improved the ability of the line to run smoothly. The plethora of bottle sizes and flavors even for single The existing method within the plant to determinebrand of beverage necessitates flexible bottling equipment equipment availability used MTBF and MTTR and thecapable of ‘change overs’ between flavors and bottle sizes. underlying assumption of the exponential distribution. TheThe equipment for bottling originally primarily only worked design team recognized the lack of time dependence andwith one bottle size and shape. As market demands increase therefore asked us to perform the data analysis.the equipment continued to evolve and now permits the samebottling line to fill, label and box a relatively large selection ofbottle sizes. A flavor change requires only the cleaning of the 1.1 Project Questionfilling equipment and changing the labels, creating the The basic question explored in this paper is just one ofpreference to filling many flavors for one bottle size, when many analysis performed in support of the design team. Oneever possible. In contrast the bottle size change tended to question was how to properly model the equipment data such
  2. 2. that the design team could explore the differences in 2.1 MTBFequipment availability over time. For example, with no The unbiased estimator for the exponential distribution’sequipment design changes, was it possible to achieve suitable single fitting parameter, θ, isthroughput with only 4-hour runs rather than 12-hour runs? (1)Another was the exploration of the demonstrated throughputafter extended runs suggested what was possible if theequipment design made ‘change overs’ that did not thenrequire adjustments to improve it’s performance. where, θ is called the MTBF by definition within the This paper will explore one piece of equipment, the filler, factory. Also the operating time is determined by summing alland fit appropriate distributions to the data. The fitted the time segments representing when the filler equipments wasdistributions for the uptime (operating) and the downtime actually filling or ready to fill bottles.(under repair) permit the calculation of the equipment The number of downtime events is just the simple countavailability at various run durations. of events that occurred. And, with the filtered data only counts1.2 Data events associated with the filler equipment, thus providing the filler equipment’s average uptime. The data has been disguised to shield the equipment As is practice within the factory, the MTBF value ismanufacturer and bottling plant from identification. While the determined by calculating MTBF over many similar bottleactual data has a linear transformation, the trends have size runs. As an example, the data for the ‘small bottles’remained the same. Furthermore the codes for downtime, provides an estimate of MTBF of 46.5 minutes.which included blockage, jams, alignment issues, fill sensorreadings, and many more, have also been altered to represent 2.2 MTTRgeneric reasons unrelated to the actual reasons. For the Using the same formula above with the substitution ofpurpose of this discussion the downtime reasons are downtime for run time and again assuming an exponentialimmaterial. distribution, the factory personal calculate (what they defined) The actual raw data included downtime for shift change, the MTTR or average downtime.meetings, scheduled maintenance, and lack of raw materials.We removed such data since the purpose of the analysis was to (2)focus only on the individual piece of equipment.Condition Start End Using the same dataset as for MTBF and making the 04:50:18 04:52:23 substitution of downtime for runtime, we find MTTR of 2.45Supply Tank Low Level Sep/24/2007 Sep/24/2007 05:04:19 05:08:29 minutes.Capper Infeed Star Jam Sep/24/2007 Sep/24/2007 05:08:42 05:17:28 2.3 AvailabilityCapper Infeed Star Jam Sep/24/2007 Sep/24/2007 The well known formula for availabilityBlocked - Discharge Conveyor 05:51:19 05:51:51Stopped Sep/24/2007 Sep/24/2007 05:52:28 05:52:58 MTBFDischarge Jam Alarm At S203 Sep/24/2007 Sep/24/2007 Availiability = (3) 05:52:59 05:54:30 MTBF + MTTRDischarge Jam Alarm At S203 Sep/24/2007 Sep/24/2007 05:55:34 05:58:31Jog Mode Selected Sep/24/2007 Sep/24/2007 was given as the reason for estimating the MTBF and 06:00:27 06:00:32 MTTR values by factory personal. Using the values providedDischarge Jam Alarm At S204 Sep/24/2007 Sep/24/2007 06:33:54 07:17:03 and the availability formula (3) we find the average fillerFiller Run Switch Off Sep/24/2007 Sep/24/2007 availability of 95% over the recent 6 months of operation. 07:47:39 07:53:02Jog Mode Selected Sep/24/2007 Sep/24/2007 2.4 Throughput 07:56:55 07:58:56Jog Mode Selected Sep/24/2007 Sep/24/2007 The filler equipment has the capability to fill bottles at the 08:34:11 08:42:50 rate of approximately 425 bottles a minute. And, theDoor 6 Open Sep/24/2007 Sep/24/2007 equipment has the capability to run for short periods of time much faster. Plus, for restarting (after clearing a bottle jam, for 2 CURRENT MEASURES example) or when troubleshooting, the filler has a run mode that is much slower. On average the filler is considered to The following analysis illustrates the plant’s methods for have an average fill rate of 400 bottles per minute.calculating the equipment availability and throughput. The throughput calculation is: Throughput = Fill Rate × Availability (4)
  3. 3. run with fewer failures. Furthermore, this supports the use of Thus, for small bottles and this particular filler, the simple constant failure rate estimates for scheduling and theaverage throughput is 380 bottles per minute. improved line design decisions. Finally, in order to schedule the line to produce a desired Taking a closer look at the underlying data, we noticedamount of filled bottles, the scheduling department woulddivide the amount desired by the average throughput. Afterapplying ‘historical knowledge’ to adjust the run schedule to aslightly longer duration for short runs and slightly shorterduration for longer runs when compared to the average runduration, the scheduling department would publish the factoryschedule. 3 THE DILEMMA Anecdotally the design team and factory personal knowthe longer runs tend to produce more bottles per hour thenshort runs. Yet, the values used to calculate equipment andline availability do not reflect the changing nature of theequipment operation. that only a few of the runs lasted more than one or two shifts. The use of exponentially based distributions and Some flavors only required a small quantity of bottles filled toavailability calculation does not permit the team to consider keep up with demand, while only a few commanded a largedifferent run times and associated inversely proportional demand. It is the same equipment for short or long run, andavailability values. Knowing the equipments capability when the design team desired information that quantified theoperated over a long run may suggest to the design team that changing nature of the failure rates for various lengths ofaltering the equipment set-up methods may reduce downtime planned runs.sufficiently to permit shorter runs. Or, they may find, that evenwith the better equipment availability in the latter parts of longrun may not be sufficient to provide the cost savings 5 GENERAL RENEWAL PROCESSanticipated, thus suggesting the use of redundant sets of Advances in the development of the treatment ofequipment to improve line availability. repairable systems’ data analysis permit the fitting of a Another troublesome unknown is the rate of change of parametric model to the factory data. (Mettas and Wenbiaoequipment and line availability. A rapid or slow change would 2005) The data provided by the factory meet the two primarysuggest different strategies to design the improved line. The assumptions:same information on the time dependency of availability 1. The time to first failure (TTFF) distribution is known andwould also permit additional accuracy in line scheduling, even can be estimated from the data. There are over 2000for the current line configuration. failure events within the dataset. The current data analysis methods do not providesufficient information related to the changing equipment The Weibull probability plot shows a beta ofavailability. Therefore, the design team decided to employ approximately 0.6. The fit of the two parameters Weibull wasdata analysis that included the time element and the associated done with the rank regression on X using median ranks. Thechanges in equipment availability. 4 GRAPHICAL ANALYSIS The Mean Cumulative Function (MCF) is a non-parametric graph of the cumulative failures plotted versustime. The following plot has 6 months of operations for onepiece of equipment on the production line. There areapproximately 40 different runs (different bottle size/flavorconfigurations or ‘setups’). Overall, from this plot, which appears to be a fairlystraight line, the conclusion is the system is not improving ordegrading over time as the repairs occur. It remains atapproximately the same condition or failure rate over variouslength runs. (Trindade and Nathan 2006) This is in conflict with the common knowledge within thefactory, where over the time of the run, the equipment tends to
  4. 4. beta less than one indicate a system that has a decreasing βfailure rate over time. This suggests that the repairs made − λ ( xi + vi−1 )β − vi−1  (8) f (t i t i − 1) = λβ (xi + vi −1 )β −1 e  during the earlier part of the run assist in preventing futurefailures. For further details on the derivation and fitting algorithms for this model see (Mettas and Wenbiao 2005).2. The repair time is negligible relative to the run time. Most repairs occur within 1 minute of failure occurrence and compared to the average runtime of approximately 45 minutes is negligible. The fit of the repair times was done within Weibull++using rank regression on X and median ranks to fit thelognormal distribution. The plot shows that approximately50% of the repairs are accomplished within one minute andapproximately 90% are accomplished within 10 minutes.While a larger difference between runtime and repair timewould be desirable, the single order of magnitude difference issufficient for this analysis. The general renewal process model uses a concept ofvirtual age. Let t1, t2, …,tn represent the successive failure time.And, let x1, x2, …,xn represent the time between failures where ti = ∑ j −1 x j i (5) For the Type II model of the General Renewal Process thevirtual age is determine with equation 6. vi = q(vi −1 + qxi ) = q i x1 + q i − 1x2 + L + xi (6)where vi is the virtual age of the system right after the ithrepair. Depending on the value of q the model permits thepartial improvement of the system by adjusting the apparentsystem age. The power law function models the rate of recurrentfailures within the system, which is λ (t) = λβ t β −1 (7)and, the conditional pdfis
  5. 5. 5.1 Analysis Minutes 120 240 480 960 1440Within the Weibull++ software algorithms for modelingrecurrent event data, there are two models available. The Type CumulativeI model assumes the repair only addresses the immediate 0.1395 0.1077 0.0865 0.0754 0.0706 Failure Intensityfailure. Whereas, the Type II model assumes the repairpartially of completely repairs or possibly improves the Instantaneoussystem, not just fixing the immediate fault. Given the nature of 0.0482 0.0377 0.0307 0.0267 0.0288 Failure Intensityfixes on the production line that often include equipmentadjustments (alignment, timing, etc.) we use the Type II model Considering the MTBF is the inverse of the failure intensity,for this analysis. we can calculate the MTBF values for specific durations orWeibull++ using the General Renewal Process, type II, three- instants.parameter model, accomplishes the fit. The results are Minutes 120 240 480 960 1440Beta = 0.27Lambda = 2.09 Cumulative 7.17 9.29 11.56 13.26 14.16 MTBFq = 0.38The third parameter, q, may be considered an index for repair Instantaneous 20.75 26.53 32.57 37.45 34.72effectiveness. Where q=0 represents a perfect repair, ‘as good MTBFas new’ state. And, where q=1 represents a minimal repair,permitting the use of non-homogenous Poison process analysis The MTBF values above along with the MTTR value of 2.45(MTBF) or the system is considered in an ‘as bad of old’ state. minutes determined as the expected value of the fittedThis model permits the repair to only partial make they system lognormal distribution, we can use the availability formula (3)better, 0<q<1 or an imperfect repair. The q=0.38 indicates that above to determine the expected availability values for selectin general the repairs make a slight improvement. durations or instants.5.2 Discussion Minutes 120 240 480 960 1440The plot of cumulative failure intensity vs. time shows therapid improvement in equipment performance after the early Cumulativefailures receive attention. Note the jog upward in the data at 0.75 0.79 0.83 0.84 0.85 Availabilityapproximately 500 minutes, where two plant behaviorscontribute to cause this data. First, a significant number of Instantaneousruns are scheduled to occur over one shift, which is 480 0.89 0.92 0.93 0.94 0.93 Availabilityminutes long. Second, the shift change incurs a change ofpersonal and during the shift briefing time, the line is Finally, using the equation to determine the expectedadministratively shut down. The restart incurs additional throughput, equation (4), we can determine the expectedfailures and adjustments. production for various durations of runs. The instantaneousAfter approximately two shifts or 1000 minutes of running, throughput provides information on the improving nature ofthe equipment tends to run smoothly and repairs do not the system over time.improve or degrade the equipment performance. Minutes 120 240 480 960 14405.3 Model UseThe GRP model permits us to determine the cumulative, Cumulative 283 301 314 321 324instantaneous and conditional failure intensities at a given Throughputtime and duration of our choosing. This addresses the desire todetermine the equipment availability and throughput for Instantaneous 340 348 353 357 355specific run durations. ThroughputUsing the quick calculation pad within Weibull++ for thefitted data we can calculate the for the cumulative andinstantaneous failure intensities at select duration or times,respectively. The following table summaries the failure 6 ANALYSIS.intensity calculations: With the improvement in calculating the changing nature of the filler’s MTBF, we are not able to determine the potential impact on final goods inventory reduction. The
  6. 6. comparison of the current short run performance to thepotential performance provides a basis for the potential This suggests a 20% reduction in time to produce the sameinventory reduction. amount of finished goods for a four-hour duration run. Of6.1 Inventory vs. Throughput course, this is only possible if the equipment improvements permit the filler to have the same average throughput over a 4 When analyzing the opportunity of increasing throughput hours run as the long run average throughput of 380 bottlesby improving the line availability, we are able to determine the per minute. The reduced runtime values permit the reductionpotential inventory savings using an application of Little’s in finished goods, as the increased capacity of the factoryLaw. permit the factory to replenish the inventory more often. Finished Goods Inventory = The cost savings in inventory provides a basis for the engineering improvement project. If the engineering team Throughput x Flow Time (9) expects to make improvements to achieve four-hour runs with a 380 bottles/minute throughput, they may achieve at least a The above Little’s Law (Silver, E. et.al. 1998) can be 20% reduction in inventory. Assume the cost to carry theapplied to evaluate the tradeoff between the throughput and inventory for a year is $20 million within this site. Thisthe inventory cost. It is clear that increasing throughput while suggests the engineering team can spend $5 million forholding flow time constant will take less runtime to build the improvements and achieve a one-year payback on thesame amount of finished goods. investment. 7 CONCLUSION The results show the lack of accuracy of the existing method Length of run 120 240 480 960 1440 (minutes) Time to build 3.53 3.33 3.19 3.12 3.09 1000 units %Improvement 25.5 20.9 17.5 15.6 14.7 with 380/min when evaluating equipment availability using traditionally calculated MTBF and MTTR. The traditional method has only one, non-time dependant estimate for MTBF. In order to provide a better overall analysis of equipment availability and throughput, include within the analysis a time dependence variable such as run durations. The GPP model permits such an analysis. As seen in the calculations using the GPP model, it takes approximately 4 hours (240 minutes) of runtime to stabilize the instantaneous availability and throughput. Engineering changes to the equipment to either accelerate or improve the initial performance effectively eliminating the first four hours of adjustments will permit the line to run more efficiently with short runs. Simply implementing shorter runs will not achieve the goal without fundamental changes to the production equipment. Running more effectively permits the reduction of final goods inventory by as much as 20% for a 4 hour run. Further inventory reduction is also possibly due to the additional capacity of the factory and is not consider in this analysis. The cost savings associated with the inventory reduction provides a boundary for the improvement costs. 8 REFERENCES
  7. 7. 1. Mettas, A. and Z. Wenbiao (2005). Modeling and currently the Chair of the American Society of Quality analysis of repairable systems with general repair. Reliability Division, active at the local level with the Society Reliability and Maintainability Symposium, 2005. of Reliability Engineers and IEEE’s Reliability Society, IEEE Proceedings, Annual. reliability standards development teams and recently joined2. Trindade, D. and S. Nathan (2006). Simple plots for the US delegation as a voting member of the IEC TAG 56 - monitoring the field reliability of repairable systems. Durability. He is a Senior Member of ASQ and IEEE. He is Reliability and Maintainability Symposium, 2006. an ASQ Certified Quality and Reliability Engineer. Proceedings, Annual.3. Silver, E., D. Pyke, and R. Peterson (1998). Inventory Angela Lo Management and Production Planning and Scheduling, 7313 Shelter Creek Lane 3rd Ed. Wiley, New York, 1998. San Bruno, CA 94066, USA e-mail: angelalo928@gmail.com 9 BIOGRAPHIES Fred Schenkelberg Angela Lo is Senior Financial Analyst at Kaiser Ops A La Carte, LLC Permanente – South San Francisco Medical Office. In her 990 Richard Avenue, Suite 101 current job role, she provides operational analysis and process Santa Clara, CA 95050, USA improvement recommendations to front office operations. e-mail: fms@opsalacarte.com Prior to this position, she worked for a few domestic and international companies with focus areas in supply chain Fred Schenkelberg is a reliability engineering and management, operations improvement, and six sigmamanagement consultant with Ops A La Carte, with areas of initiatives. Her knowledge in process improvement was notfocus including reliability engineering management training only utilized in manufacturing operations but also in serviceand accelerated life testing. Previously, he co-founded and environment. She earned her bachelor’s degree in Industrialbuilt the HP corporate reliability program, including Engineering and Operations Research at University ofconsulting on a broad range of HP products. He is a lecturer California, Berkeley in 2005 and her master’s degree inwith the University of Maryland teaching a graduate level Industrial and Systems Engineering at San Jose Statecourse on reliability engineering management. He earned a University in 2007. She also obtained her Six Sigma BlackMaster of Science degree in statistics at Stanford University in Belt Certification through American Society for Quality in1996. He earned his bachelors degrees in Physics at the 2009. Angela is currently an active member in AmericanUnited State Military Academy in 1983. Fredis an active Society for Quality.volunteer with the management committee of RAMS,
  8. 8. 1. Mettas, A. and Z. Wenbiao (2005). Modeling and currently the Chair of the American Society of Quality analysis of repairable systems with general repair. Reliability Division, active at the local level with the Society Reliability and Maintainability Symposium, 2005. of Reliability Engineers and IEEE’s Reliability Society, IEEE Proceedings, Annual. reliability standards development teams and recently joined2. Trindade, D. and S. Nathan (2006). Simple plots for the US delegation as a voting member of the IEC TAG 56 - monitoring the field reliability of repairable systems. Durability. He is a Senior Member of ASQ and IEEE. He is Reliability and Maintainability Symposium, 2006. an ASQ Certified Quality and Reliability Engineer. Proceedings, Annual.3. Silver, E., D. Pyke, and R. Peterson (1998). Inventory Angela Lo Management and Production Planning and Scheduling, 7313 Shelter Creek Lane 3rd Ed. Wiley, New York, 1998. San Bruno, CA 94066, USA e-mail: angelalo928@gmail.com 9 BIOGRAPHIES Fred Schenkelberg Angela Lo is Senior Financial Analyst at Kaiser Ops A La Carte, LLC Permanente – South San Francisco Medical Office. In her 990 Richard Avenue, Suite 101 current job role, she provides operational analysis and process Santa Clara, CA 95050, USA improvement recommendations to front office operations. e-mail: fms@opsalacarte.com Prior to this position, she worked for a few domestic and international companies with focus areas in supply chain Fred Schenkelberg is a reliability engineering and management, operations improvement, and six sigmamanagement consultant with Ops A La Carte, with areas of initiatives. Her knowledge in process improvement was notfocus including reliability engineering management training only utilized in manufacturing operations but also in serviceand accelerated life testing. Previously, he co-founded and environment. She earned her bachelor’s degree in Industrialbuilt the HP corporate reliability program, including Engineering and Operations Research at University ofconsulting on a broad range of HP products. He is a lecturer California, Berkeley in 2005 and her master’s degree inwith the University of Maryland teaching a graduate level Industrial and Systems Engineering at San Jose Statecourse on reliability engineering management. He earned a University in 2007. She also obtained her Six Sigma BlackMaster of Science degree in statistics at Stanford University in Belt Certification through American Society for Quality in1996. He earned his bachelors degrees in Physics at the 2009. Angela is currently an active member in AmericanUnited State Military Academy in 1983. Fredis an active Society for Quality.volunteer with the management committee of RAMS,

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