【翻译】第四十二篇 Divide and Conquer In Reliability Analyses
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Divideand Conquer In Reliability Analyses
Gain understanding by lookingat different population segments
by Necip Doganaksoy, Gerald J. Hahn andWilliam Q. Meeker
All product is not created equal. Someunits are more likely to fail in service than others. Thus, in reliabilityevaluations, you need to identify subpopulations with different failuresusceptibility. This is accomplished through segmentation—a divide-and-conquerstrategy that breaks down the product population into meaningful subpopulationsso you can conduct separate analyses on each and then act on the resultinginformation.
Segmentation (also known as datastratification) is one of the so-called seven basic quality tools.1 Inthis column, we describe and illustrate the use of segmentation for,principally, reliability applications.2
What creates subpopulations?In a specific product application,subpopulations result from differences in the manufacture and use of a product.Differences in reliability may, for example, be due to variability in rawmaterials and components or differences in manufacturing processing conditions.
In a recent application, Yili Hong,William Q. Meeker and James D. McCalley segmented data on a fleet ofhigh-voltage power transformers according to manufacturer and manufacturingperiod—first to model lifetime and then to predict the remaining life for theunits in the fleet.3 In another application dealing with the prediction ofwarranty costs for an electronic product, the population was broken down intocomponent genealogy groups consisting of combinations of part numbers.
Segmentation is especially appropriate whenfailures due to a particular defect occur in only some production lots. Instudying the cracking of the plastic casing of a laptop computer, for example,segmentation revealed such failures took place exclusively on units builtduring a one-month period at one of several assembly plants. This led tofurther study, which revealed the wrong type of screw was used in assembly atthis plant during this time period, and grease on the screws led to chemicaldegradation of the plastic casing.
Isolating the problem facilitated rootcause identification and steps to ensure the problem would not recur in futureproduct. More immediately, it led to identifying and, when needed, repairingpreviously built computers that were vulnerable to this failure.
Also, different units of a productpopulation often experience different use environments. A problem may beaccentuated or perhaps limited to occur at only extreme ambient conditions,such as severe heat or cold. Moreover, the performance of a dishwasher maydepend on the characteristics of the local water supply. In such cases, you mightfocus immediate corrective action on product in the most vulnerablegeographical regions; segmentation of the data by region will help identify thesubpopulations that warrant special attention.
Example: aircraft engineThe following example deals with a systemthat bleeds off air pressure from an aircraft engine to operate a compressor:4,5
Initial analysis. Lifetime data wereavailable on bleed systems from 2,256 engines in military aircraft operatingfrom various bases. Figure 1 shows a Weibull distribution probability plot forthe 19 failures that occurred. Note that unfailed units, although not shown inthe plot, are taken into consideration in arriving at the plotting positions.
The slope of the plot seems to changearound 600 hours, indicating that a simple Weibull distribution does notprovide an adequate representation for the lifetimes. This pattern, which iscommon in our experience, suggests a mixture of early (infant mortality)failures (on the left side of the plot) and wear-out failures (on the rightside Segmented data analysis. Examination of the data revealed that 10 of the 19 failuresoccurred at base D, one of the bases where aircraft were stationed. SeparateWeibull probability plots for the lifetimes of the systems at base D and thoseat all other bases are shown in Figure 2.
The data in each of these two plots scatteraround straight lines, suggesting that simple Weibull distributions provideadequate representations if you consider base D and the other bases separately.Moreover, the probability of failure by 3,000 hours is estimated from the plotto be 0.467 for the systems at base D, as compared to 0.013 for the systems atthe other bases.6
A recent analysis suggested that lognormaldistributions might provide a better fit to the data than Weibulldistributions. Fortunately, both analyses led to similar findings.
Resulting action. Furtherinvestigation revealed the serious failure problem at base D was caused by corrosionaccelerated by salty air (base D was near the ocean), and a change inmaintenance procedures was implemented there. This resulted in essentiallyeliminating the failure mode. Note that segmentation analyses typicallydo not provide cause-and-effect conclusions by themselves. The difference infailure probabilities between base D and the other bases could have been due toone factor or a combination of many factors. The determination that theunderlying cause was corrosion due to salty air involved an engineeringassessment of failed parts. The segmentation analysis, however, helped focusand expedite the physical evaluations.
Identification ofsubpopulationsIf at all possible, the selection ofsubpopulations should be based on physical considerations. This requires anin-depth understanding of the design, manufacture and use conditions of theproduct.
In practice, however, the reasons fordifferences between subpopulations may not be known and, therefore, effectivesubpopulations often cannot be readily determined. If you knew what created thedifferences—at least, to the degree that these pertain to the manufacture ofthe product and are controllable—you would, in fact, want to act to removethem. Thus, identifying subpopulations may be a trial-and-error process.
Initially, subpopulations are often arrivedat somewhat arbitrarily, based upon, for example, the period of production(week, month, quarter or year Such choices should, however, be trumped bymanufacturing knowledge. The times at which changes are introduced on line, forexample, generally provide an improved criterion for segmentation. Segmentationmight also be based on factors such as parts supplier, the geographical regionwhere the product is being used, customer type or a combination of these.
The fact that a Weibull probability plot ofthe data does not result in a straight line, as in the bleed system example,also suggests the existence of subpopulations (and multiple failure modes, asdiscussed later) and might provide clues for defining subpopulations.
Segmenting data elsewhereWe have discussed segmentation in thecontext of reliability data tracking for nonrepairable products. Segmentationof data, however, is useful in many other situations.
For example, a chemical cure process showedinconsistent results. To gain improved understanding, the data were segmentedand plotted in various ways, including by shift. The resulting plot showed twoof the shifts were providing satisfactory product, but the night shift was not.
To find the cause for this difference, alate-night visit to the factory floor revealed the third-shift operatorsfrequently turned off the plant’s air conditioning. This increased humidity,which in turn had a negative impact on product performance. After correctingthe problem, it was decided to control chart the performance segmented byshift.
Another example arises in the comparison ofdrugs, an area that has become known as comparative effectiveness research andwas part of the 2009 U.S. economic stimulus bill. In assessing theeffectiveness of competing drugs or medical devices, you want to know if aparticular drug is effective in one or more parts of the population, such asthe elderly, even if it may not be so in other parts. This calls for segmentationin the data analysis.7
Multiple failure modeanalysesSegmentation bears some similarity to theanalysis of multiple failure modes discussed in one of our earliercolumns.8 In both cases, the life data cannot be described adequately by asingle, simple distribution.
In studying multiple failure modes,information on the mode of failure of each failed unit is required. All of thedata is then used in each analysis, but observations from failure modes otherthan the one under consideration are taken as censored.
In contrast, for the bleed system example,failure mode information was not available at the time of the analysis (andpossibly one or more of the base D failures was not actually from corrosion Thus, the data were segmented into subpopulations, and separate analyses wereconducted for each subpopulation.
In both situations, the results of theindividual analyses can subsequently be combined to obtain an omnibus analysisfor the entire population. For segmentation, this requires knowledge of theproportion of units in the population belonging to each subpopulation.
Short term vs. long term In the short term, segmentation may resultin the speedy and accurate isolation of field problems to well-identifiedsegments of the total product population, so you can identify the mostsusceptible units and take corrective action. Segmentation may, for example,help determine whether a recall is needed, and if so, what part of the productpopulation needs to be recalled.
By isolating a problem to a relativelysmall part of the population, you may be able to address an otherwise extremelycostly problem without inconveniencing customers not impacted by the problem.The long-term answer, however, is to eliminate the problem in future units,perhaps by designing a sufficiently robust product whose performance isinsensitive to the use environment.
Necip Doganaksoy is a principaltechnologist-statistician at the GE Global Research Center in Schenectady, NY.He has a doctorate in administrative and engineering systems from Union Collegein Schenectady. Doganaksoy is a fellow of ASQ and the American StatisticalAssociation.
Gerald J. Hahn is a retired manager of statistics at the GE Global ResearchCenter in Schenectady, NY. He has a doctorate in statistics and operationsresearch from Rensselaer Polytechnic Institute in Troy, NY. Hahn is a fellow ofASQ and the American Statistical Association.
William Q. Meeker is professor of statistics and distinguished professor ofliberal arts and sciences at Iowa State University in Ames, IA. He has adoctorate in administrative and engineering systems from Union College inSchenectady, NY. Meeker is a fellow of ASQ and the American StatisticalAssociation.
你好，我是小编H。请对以下文章有翻译兴趣的组员留下你的预计完成时间，并发短信息联系小编H，以便小编登记翻译者信息以及文章最终完成时的奖惩工作。感谢支持翻译组！
Divideand Conquer In Reliability Analyses
Gain understanding by lookingat different population segments
by Necip Doganaksoy, Gerald J. Hahn andWilliam Q. Meeker
All product is not created equal. Someunits are more likely to fail in service than others. Thus, in reliabilityevaluations, you need to identify subpopulations with different failuresusceptibility. This is accomplished through segmentation—a divide-and-conquerstrategy that breaks down the product population into meaningful subpopulationsso you can conduct separate analyses on each and then act on the resultinginformation.
Segmentation (also known as datastratification) is one of the so-called seven basic quality tools.1 Inthis column, we describe and illustrate the use of segmentation for,principally, reliability applications.2
What creates subpopulations?In a specific product application,subpopulations result from differences in the manufacture and use of a product.Differences in reliability may, for example, be due to variability in rawmaterials and components or differences in manufacturing processing conditions.
In a recent application, Yili Hong,William Q. Meeker and James D. McCalley segmented data on a fleet ofhigh-voltage power transformers according to manufacturer and manufacturingperiod—first to model lifetime and then to predict the remaining life for theunits in the fleet.3 In another application dealing with the prediction ofwarranty costs for an electronic product, the population was broken down intocomponent genealogy groups consisting of combinations of part numbers.
Segmentation is especially appropriate whenfailures due to a particular defect occur in only some production lots. Instudying the cracking of the plastic casing of a laptop computer, for example,segmentation revealed such failures took place exclusively on units builtduring a one-month period at one of several assembly plants. This led tofurther study, which revealed the wrong type of screw was used in assembly atthis plant during this time period, and grease on the screws led to chemicaldegradation of the plastic casing.
Isolating the problem facilitated rootcause identification and steps to ensure the problem would not recur in futureproduct. More immediately, it led to identifying and, when needed, repairingpreviously built computers that were vulnerable to this failure.
Also, different units of a productpopulation often experience different use environments. A problem may beaccentuated or perhaps limited to occur at only extreme ambient conditions,such as severe heat or cold. Moreover, the performance of a dishwasher maydepend on the characteristics of the local water supply. In such cases, you mightfocus immediate corrective action on product in the most vulnerablegeographical regions; segmentation of the data by region will help identify thesubpopulations that warrant special attention.
Example: aircraft engineThe following example deals with a systemthat bleeds off air pressure from an aircraft engine to operate a compressor:4,5
Initial analysis. Lifetime data wereavailable on bleed systems from 2,256 engines in military aircraft operatingfrom various bases. Figure 1 shows a Weibull distribution probability plot forthe 19 failures that occurred. Note that unfailed units, although not shown inthe plot, are taken into consideration in arriving at the plotting positions.
The slope of the plot seems to changearound 600 hours, indicating that a simple Weibull distribution does notprovide an adequate representation for the lifetimes. This pattern, which iscommon in our experience, suggests a mixture of early (infant mortality)failures (on the left side of the plot) and wear-out failures (on the rightside Segmented data analysis. Examination of the data revealed that 10 of the 19 failuresoccurred at base D, one of the bases where aircraft were stationed. SeparateWeibull probability plots for the lifetimes of the systems at base D and thoseat all other bases are shown in Figure 2.
The data in each of these two plots scatteraround straight lines, suggesting that simple Weibull distributions provideadequate representations if you consider base D and the other bases separately.Moreover, the probability of failure by 3,000 hours is estimated from the plotto be 0.467 for the systems at base D, as compared to 0.013 for the systems atthe other bases.6
A recent analysis suggested that lognormaldistributions might provide a better fit to the data than Weibulldistributions. Fortunately, both analyses led to similar findings.
Resulting action. Furtherinvestigation revealed the serious failure problem at base D was caused by corrosionaccelerated by salty air (base D was near the ocean), and a change inmaintenance procedures was implemented there. This resulted in essentiallyeliminating the failure mode. Note that segmentation analyses typicallydo not provide cause-and-effect conclusions by themselves. The difference infailure probabilities between base D and the other bases could have been due toone factor or a combination of many factors. The determination that theunderlying cause was corrosion due to salty air involved an engineeringassessment of failed parts. The segmentation analysis, however, helped focusand expedite the physical evaluations.
Identification ofsubpopulationsIf at all possible, the selection ofsubpopulations should be based on physical considerations. This requires anin-depth understanding of the design, manufacture and use conditions of theproduct.
In practice, however, the reasons fordifferences between subpopulations may not be known and, therefore, effectivesubpopulations often cannot be readily determined. If you knew what created thedifferences—at least, to the degree that these pertain to the manufacture ofthe product and are controllable—you would, in fact, want to act to removethem. Thus, identifying subpopulations may be a trial-and-error process.
Initially, subpopulations are often arrivedat somewhat arbitrarily, based upon, for example, the period of production(week, month, quarter or year Such choices should, however, be trumped bymanufacturing knowledge. The times at which changes are introduced on line, forexample, generally provide an improved criterion for segmentation. Segmentationmight also be based on factors such as parts supplier, the geographical regionwhere the product is being used, customer type or a combination of these.
The fact that a Weibull probability plot ofthe data does not result in a straight line, as in the bleed system example,also suggests the existence of subpopulations (and multiple failure modes, asdiscussed later) and might provide clues for defining subpopulations.
Segmenting data elsewhereWe have discussed segmentation in thecontext of reliability data tracking for nonrepairable products. Segmentationof data, however, is useful in many other situations.
For example, a chemical cure process showedinconsistent results. To gain improved understanding, the data were segmentedand plotted in various ways, including by shift. The resulting plot showed twoof the shifts were providing satisfactory product, but the night shift was not.
To find the cause for this difference, alate-night visit to the factory floor revealed the third-shift operatorsfrequently turned off the plant’s air conditioning. This increased humidity,which in turn had a negative impact on product performance. After correctingthe problem, it was decided to control chart the performance segmented byshift.
Another example arises in the comparison ofdrugs, an area that has become known as comparative effectiveness research andwas part of the 2009 U.S. economic stimulus bill. In assessing theeffectiveness of competing drugs or medical devices, you want to know if aparticular drug is effective in one or more parts of the population, such asthe elderly, even if it may not be so in other parts. This calls for segmentationin the data analysis.7
Multiple failure modeanalysesSegmentation bears some similarity to theanalysis of multiple failure modes discussed in one of our earliercolumns.8 In both cases, the life data cannot be described adequately by asingle, simple distribution.
In studying multiple failure modes,information on the mode of failure of each failed unit is required. All of thedata is then used in each analysis, but observations from failure modes otherthan the one under consideration are taken as censored.
In contrast, for the bleed system example,failure mode information was not available at the time of the analysis (andpossibly one or more of the base D failures was not actually from corrosion Thus, the data were segmented into subpopulations, and separate analyses wereconducted for each subpopulation.
In both situations, the results of theindividual analyses can subsequently be combined to obtain an omnibus analysisfor the entire population. For segmentation, this requires knowledge of theproportion of units in the population belonging to each subpopulation.
Short term vs. long term In the short term, segmentation may resultin the speedy and accurate isolation of field problems to well-identifiedsegments of the total product population, so you can identify the mostsusceptible units and take corrective action. Segmentation may, for example,help determine whether a recall is needed, and if so, what part of the productpopulation needs to be recalled.
By isolating a problem to a relativelysmall part of the population, you may be able to address an otherwise extremelycostly problem without inconveniencing customers not impacted by the problem.The long-term answer, however, is to eliminate the problem in future units,perhaps by designing a sufficiently robust product whose performance isinsensitive to the use environment.
Necip Doganaksoy is a principaltechnologist-statistician at the GE Global Research Center in Schenectady, NY.He has a doctorate in administrative and engineering systems from Union Collegein Schenectady. Doganaksoy is a fellow of ASQ and the American StatisticalAssociation.
Gerald J. Hahn is a retired manager of statistics at the GE Global ResearchCenter in Schenectady, NY. He has a doctorate in statistics and operationsresearch from Rensselaer Polytechnic Institute in Troy, NY. Hahn is a fellow ofASQ and the American Statistical Association.
William Q. Meeker is professor of statistics and distinguished professor ofliberal arts and sciences at Iowa State University in Ames, IA. He has adoctorate in administrative and engineering systems from Union College inSchenectady, NY. Meeker is a fellow of ASQ and the American StatisticalAssociation.
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