Quality and Reliability Methods - SAS

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Contents Overview of the Reliability Growth Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Example Using the Reliability Growth Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Launch the Reliability Growth Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322 Time to Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Timestamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Event Count . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324 Phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324 By . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324 Data Table Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324 The Reliability Growth Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326 Observed Data Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326 Reliability Growth Platform Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 Fit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 Script. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .329 Fit Model Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .329 Crow AMSAA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .329 Fixed Parameter Crow AMSAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Piecewise Weibull NHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Reinitialized Weibull NHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Piecewise Weibull NHPP Change Point Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Additional Examples of the Reliability Growth Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342 Piecewise NHPP Weibull Model Fitting with Interval-Censored Data . . . . . . . . . . . . . . . . . . . . . . .342 Piecewise Weibull NHP Change Point Detection with Time in Dates Format . . . . . . . . . . . . . . . . . 345 Statistical Details for the Reliability Growth Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347 Statistical Details for the Crow-AMSAA Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347 Statistical Details for the Piecewise Weibull NHPP Change Point Detection Report . . . . . . . . . . . . .348 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .348
Chapter 18 Reliability Growth 319 Overview of the Reliability Growth Platform Overview of the Reliability Growth Platform The Reliability Growth platform fits Crow-AMSAA models, described in MIL-HDBK-189 (1981). A Crow-AMSAA model is a non-homogeneous Poisson process (NHPP) model with Weibull intensity; it is also known as a power law process. Such a model allows the failure intensity, which is defined by two parameters, to vary over time. The platform fits four classes of models and performs automatic change-point detection, providing reports for the following: • Simple Crow-AMSAA model, where both parameters are estimated using maximum likelihood • Fixed Parameter Crow-AMSAA model, where the user is allowed to fix either or both parameters • Piecewise Weibull NHPP model, where the parameters are estimated for each test phase, taking failure history from previous phases into account • Reinitialized Weibull NHPP model, where both parameters are estimated for each test phase in a manner that ignores failure history from previous phases • Automatic estimation of a change-point and the associated piecewise Weibull NHPP model, for reliability growth situations where different failure intensities can define two distinct test phases Example Using the Reliability Growth Platform Suppose that you are testing a prototype for a new class of turbine engines. The testing program has been ongoing for over a year and has been through three phases. The data are given in the TurbineEngineDesign1.jmp sample data table, found in the Reliability subfolder. For each failure that occurred, the number of days since test initiation was recorded in the column Day. The number of failures on a given day, or equivalently, the number of required fixes, was recorded in the column Fixes. The first 100-day phase of the program was considered the initial testing phase. Failures were addressed with aggressive design changes, resulting in a substantially revised design. This was followed by another 100-day phase, during which failures in the revised design were addressed with design changes to subsystems. The third and final testing phase ran for 250 days. During this final phase, failures were addressed with local design changes. Each phase of the testing was terminated based on the designated number of days, so that the phases are time terminated. Specifically, a given phase is time terminated at the start time of the next phase. However, the failure times are exact (not censored). 1. Open the TurbineEngineDesign1.jmp sample data table. 2. Select Analyze > Reliability and Survival > Reliability Growth. 3. On the Time to Event Format tab, select Day and click Time to Event. 4. Select Fixes and click Event Count. 5. Select Design Phase and click Phase.
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References Abernethy, Robert B. (19
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References 409 Haaland, P.D. (1989)
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Index JMP Quality and Reliability M
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Index 419 Fit SEV 242 Fit Weibull 2
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Index 421 Q Quantiles table 356 R R
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Index 423 Weibull Plot 360 Westgard
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