Quality and Reliability Methods - SAS

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338 Reliability Growth Chapter 18 Fit Model Options Show MTBF Plot The MTBF plot and an Estimates report open by default when the Piecewise Weibull NHPP option is chosen (Figure 18.16). When Time to Event Format is used, the axes are logarithmically scaled. For further details on the plot, see “Show MTBF Plot” on page 330. Estimates The Estimates report gives estimates of the model parameters. Note that only the estimate for the value of λ corresponding to the first phase is given. In the piecewise model, the cumulative events at the end of one phase must match the number at the beginning of the subsequent phase. Because of these constraints, the estimate of λ for the first phase and the estimates of the βs determine the remaining λs. The method used to calculate the estimates, their standard errors, and the confidence limits is similar to that used for the simple Crow-AMSAA model. For further details, see “Parameter Estimates” on page 347. The likelihood function reflects the additional parameters and the constraints on the cumulative numbers of events. Show Intensity Plot The Intensity plot shows the estimated intensity function and confidence bounds over the design phases. The intensity function is generally discontinuous at a phase transition. Color coding facilitates differentiation of phases. If Time to Event Format is used, the axes are logarithmically scaled. For further details, see “Show Intensity Plot” on page 331. Show Cumulative Events Plot The Cumulative Events plot shows the estimated cumulative number of events, along with confidence bounds, over the design phases. The model requires that the cumulative events at the end of one phase match the number at the beginning of the subsequent phase. Color coding facilitates differentiation of phases. If Time to Event Format is used, the axes are logarithmically scaled. For further details, see “Show Cumulative Events Plot” on page 332. Show Profilers Three profilers are displayed, showing estimated MTBF, Failure Intensity, and Cumulative Events. These profilers do not use logarithmic scaling. For more detail on interpreting and using these profilers, see the section “Show Profilers” on page 333. It is important to note that, due to the default resolution of the profiler plot, discontinuities do not display clearly in the MTBF or Failure Intensity Profilers. In the neighborhood of a phase transition, the profiler trace shows a nearly vertical, but slightly sloped, line; this line represents a discontinuity. (See Figure 18.17.) Such a line at a phase transition should not be used for estimation. You can obtain a higher-resolution display making these lines appear more vertical as follows. Press CTRL while clicking in the profiler plot, and then enter a larger value for Number of Plotted Points in the dialog window. (See Figure 18.18, where we have specified 500 as the Number of Plotted Points.)
Chapter 18 Reliability Growth 339 Fit Model Options Figure 18.17 Profilers Figure 18.18 Factor Settings Window Reinitialized Weibull NHPP This option fits an independent growth model to the data from each test phase. Fitting models in this fashion can be useful when the factors influencing the growth rate, either in terms of testing or engineering, have changed substantially between phases. In such a situation, you may want to compare the test phases independently. The Reinitialized Weibull NHPP option is available when a Phase column specifying at least two phases has been entered in the launch window. For the algorithm to fit this model, each row that contains the first occurrence of a new phase must contain the start date. • Suppose that a single column is entered as Time to Event or Timestamp. Then the start time for a new phase, with a zero Event Count, must appear in the first row for that phase. See the sample data table ProductionEquipment.jmp, in the Reliability subfolder, for an example. • If two columns are entered, then an interval whose left endpoint is that start time must appear in the first row, with the appropriate event count. The sample data table TurbineEngineDesign2.jmp, found in
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Chapter 11 Pareto Plots The Pareto
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Chapter 11 Pareto Plots 187 Launch
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Chapter 11 Pareto Plots 193 Defect
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Chapter 20 Reliability and Survival
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References Abernethy, Robert B. (19
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References 407 Carroll, R.J., Ruppe
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References 409 Haaland, P.D. (1989)
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References 411 Lawless, J.F. (1982)
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References 413 Nelson, W.B. (2003),
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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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