Hazard plots

Graphical analysis of failure data is most commonly plotted using probability. However, in order to understand the hazard plotting method presented here, is not necessary to understand probability plotting. While it is difficult to utilize probability plotting for multiply-censored data, it is... 

The hazard plotting method is presented in detail in the next section followed by the step-by-step instructions on... 

Figures 62.8, 62.9, 62.10 show the data for generator fan failure plotted on exponential, normal and log normal hazard paper respectively. The exponential plot is a reasonably straight line which indicates that the failure rate is relatively constant over the range of the data. It should be noted that the reason the probability scale on the exponential hazard plot is crossed out is because that is not the proper way to plot data. (This will be discussed later.) The normal plot is curved concave upward which...

Like all other methods for analyzing censored failure data, the hazard plotting method is also based on a certain assumption that must be satisfied if we are going to rely on the results. The assumption is that if the unfailed units were mn to failure, their failure times would be statistically independent of their censoring times. In other words, there is no relationship or correlation between the censoring time of a unit and the failure time. For example. 

Figure 62.8 Normal hazard plot of generator fan failure data...

Figure 62.10 Exponential hazard plot of simulated exponential data...

The line the data supports on a hazard plot determines engineering information relating to the distribution of time to failure. Fan failure data and simulated data are illustrated here to explain how the information is obtained. The methods provide estimates of distribution parameters, percentiles, and probabilities of failure. The methods that give estimates of distribution parameters differ slightly from the hazard paper of one theoretical distribution to another and are given separately for each distribution. The methods that give estimates of distribution percentiles and failure probabilities are the same for all papers and are given first. 

Given next are the different methods for estimating distribution parameters on exponential, Weibull, normal, log normal, and extreme-value hazard papers. The methods are explained with the aid of simulated data from known distributions. Thus, we can judge from the hazard plots how well the hazard-plotting method does. 

For the purpose of showing how to obtain from an exponential hazard plot an estimate of the exponential mean time to failure, assume that the straight line on Figure 62.9 is the one fitted to the data. Enter the plot at the 100 per cent point on the horizontal cumulative hazard scale at the bottom of the paper. Go up to the fitted line and then across horizontally to the vertical time scale where the estimate of the mean time to failure is read and is 1000 hours. The corresponding estimate of the failure rate is the reciprocal of the mean time to failure and is 1/100 = 0.001 failures per hour. 

Figure 62.11 Weibull hazard plot of simulated Weibull data...

The behavior of the failure rate as a function of time can be gaged from a hazard plot. If data are plotted on exponential hazard paper, the derivative of the cumulative hazard function at some time is the instantaneous failure rate at that time. Since time to failure is plotted as a function of the cumulative hazard, the instantaneous failure rate is actually the reciprocal of the slope of the plotted data, and the slope of the plotted data corresponds to the instantaneous mean time to failure. For the data that are plotted on one of the other hazard papers and that give a curved plot, one can determine from examining the changing slope of the plot whether the tme failure rate is increasing or decreasing relative to the failure rate of the theoretical distribution for the paper. Such information on the behavior of the failure rate cannot be obtained from probability plots. 

The cumulative hazard plotting method and papers presented here provide simple means for statistical analyses of multiply censored failure data to obtain engineering information. The hazard-plotting method is simpler to use for multiply censored data than other plotting methods given in the literature and directly gives failure-rate information not provided by others. 

Tooele County agrees to review DCD s daily chemical operations work plans, the hazard plots and the PARs from DCD at least twice daily. After review of the data provided by DCD, and giving consideration to off-post weather station readings and other community conditions, Tooele County will provide DCD and Utah Comprehensive Emergency Management with an appropriate protective action decision (PAD), including which communities would be instructed to evacuate or in-place shelter, specific evacuation routes, designated reception centers, etc. Tooele County will provide PAD updates... 

For Category II, Limited Area, Post Only, and Category III, Community level emergencies, DCD will also provide, as soon as possible, an EMIS Event Notification , as well as updated hazard plots and revised protective action recommendations as required. Until updated protective action recommendations are prepared and transmitted, the most recent work plan hazard plot and protective action recommendation will be implemented. Tooele County will provide notification to Utah Comprehensive Emergency Management according to established procedures. 

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Homan Remains DecoABiatfm Equipment COBtaaraieat Mitigation Risk-Based Hazard Plots... 

Nelson, W. 1969. Hazard Plotting For Incomplete Failure Data , Journal of Quahty Technology 1, pp. 27-52. 

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