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Forum: Reliability & Maintainability Questions and Answers

Topic: Reliability & Maintainability Questions and Answers

Topic Posted by: Reliability & Maintainability Forum (src_forum@alionscience.com )
Organization: System Reliability Center
Date Posted: Mon Aug 31 12:47:36 US/Eastern 1998

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Original Message:

Posted by: Tim Daniels (Tim.Daniels@Fernau.Com )
Date posted: Tue Oct 26 10:09:55 US/Eastern 2004
Subject: Spares level over set period of time
Message:
Sorry this may be a silly question but it's the first time I've done anything like this. I need to calculate the number of spare LRUs required for a product to have 95% confidence level (of having a spare available) when the repair time is 10 months. I have failures/million hours figures and thought the RAC Poisson calculator for sparing was the answer! But now I have to consider a mission time of 18 months and calculate spares for this time only. I cannot see what will change. Can anybody give me any clues? Any ideas will be very much appreciated. Tim


Reply:

Subject: Spares
Reply Posted by: John Cloarec (jmcloarec@systra.com )
Organization: SYSTRA
Date Posted: Wed Oct 27 4:20:19 US/Eastern 2004
Message:
Hello Tim, the calculation for 10 months gave you the quantity of spares you need to achieve the mission. For 18 months you will calculate a new quantity higher than for 10 months, that's all !!! This means that for 10 or 18 months you will not buy extra spares (you will use only the spares you've bought at the beginning of the mission) and that the probability to achieve your mission is 95%.


Reply:

Subject: Spares for finite mission time
Reply Posted by: Larry George (pstlarry@yahoo.com )
Organization: Problem Solving Tools
Date Posted: Sat Oct 30 19:18:09 US/Eastern 2004
Message:
Good qustion! You don't need as many spares for a finite mission time as you need for continuing operation. Compare the following probability statements to see if the last suits your desired 95% confidence of no stockout: 1. 1.8*P[Demand > Spares in 10 months] < 0.05 (The 1.8 is because the mission is 18 months. 2. P[Demand <= Spares in 10 months]*P[No Demand in 8 months]+ P[One demand in 10 months]*P[Repair is done before next demand in remaining 8 months]+ P[Two demands in 10 months] and so on > 0.95 I'll try to work out the computation of the latter and send it, assuming constant demand rate, which implies demand is Poisson. Try to estimate age-specific failure rates, because failure rates aren't constant. Infant mortality could quickly consume your spares and you'd have to hope repairs are done in time. Don't rule out premature wearout in 18 months that could wipe out spares. Generally accepted accounting principles require ships and returns counts. These data are statistically sufficient to make nonparametric estimates of age-specific failure (actuarial) rates, actuarial forecasts, and estimates of the demand distribution. Send data, and I will do that, free of charge.


Reply:

Subject: Spreadsheet simulation of finite mission with repair
Reply Posted by: Larry George (pstlarry@yahoo.com )
Organization: Problem Solving Tools
Date Posted: Sun Oct 31 20:16:55 US/Eastern 2004
Message:
Thank you for sharing your interesting problem of finding the minimum spares level for specified probability of no stockout, for a finite mission with repair. That is not covered by the usual Poisson spares solution. A spreadsheet simulates the probability of no stockout during a mission as a function of failure (demand) rate, repair time, mission horizon time, and spares level. In the spreadsheet, enter your failure (demand) rate, repair time, mission horizon time, and a trial spares value in the attached spreadsheet table 1. Hit F9 to recalculate. Table 1 reports P[No stockout|spares, etc.] for each simulation. If P[No stockout|spares, etc.] is greater than desired Hold down F9 and watch for P[No stockout|spares, etc.] to flicker. If it flickers, there are several values of P[No stockout|spares, etc.]. Press F9 repeatedly and do an eyeball analysis to see whether the eyeball average P[No stockout|spares, etc.] is sufficiently great and to see if any values of P[No stockout|spares, etc.] are scary or scarily frequent. Adjust the spares value to achieve a comfortable average P[No stockout|spares, etc.] without frequent, scary deviations. Please let me know whether the spreadsheet simulation suits your needs and the implementation is adequate. Alternatives are: 1. Replicate table 1 many times and take the average P[No stockout|spares, etc.] and manually optimize the spares value. 2. Program the simulation in VBA, with a search for the min. spares level that achieves at least a desired P[No stockout|spares, etc.]. 3. Question the constant failure rate assumption! Test that assumption. Send field data and I will send back nonparametric estimates of age-specific field failure rates, and modify the simulation to suit.


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