Reliability Demonstration Test Plan
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- Milo Butler
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1 Rliability Dmonstration Tst Plan STATGRAPHICS Cnturion Rv. 6/7/04 Summary... Exampl... Analysis Window... Output... 4 Calculations... 5 Distributions... 5 Summary This procdur crats tst plans to dmonstrat that a failur tim distribution satisfis statd conditions. For xampl, it may b dsird to show with 95% confidnc that th rliability of a product quals or xcds 90% at th nd of th warranty priod. During th dmonstration, n units will b tstd for a duration qual to t. Th dmonstration will b considrd succssful if no mor than f units fail during th tst. Th usr spcifis ithr th numbr of units to b tstd or th duration of th tst. Th procdur solvs for th othr quantity. Exampl As an xampl, suppos w wish to solv th following problm: Assuming that th failur tims of an itm follow a Wibull distribution with a shap paramtr qual to.5, dmonstrat with 95% confidnc that th rliability of th itm aftr,000 hours quals 90%. Construct a tst of duration qual to 50 hours, whr th dmonstration is dmd succssful if non of th tst units fail during th tst. 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan -
2 STATGRAPHICS Cnturion Rv. 6/7/04 Analysis Window To xcut th procdur, slct Dscrib Lif Data Rliability Dmonstration Tst Plan from th Statgraphics mnu. This will display an analysis window similar to that shown blow: Th toolbar contains a numbr of controls that allow you to spcify dsird options: Dmonstrat: th condition to b dmonstratd. Thr ar 4 choics: o Rliability th probability that an itm has not faild aftr a duration qual to t. Entr th rliability and th valu of t. o Prcntil - th probability that an itm has faild aftr a duration qual to t. Entr th prcntil and th valu of t. o MTTF th man tim to failur. Entr th valu of th man. o Paramtr th unknown paramtr of th assumd distribution for failur tims (s paramtr to b stimatd blow). Entr th valu of th paramtr. 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan -
3 STATGRAPHICS Cnturion Rv. 6/7/04 Dist.: th assumd distribution of failur tims and th valu of th shap or scal paramtr. Thr ar 0 choics: Distribution Spcifid paramtr Paramtr to b stimatd Wibull Shap Scal Exponntial Non Man / Gamma Shap Scal Birnbaum-Saundrs Shap Scal Smallst xtrm valu Scal Mod Largst xtrm valu Scal Mod Normal Standard dviation Man Lognormal Standard dviation Man / Logistic Standard dviation Man Loglogistic Shap Mdian xp() Conf. lvl: th confidnc lvl for th dmonstration. Max. failurs: th maximum numbr of units f that ar allowd to fail but still rsult in a succssful dmonstration. Fix: th quantity to fix for th txt. Thr ar choics: o Numbr of units: th numbr of units n to b tstd. Th procdur will dtrmin th rquird tst duration t. o Tst duration: th tst duration t. Th procdur will dtrmin th numbr of units n to b tstd. Options: displays a dialog box with additional options: 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 3
4 STATGRAPHICS Cnturion Rv. 6/7/04 Th Options dialog box is usd to control th minimum valu, maximum valu, and incrmnt of th Statlt scrollbars. Exampl To solv th problm statd arlir, st th controls on th toolbar as shown blow: 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 4
5 In particular: STATGRAPHICS Cnturion Rv. 6/7/04. St th Dmonstrat fild to dmonstrat that Rliability quals 90.0% at a liftim qual to St th Max. failurs fild to St th Dist. fild to Wibull with a shap paramtr qual to St th confidnc lvl to 95%. 5. Fix th Tst duration at t = Prss th Updat button. Output Th output of th Statlt shows svral important rsults:. Th scond lin of th titl shows th duration of th tst t and th numbr of units n. For th xampl, n = 8 units must b tstd for a duration of t = 50.. Th plottd probability of passing curv shows th probability of a succssful dmonstration as a function of th probability that any singl unit will surviv until th targt liftim of 000 hours. Th chanc of passing th tst rangs from about 5% if units surviv 000 hours only 90% of th tim, to clos to 00% if th probability of surviving 000 hours is vry high. Th shap of th curv is most snsitiv to th maximum numbr of allowabl failurs. Calculations Th basic procdur is as follows: Stp : Givn th assumd distribution of failur tims, dtrmin th valu of any unknown paramtrs that will rsult in th spcifid rliability, prcntil, MTTF, or paramtr valu. Stp : Solv for th rliability at th nd of th tsting priod. Stp 3: Dtrmin th valus of n and t that will rsult in a succssful dmonstration with probability qual to alpha ( minus th confidnc lvl) whn th statmnt to b dmonstratd is xactly tru. This insurs that if th tst is passd, th lowr confidnc bound for th quantity to b dmonstratd is no wors than statd. Distributions 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 5
6 STATGRAPHICS Cnturion Rv. 6/7/04 Statgraphics dfins th distributions usd in this procdur as indicatd blow. Birnbaum-Saundrs Distribution Rang of X: X > 0 Common us: modl for th numbr of cycls ndd to caus a crack to grow to a siz that would caus a fractur to occur. x x f x x ( ) whr (z) is th standard normal pdf x x Paramtrs: shap > 0, scal > 0 Man: 5 4 Varianc: 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 6
7 Exponntial Distribution Rang of X: X > 0 STATGRAPHICS Cnturion Rv. 6/7/04 Common us: tim btwn conscutiv arrivals in a Poisson procss. Liftim of itms with a constant hazard rat. x Paramtrs: man > 0 Man: Varianc: Gamma Distribution Rang of X: X 0 Common us: modl for positivly skwd masurmnts. Tim to complt a task, such as a rpair. x x Paramtrs: shap >0, scal > 0 Man: Varianc: Largst Extrm Valu Distribution Rang of X: all ral X Common us: distribution of th largst valu in a sampl from many distributions. Also usd for positivly skwd masurmnt data. x xa xp xp Paramtrs: Man: Varianc: 6 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 7
8 Logistic Distribution Rang of X: all ral X STATGRAPHICS Cnturion Rv. 6/7/04 Common us: usd as a modl for growth and as an altrnativ to th normal distribution. xp( z) xp( z) whr z x Paramtrs: man, standard dviation Man: Varianc: Loglogistic Distribution Rang of X: X > 0 Common us: usd for data whr th logarithms follow a logistic distribution. x xp( z) xp( z) whr Paramtrs: mdian xp(, shap Man: xp( ) ln(x) z Varianc: xp( ) Lognormal Distribution Rang of X: X > 0 Common us: usd for data whr th logarithms follow a normal distribution. f ln x ( x) x Paramtrs: location, scal > 0 Man: / Varianc: Normal Distribution Rang of X: all ral X Common us: widly usd for masurmnt data, particularly whn variability is du to many sourcs. x Paramtrs: man, standard dviation > 0 Man: Varianc: 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 8
9 Smallst Extrm Valu Distribution Rang of X: all ral X STATGRAPHICS Cnturion Rv. 6/7/04 Common us: distribution of th smallst valu in a sampl from many distributions. Also usd for ngativly skwd masurmnt data. x xa f x ( ) xp xp Paramtrs: mod, scal > 0 Man: Varianc: 6 Wibull Distribution Rang of X: X 0 Common us: widly usd in rliability analysis to modl product liftims. ( x / ) x Paramtrs: shap > 0, scal > 0 Man: Varianc: 03 by StatPoint Tchnologis, Inc. Rliability Dmonstration Tst Plan - 9
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