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Material, leading to initiation of cracking and subsequent crack growth. The system under evaluation is a resistor used for energy dissipation (Figure 1). The resistor material is a steel based alloy. During braking, the motor fields are connected across either the main traction generator (diesel-electric locomotive.
To receive a demo version of a ReliaSoft software product, please complete the form below. Lg w1941s drivers for mac pro. Your demo license will be provided by our sales team, who will help you identify the product options to leverage and ensure you have a successful demo. ReliaSoft’s ALTA PRO employs a physics of failure approach and can be used to analyze test data for single or multiple stress conditions. (Weibull distribution), mean (exponential distribution) or median (lognormal distribution). 40 electronic components were tested to failure due to crack growth in solder joints as a result of repeated. free download. software weibull 6. Photo & Graphics tools downloads - ReliaSoft Weibull MT by ReliaSoft Corporation and many more programs are available for instant and free download. Email: Crackrequest2014@Gmail.com.Sort by: Relevance
ReliaSoft ALTA
Quantitative accelerated life testing techniques in conjunction with powerful QALT data analysis methodologies give design and reliability engineers the power to significantly reduce test times, which can provide faster time to market, lower product development costs, lower warranty costs and other benefits!
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: August 2nd, 2012ReliaSoft BlockSimReliasoft Wiki
ReliaSoft’s BlockSim software tool provides a comprehensive platform for system reliability, availability, maintainability and related analyses. The software offers a sophisticated graphical interface that allows you to model the simplest or most complex systems and processes using reliability block diagrams (RBDs) or fault tree analysis (FTA) — or a combination of both approaches!
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: July 1st, 2011ReliaSoft DOE++
DOE++ facilitates traditional Design of Experiments ( DOE ) techniques for studying the factors that may affect a product or process in order to identify significant factors and optimize designs. The software also expands upon standard methods to provide the proper analysis treatment for interval and right censored data — offering a major breakthrough for reliability-related analyses!
*Publisher: ReliaSoft Corporation
*Last updated: May 24th, 2011MediaGet2
This piece of software helps you download torrent files with an impressive speed. Available for both Mac and Windows operating systems. Besides downloading torrent files, this program also lets you watch movies while they are being downloaded and you have the possibility to organize all of your downloaded files into categories.
*Publisher: MediaGet LLC
*Home page:mediaget.com
*Last updated: July 7th, 2014ReliaSoft Synthesis
ReliaSoft Synthesis is an integrated reliability platform that can unite any or all of ReliaSoft’s reliability engineering applications into an easy-to-deploy, enterprise-capable, integrated reliability solution. You can use the Synthesis Platform to facilitate collaboration between subject matter experts, fluidly share information between different reliability activities and more.
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: February 21st, 2016Arctic Torrent
Arctic Torrent is an open source C++ application to manage all your P2P transactions based on torrent files. Its simple layout gives you all the basic information you need to know the progress of your file-sharing operations, and will not take up any more system resources than those strictly necessary.
*Publisher: Int64.org
*Home page:int64.org
*Last updated: July 19th, 2008Torrent Assault
Torrent Assault is a mass BitTorrent uploader. It allows you to easily announce your torrent files to over 10 different torrent sites, all on autopilot. Torrent Assault can automatically crack and fill in CAPTCHA’s and much more like assign categories to groups of torrent files for example.
*Publisher: Torrent Assault
*Last updated: January 6th, 2010CuteTorrent
CuteTorrent comes with some interesting features such as Proxy support, Global and per-torrent speed limits, IPv6 support, the ability to mount Disk Images to DaemonTools, and a convenient and easy-to-use web interface that lets you manage your downloads remotely.
*Publisher: Ruslan Fedoseenko
*Last updated: September 29th, 2016µTorrent (uTorrent)
µTorrent is an easy-to-use BitTorrent download client for Windows OS. Download your files as quickly and efficiently as possible without slowing down your other online activities. uTorrent offers advanced settings such as automation, scripting, remote management and more.
*Publisher: BitTorrent Inc
*Home page:www.utorrent.com
*Last updated: December 4th, 2020Torrent Stream
Torrent Stream is a media platform that allows distributed and decentralized multimedia data transfer. The program provides audio-visual online broadcast, without the need for maintenance of the park servers and expenditures for payment of the network traffic. The Torrent Stream package contains a TS Engine, a TS Player, a multimedia plug-in and Magic Player.
*Publisher: Torrent Stream
*Home page:torrentstream.org
*Last updated: April 28th, 2013Movie Torrent
Movie Torrent is a powerful and reliable application for searching, downloading and sharing any type of file you wish. It allows you to add multi-tracker information to the torrent and bears simultaneous downloads, download queue, selected downloads in torrent package, fast-resume, disk cache, speed limits, port mapping, proxy and IP-filter.
*Publisher: GoodKatShare
*Home page:www.goodkatshare.com
*Last updated: July 2nd, 2018Torrent Search
Search Torrents in more than 32 Top Torrent Search engines.
*Publisher: Allen Smithy
*Home page:www.torrent-search-bar.com
*Last updated: March 16th, 2008Torrent Video Player
Torrent Video Player is a tool which allows you to watch free movies and videos or listen to music online. The interface is easy to use and it is based on the immensely popular and highly versatile media player. It allows to play the media before it has finished downloading.
*Publisher: MobilityFlow
*Last updated: January 1st, 2013Torrent Episode Downloader
Torrent Episode Downloder, or TED, is a TV-show downloader. Legal issues aside, TED is one of the best applications ever designed for the downloading of TV torrents. TED completely automates the process of finding a torrent and downloading it. This tool comes packaged with a list of popular TV shows.
*Publisher: ted
*Home page:www.ted.nu
*Last updated: May 22nd, 2011VIP Torrent
VIP Torrent is a free-to-use file-sharing program for Windows OS. With VIP Torrent, you can use either its embedded tracker or an external one. It is designed to connect to multiple networks at the same time. An attractive, straightforward interface turns searching into joy, plus, downloading is quick and without problems.
*Publisher: VIP Rumor
*Home page:www.viprumor.com
*Last updated: November 26th, 2015Torrent Video Cutter
Torrent Video Cutter is an easy-to-use tool that allows you to cut a segment or various segments of a video file. Many media formats are supported (AVI, MPEG, VOB, WMV, ASF, RM, RMVB, 3GP, and MP4). The process to cut a media file is simple.First, you have to open the source file.
*Publisher: Torrent Computing Inc.
*Home page:www.torrentrockyou.com
*Last updated: November 7th, 2010Torrent Opener
Torrent Opener is a simple torrent file viewer and downloader, it is a tiny BT client. A torrent file is a BT (BitTorrent) metainfo file, it contains metadata about files and folders to be distributed, these files can help BT clients to initiate file transfer using the BT protocol.
*Publisher: TorrentOpener
*Home page:www.torrentopener.com
*Last updated: July 5th, 2013Remote Torrent Adder
Remote Torrent Adder is a browser extension that allows you to add torrents using several programs’ WebUIs. This extension allows you to send torrent files from your browser to your remote or local Bittorrent client’s web interface. It doesn’t just send the URLs to the WebUIs, but downloads the torrent and uses the file upload function of the UIs to add the torrent.
*Publisher: BOG
*Home page:code.google.com
*Last updated: February 27th, 2015
Index Additional Reliability Analysis Tools Maintenance Planning
*1Optimal Preventive Replacement Interval
*2Optimal Inspection Interval
More Resources:
Weibull++ Examples Collection
For components and systems with increasing failure rates, planned replacements and inspections are often used to prevent failures in order to improve system availability and reduce overall maintenance cost. For example, the commonly used preventive maintenance strategy is to replace an aged item at a given time interval in order to minimize the long term cost per unit time. An optimal time interval exists if the failure rate increases with time and the cost of failure is much higher than the cost of a scheduled replacement.
Another alternative is to minimize the short term cost per unit time, such as in one replacement cycle. A replacement cycle is defined as the time when a failure occurs or the time of the scheduled replacement when no failure occurs. Similarly, periodic inspections are done to detect oncoming failures and replace the component before a failure occurs. Inspections can also be used to minimize either the long-term or short-term costs. In this section, we will discuss how to find the optimal maintenance and inspection intervals in order to minimize the long-term and short-term maintenance costs.Optimal Preventive Replacement IntervalMinimize the Long Term Cost Per Unit Time
Minimizing the long term maintenance cost per unit time is the most popular objective for adopting a preventive replacement strategy. The theory behind this strategy is discussed in the Systems Reliability Analysis Reference book, but we will provide a brief explanation here.
For an item that is replaced either at the time of failure or at the time of the scheduled maintenance interval [math]x,![/math], the expected cycle length is:
[math]E(text{Cycle Length})=int_{0}^{x}{tf(t)dt}+R(x)x=int_{0}^{x}{R(t)dt}[/math]
The expected cost for one cycle is:
[math]E(text{Cost Per Cycle})={{C}_{P}}R(x)+{{C}_{U}}left( 1-R(x) right)[/math]
Therefore, the expected long term cost per unit time is:
[math]CPU{{T}_{L}}(x)=frac{E(text{Cost Per Cycle})}{Eleft( text{Cycle Length} right)}=frac{{{C}_{P}}R(x)+{{C}_{U}}left( 1-R(x) right)}{int_{0}^{x}{R(t)dt}}[/math]
The optimal preventive maintenance interval will be the value [math]x,![/math] which minimizes [math]CPU{{T}_{L}},![/math]. In the above equations:
*[math]f(x),![/math] is the probability density function of the failure time.
*[math]R(x),![/math] is the reliability function of the failure time.
*[math]{{C}_{P}},![/math] is the average cost due to a planned maintenance.
*[math]{{C}_{U}},![/math] is the average cost due to a unplanned maintenance.Minimize the Short Term Cost Per Unit Time
The equations above are based on the reward renewal theory and are used for minimizing the long term maintenance cost. There may be cases, however, where the average costs change with time, or when components are replaced with either costlier or less expensive versions. In this situation, the failure time distribution and the cost function need to be updated every time the costs change. Therefore, an optimal interval to minimize the short term cost is needed.
The expected cost per unit time in one replacement cycle is defined as:
[math]CPU{{T}_{S}}(x)=Eleft( frac{text{Cost Per Cycle}}{text{Cycle Length}} right)=int_{0}^{x}{frac{{{C}_{U}}}{t}f(t)dt}+frac{{{C}_{P}}}{x}left( 1-F(x) right)[/math]
For a Weibull distribution with its shape parameter [math]beta gt 1,![/math], the optimal interval [math]{{x}_{0}},![/math] is:
[math]{{x}_{o}}=eta {{left( frac{{{C}_{P}}}{beta left( {{C}_{U}}-{{C}_{P}} right)} right)}^{frac{1}{beta }}}[/math]
where [math]eta ,![/math] is the scale parameter of the Weibull distribution.Optimal Inspection Interval
Inspection is often used to test if a device is working properly. For example, signs of a device’s impending failure due to degradation, such as corrosion and crack, can be detected via inspection. The device can then be replaced before the failure actually occurs. If a failure cannot be detected during the inspection, it will be noticed immediately when the failure occurs, and the device will be replaced at the time of the failure. Reliasoft Download
Assume that a failure occurs at time [math]t,![/math]. If an inspection is conducted within the range of [math][ptimes t,t],!,![/math], the failure will be detected and the component will be replaced. The term [math]p,![/math] is a value between 0 and 1. This is illustrated in the following plot.
In the plot, the inspection is conducted at every X hours. ’No’ means that an oncoming failure will not be detected by inspection, while ’Yes’ means it can be detected by inspection since the inspection time is within [math][ptimes t,t][/math]. In this case, whenever a replacement occurs, a new maintenance cycle starts.
Minimize the Long Term Cost Per Unit Time
Define:
M is the largest inspection interval where there is no overlap between the detection zones of two adjunct inspections. Any failures that occur after the Mth inspection will always be detected.
The expected long term cost per unit time is:
[math]begin{align} & E(text{Cost Per Cycle})=int_{0}^{x}{{{C}_{U}}f(t)dt}+sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{left[ {{C}_{P}}+k{{C}_{I}} right]}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{left[ {{C}_{U}}+k{{C}_{I}} right]}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{left[ {{C}_{P}}+(M+1){{C}_{I}} right]}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{left[ {{C}_{P}}+(k+1){{C}_{I}} right]f(t)dt}} end{align}[/math]
The expected replacement cycle length is:
[math]begin{align} & E(text{Cycle Length})=int_{0}^{x}{tf(t)dt}+sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{left( kx right)}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{t}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{left[ (M+1)x right]}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{left[ (k+1)x right]f(t)dt}} end{align}[/math]
The expected long term cost per unit time is:
[math]CPU{{T}_{L}}(x)=frac{E(text{Cost Per Cycle})}{Eleft( text{Cycle Length} right)}[/math]
where [math]{{C}_{I}},![/math] is the average cost per inspection.Minimize the Short Term Cost Per Unit Time
The short term (one replacement cycle) cost per unit time is:
[math]begin{align} & CPU{{T}_{S}}=Eleft( frac{text{Cost per Cycle}}{text{Cycle Length}} right)=int_{0}^{x}{frac{{{C}_{U}}}{t}f(t)dt} & +sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{frac{{{C}_{P}}+k{{C}_{I}}}{kx}}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{frac{{{C}_{U}}+k{{C}_{I}}}{t}}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{frac{{{C}_{P}}+(M+1){{C}_{I}}}{(M+1)x}}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{frac{{{C}_{P}}+(k+1){{C}_{I}}}{(k+1)x}f(t)dt}} end{align}[/math]Example
Assume that we are going to use the Maintenance Planning tool in Weibull++ to analyze a device that is assembled as part of a system. The failure times of the device are recorded and a Weibull distribution is used to model the data. The following picture shows the Weibull++ standard folio that contains the data and distribution. The Weibull distribution has parameters [math]beta,![/math] = 2.847494 and [math]eta,![/math] = 108.420135.
Assume that the average cost for a planned replacement of the device is $20. For an unplanned replacement, the cost is $500. The cost for each inspection is $10, and the fraction of the failure time for detecting an oncoming failure is 0.9. The objectives are:
*Find the optimal inspection interval and the optimal scheduled replacement interval for minimizing the cost in the long term.
*Find the optimal inspection interval and the optimal scheduled replacement interval for minimizing the cost in one replacement cycle.
Solution
In the Maintenance Planning tool, choose the Inspection Replacement plot type on the control panel, and then enter the estimated costs. Click the Plot icon to calculate the results and draw the plot. The following results show that the optimal inspection interval is about 8.28 hours, and the minimal cost is about $1.98 per hour.
To use a scheduled replacement strategy, choose the Planned Replacement plot type on the control panel, and then click the Plot icon again to recalculate results and redraw the plot. The following results show that the optimal replacement interval is about 28.657 hours, and the minimal cost is about $1.079 per hour.
To find the optimal times for minimizing the cost in one replacement cycle, select the Plot One Cycle Cost/Time option on the Settings page of the control panel.
Next, choose the Inspection Replacement plot type on the Main page of the control panel and recalculate the results. The results show that the optimal inspection interval for one replacement cycle is about 6.437 hours, and the minimal cost is about $2.683 per hour.
Change the plot type to Planned Replacement and recalculate the results. The results show that the optimal replacement interval is about 24.592 hours, and the minimal cost is about $1.257 per hour.
To plot both the planned replacement and inspection replacement plots, choose the Both Planned and Inspection plot type. The results are shown next.Reliasoft Training
Based on the above results, we can now make decisions about our maintenance strategy. For example, if our plan is to reduce the short term maintenance cost, then the device should be scheduled for replacement at about every 24 hours. This will give us a minimal maintenance cost of $1.257 per hour.Retrieved from ’https://www.reliawiki.com/index.php?title=Maintenance_Planning&oldid=46122’
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Multimedia |Business |Messengers |Desktop |Development |Education |Games |Graphics |Home |Networking |Security |Servers |Utilities |Web Dev| Other
*Reliasoft Wiki
*Reliasoft Download
*Reliasoft Training
Material, leading to initiation of cracking and subsequent crack growth. The system under evaluation is a resistor used for energy dissipation (Figure 1). The resistor material is a steel based alloy. During braking, the motor fields are connected across either the main traction generator (diesel-electric locomotive.
To receive a demo version of a ReliaSoft software product, please complete the form below. Lg w1941s drivers for mac pro. Your demo license will be provided by our sales team, who will help you identify the product options to leverage and ensure you have a successful demo. ReliaSoft’s ALTA PRO employs a physics of failure approach and can be used to analyze test data for single or multiple stress conditions. (Weibull distribution), mean (exponential distribution) or median (lognormal distribution). 40 electronic components were tested to failure due to crack growth in solder joints as a result of repeated. free download. software weibull 6. Photo & Graphics tools downloads - ReliaSoft Weibull MT by ReliaSoft Corporation and many more programs are available for instant and free download. Email: Crackrequest2014@Gmail.com.Sort by: Relevance
ReliaSoft ALTA
Quantitative accelerated life testing techniques in conjunction with powerful QALT data analysis methodologies give design and reliability engineers the power to significantly reduce test times, which can provide faster time to market, lower product development costs, lower warranty costs and other benefits!
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: August 2nd, 2012ReliaSoft BlockSimReliasoft Wiki
ReliaSoft’s BlockSim software tool provides a comprehensive platform for system reliability, availability, maintainability and related analyses. The software offers a sophisticated graphical interface that allows you to model the simplest or most complex systems and processes using reliability block diagrams (RBDs) or fault tree analysis (FTA) — or a combination of both approaches!
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: July 1st, 2011ReliaSoft DOE++
DOE++ facilitates traditional Design of Experiments ( DOE ) techniques for studying the factors that may affect a product or process in order to identify significant factors and optimize designs. The software also expands upon standard methods to provide the proper analysis treatment for interval and right censored data — offering a major breakthrough for reliability-related analyses!
*Publisher: ReliaSoft Corporation
*Last updated: May 24th, 2011MediaGet2
This piece of software helps you download torrent files with an impressive speed. Available for both Mac and Windows operating systems. Besides downloading torrent files, this program also lets you watch movies while they are being downloaded and you have the possibility to organize all of your downloaded files into categories.
*Publisher: MediaGet LLC
*Home page:mediaget.com
*Last updated: July 7th, 2014ReliaSoft Synthesis
ReliaSoft Synthesis is an integrated reliability platform that can unite any or all of ReliaSoft’s reliability engineering applications into an easy-to-deploy, enterprise-capable, integrated reliability solution. You can use the Synthesis Platform to facilitate collaboration between subject matter experts, fluidly share information between different reliability activities and more.
*Publisher: ReliaSoft Corporation
*Home page:www.reliasoft.com
*Last updated: February 21st, 2016Arctic Torrent
Arctic Torrent is an open source C++ application to manage all your P2P transactions based on torrent files. Its simple layout gives you all the basic information you need to know the progress of your file-sharing operations, and will not take up any more system resources than those strictly necessary.
*Publisher: Int64.org
*Home page:int64.org
*Last updated: July 19th, 2008Torrent Assault
Torrent Assault is a mass BitTorrent uploader. It allows you to easily announce your torrent files to over 10 different torrent sites, all on autopilot. Torrent Assault can automatically crack and fill in CAPTCHA’s and much more like assign categories to groups of torrent files for example.
*Publisher: Torrent Assault
*Last updated: January 6th, 2010CuteTorrent
CuteTorrent comes with some interesting features such as Proxy support, Global and per-torrent speed limits, IPv6 support, the ability to mount Disk Images to DaemonTools, and a convenient and easy-to-use web interface that lets you manage your downloads remotely.
*Publisher: Ruslan Fedoseenko
*Last updated: September 29th, 2016µTorrent (uTorrent)
µTorrent is an easy-to-use BitTorrent download client for Windows OS. Download your files as quickly and efficiently as possible without slowing down your other online activities. uTorrent offers advanced settings such as automation, scripting, remote management and more.
*Publisher: BitTorrent Inc
*Home page:www.utorrent.com
*Last updated: December 4th, 2020Torrent Stream
Torrent Stream is a media platform that allows distributed and decentralized multimedia data transfer. The program provides audio-visual online broadcast, without the need for maintenance of the park servers and expenditures for payment of the network traffic. The Torrent Stream package contains a TS Engine, a TS Player, a multimedia plug-in and Magic Player.
*Publisher: Torrent Stream
*Home page:torrentstream.org
*Last updated: April 28th, 2013Movie Torrent
Movie Torrent is a powerful and reliable application for searching, downloading and sharing any type of file you wish. It allows you to add multi-tracker information to the torrent and bears simultaneous downloads, download queue, selected downloads in torrent package, fast-resume, disk cache, speed limits, port mapping, proxy and IP-filter.
*Publisher: GoodKatShare
*Home page:www.goodkatshare.com
*Last updated: July 2nd, 2018Torrent Search
Search Torrents in more than 32 Top Torrent Search engines.
*Publisher: Allen Smithy
*Home page:www.torrent-search-bar.com
*Last updated: March 16th, 2008Torrent Video Player
Torrent Video Player is a tool which allows you to watch free movies and videos or listen to music online. The interface is easy to use and it is based on the immensely popular and highly versatile media player. It allows to play the media before it has finished downloading.
*Publisher: MobilityFlow
*Last updated: January 1st, 2013Torrent Episode Downloader
Torrent Episode Downloder, or TED, is a TV-show downloader. Legal issues aside, TED is one of the best applications ever designed for the downloading of TV torrents. TED completely automates the process of finding a torrent and downloading it. This tool comes packaged with a list of popular TV shows.
*Publisher: ted
*Home page:www.ted.nu
*Last updated: May 22nd, 2011VIP Torrent
VIP Torrent is a free-to-use file-sharing program for Windows OS. With VIP Torrent, you can use either its embedded tracker or an external one. It is designed to connect to multiple networks at the same time. An attractive, straightforward interface turns searching into joy, plus, downloading is quick and without problems.
*Publisher: VIP Rumor
*Home page:www.viprumor.com
*Last updated: November 26th, 2015Torrent Video Cutter
Torrent Video Cutter is an easy-to-use tool that allows you to cut a segment or various segments of a video file. Many media formats are supported (AVI, MPEG, VOB, WMV, ASF, RM, RMVB, 3GP, and MP4). The process to cut a media file is simple.First, you have to open the source file.
*Publisher: Torrent Computing Inc.
*Home page:www.torrentrockyou.com
*Last updated: November 7th, 2010Torrent Opener
Torrent Opener is a simple torrent file viewer and downloader, it is a tiny BT client. A torrent file is a BT (BitTorrent) metainfo file, it contains metadata about files and folders to be distributed, these files can help BT clients to initiate file transfer using the BT protocol.
*Publisher: TorrentOpener
*Home page:www.torrentopener.com
*Last updated: July 5th, 2013Remote Torrent Adder
Remote Torrent Adder is a browser extension that allows you to add torrents using several programs’ WebUIs. This extension allows you to send torrent files from your browser to your remote or local Bittorrent client’s web interface. It doesn’t just send the URLs to the WebUIs, but downloads the torrent and uses the file upload function of the UIs to add the torrent.
*Publisher: BOG
*Home page:code.google.com
*Last updated: February 27th, 2015
Index Additional Reliability Analysis Tools Maintenance Planning
*1Optimal Preventive Replacement Interval
*2Optimal Inspection Interval
More Resources:
Weibull++ Examples Collection
For components and systems with increasing failure rates, planned replacements and inspections are often used to prevent failures in order to improve system availability and reduce overall maintenance cost. For example, the commonly used preventive maintenance strategy is to replace an aged item at a given time interval in order to minimize the long term cost per unit time. An optimal time interval exists if the failure rate increases with time and the cost of failure is much higher than the cost of a scheduled replacement.
Another alternative is to minimize the short term cost per unit time, such as in one replacement cycle. A replacement cycle is defined as the time when a failure occurs or the time of the scheduled replacement when no failure occurs. Similarly, periodic inspections are done to detect oncoming failures and replace the component before a failure occurs. Inspections can also be used to minimize either the long-term or short-term costs. In this section, we will discuss how to find the optimal maintenance and inspection intervals in order to minimize the long-term and short-term maintenance costs.Optimal Preventive Replacement IntervalMinimize the Long Term Cost Per Unit Time
Minimizing the long term maintenance cost per unit time is the most popular objective for adopting a preventive replacement strategy. The theory behind this strategy is discussed in the Systems Reliability Analysis Reference book, but we will provide a brief explanation here.
For an item that is replaced either at the time of failure or at the time of the scheduled maintenance interval [math]x,![/math], the expected cycle length is:
[math]E(text{Cycle Length})=int_{0}^{x}{tf(t)dt}+R(x)x=int_{0}^{x}{R(t)dt}[/math]
The expected cost for one cycle is:
[math]E(text{Cost Per Cycle})={{C}_{P}}R(x)+{{C}_{U}}left( 1-R(x) right)[/math]
Therefore, the expected long term cost per unit time is:
[math]CPU{{T}_{L}}(x)=frac{E(text{Cost Per Cycle})}{Eleft( text{Cycle Length} right)}=frac{{{C}_{P}}R(x)+{{C}_{U}}left( 1-R(x) right)}{int_{0}^{x}{R(t)dt}}[/math]
The optimal preventive maintenance interval will be the value [math]x,![/math] which minimizes [math]CPU{{T}_{L}},![/math]. In the above equations:
*[math]f(x),![/math] is the probability density function of the failure time.
*[math]R(x),![/math] is the reliability function of the failure time.
*[math]{{C}_{P}},![/math] is the average cost due to a planned maintenance.
*[math]{{C}_{U}},![/math] is the average cost due to a unplanned maintenance.Minimize the Short Term Cost Per Unit Time
The equations above are based on the reward renewal theory and are used for minimizing the long term maintenance cost. There may be cases, however, where the average costs change with time, or when components are replaced with either costlier or less expensive versions. In this situation, the failure time distribution and the cost function need to be updated every time the costs change. Therefore, an optimal interval to minimize the short term cost is needed.
The expected cost per unit time in one replacement cycle is defined as:
[math]CPU{{T}_{S}}(x)=Eleft( frac{text{Cost Per Cycle}}{text{Cycle Length}} right)=int_{0}^{x}{frac{{{C}_{U}}}{t}f(t)dt}+frac{{{C}_{P}}}{x}left( 1-F(x) right)[/math]
For a Weibull distribution with its shape parameter [math]beta gt 1,![/math], the optimal interval [math]{{x}_{0}},![/math] is:
[math]{{x}_{o}}=eta {{left( frac{{{C}_{P}}}{beta left( {{C}_{U}}-{{C}_{P}} right)} right)}^{frac{1}{beta }}}[/math]
where [math]eta ,![/math] is the scale parameter of the Weibull distribution.Optimal Inspection Interval
Inspection is often used to test if a device is working properly. For example, signs of a device’s impending failure due to degradation, such as corrosion and crack, can be detected via inspection. The device can then be replaced before the failure actually occurs. If a failure cannot be detected during the inspection, it will be noticed immediately when the failure occurs, and the device will be replaced at the time of the failure. Reliasoft Download
Assume that a failure occurs at time [math]t,![/math]. If an inspection is conducted within the range of [math][ptimes t,t],!,![/math], the failure will be detected and the component will be replaced. The term [math]p,![/math] is a value between 0 and 1. This is illustrated in the following plot.
In the plot, the inspection is conducted at every X hours. ’No’ means that an oncoming failure will not be detected by inspection, while ’Yes’ means it can be detected by inspection since the inspection time is within [math][ptimes t,t][/math]. In this case, whenever a replacement occurs, a new maintenance cycle starts.
Minimize the Long Term Cost Per Unit Time
Define:
M is the largest inspection interval where there is no overlap between the detection zones of two adjunct inspections. Any failures that occur after the Mth inspection will always be detected.
The expected long term cost per unit time is:
[math]begin{align} & E(text{Cost Per Cycle})=int_{0}^{x}{{{C}_{U}}f(t)dt}+sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{left[ {{C}_{P}}+k{{C}_{I}} right]}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{left[ {{C}_{U}}+k{{C}_{I}} right]}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{left[ {{C}_{P}}+(M+1){{C}_{I}} right]}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{left[ {{C}_{P}}+(k+1){{C}_{I}} right]f(t)dt}} end{align}[/math]
The expected replacement cycle length is:
[math]begin{align} & E(text{Cycle Length})=int_{0}^{x}{tf(t)dt}+sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{left( kx right)}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{t}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{left[ (M+1)x right]}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{left[ (k+1)x right]f(t)dt}} end{align}[/math]
The expected long term cost per unit time is:
[math]CPU{{T}_{L}}(x)=frac{E(text{Cost Per Cycle})}{Eleft( text{Cycle Length} right)}[/math]
where [math]{{C}_{I}},![/math] is the average cost per inspection.Minimize the Short Term Cost Per Unit Time
The short term (one replacement cycle) cost per unit time is:
[math]begin{align} & CPU{{T}_{S}}=Eleft( frac{text{Cost per Cycle}}{text{Cycle Length}} right)=int_{0}^{x}{frac{{{C}_{U}}}{t}f(t)dt} & +sumlimits_{k=1}^{M}{left[ intlimits_{kx}^{frac{kx}{p}}{frac{{{C}_{P}}+k{{C}_{I}}}{kx}}f(t)dt+intlimits_{frac{kx}{p}}^{(k+1)x}{frac{{{C}_{U}}+k{{C}_{I}}}{t}}f(t)dt right]} & +intlimits_{left( M+1 right)x}^{frac{(M+1)x}{p}}{frac{{{C}_{P}}+(M+1){{C}_{I}}}{(M+1)x}}f(t)dt+sumlimits_{k=M+1}^{infty }{intlimits_{frac{kx}{p}}^{frac{(k+1)x}{p}}{frac{{{C}_{P}}+(k+1){{C}_{I}}}{(k+1)x}f(t)dt}} end{align}[/math]Example
Assume that we are going to use the Maintenance Planning tool in Weibull++ to analyze a device that is assembled as part of a system. The failure times of the device are recorded and a Weibull distribution is used to model the data. The following picture shows the Weibull++ standard folio that contains the data and distribution. The Weibull distribution has parameters [math]beta,![/math] = 2.847494 and [math]eta,![/math] = 108.420135.
Assume that the average cost for a planned replacement of the device is $20. For an unplanned replacement, the cost is $500. The cost for each inspection is $10, and the fraction of the failure time for detecting an oncoming failure is 0.9. The objectives are:
*Find the optimal inspection interval and the optimal scheduled replacement interval for minimizing the cost in the long term.
*Find the optimal inspection interval and the optimal scheduled replacement interval for minimizing the cost in one replacement cycle.
Solution
In the Maintenance Planning tool, choose the Inspection Replacement plot type on the control panel, and then enter the estimated costs. Click the Plot icon to calculate the results and draw the plot. The following results show that the optimal inspection interval is about 8.28 hours, and the minimal cost is about $1.98 per hour.
To use a scheduled replacement strategy, choose the Planned Replacement plot type on the control panel, and then click the Plot icon again to recalculate results and redraw the plot. The following results show that the optimal replacement interval is about 28.657 hours, and the minimal cost is about $1.079 per hour.
To find the optimal times for minimizing the cost in one replacement cycle, select the Plot One Cycle Cost/Time option on the Settings page of the control panel.
Next, choose the Inspection Replacement plot type on the Main page of the control panel and recalculate the results. The results show that the optimal inspection interval for one replacement cycle is about 6.437 hours, and the minimal cost is about $2.683 per hour.
Change the plot type to Planned Replacement and recalculate the results. The results show that the optimal replacement interval is about 24.592 hours, and the minimal cost is about $1.257 per hour.
To plot both the planned replacement and inspection replacement plots, choose the Both Planned and Inspection plot type. The results are shown next.Reliasoft Training
Based on the above results, we can now make decisions about our maintenance strategy. For example, if our plan is to reduce the short term maintenance cost, then the device should be scheduled for replacement at about every 24 hours. This will give us a minimal maintenance cost of $1.257 per hour.Retrieved from ’https://www.reliawiki.com/index.php?title=Maintenance_Planning&oldid=46122’
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