DEVELOPMENT OF FAILURE PATTERNS
In order to understand failure patterns, we will go through the calculation routine, using a set of artificially created failure data. We will use simplified and idealized circumstances in the following discussion.
In a hypothetical chemical process plant, imagine that there are 1000 bearings of the same make, type, and size in use. Further, let us say that they operate in identical service conditions. In the same manner, there are 1000 impellers, 1000 pressure switches, 1000 orifice plates, etc., each set of items operating in identical service. Assume that we are in a position to track their performance against operating age. The installation and commissioning dates are also identical.
In Table 3-1.1*, we can see the number of items that fail every week. We will examine six such elements, labeled A-F. There cord shows failures of the originally installed items, over a hundred week period. If an item fails in service, we do not record the history of the replacement item.
Figures 3-1.1 through 3-1.6 illustrate the failures. If we divide the number of failures by the sample size and plot these along the y-axis, the resulting pdf curves will look identical to this set.
In each case, at the start there were 1000 items in the sample. We can therefore work out the number of survivors at the end of each week. We simply deduct the number of failures in that week, from the survivors at the beginning of the week. Table 3-1.2* shows the number of survivors.
Figures 3-1.7 through 3-1.12 are survival plots for the six samples.
We calculate the hazard rate by dividing the failures in any week, by the number of survivors. These are in Table 3-1.3* and the corresponding hazard rate plots are in Figures 3-1.13 through 3-1.18.
These charts illustrate how we derive the failures, survivors, and hazard rates from the raw data. As explained earlier, the data is hypothetical, and created to illustrate the shape of the reliability curves which one may expect to see with real failure history data.
Table 3-1.1 Number of failures recorded per week—elements A to F. Note: Data for weeks 11-44 and 55-90 not shown
Figure 3-1.1 Failures recorded—element A.
Figure 3-1.2 Failures recorded—element B.
Figure3-1.3 Failures recorded—element C.
Figure 3-1.4 Failuresrecorded—element D.
Figure3-1.5 Failures recorded—element E.
Figure 3-1.6 Failures recorded—element F.
Table3-1.2 Number of survivors—elements A to F Note: Data for weeks 11-44 and 55-99
Figure 3-1.7 Survivors from original sample—element A.
Figure3-1.8 Survivors from original sample—element B.
Figure3-1.9 Survivors from original sample—element C.
Figure 3-1.10 Survivors from original sample—element D.
Figure 3-1.11 Survivors from original sample—element E.
Figure3-1.12 Survivors from original sample—element F.
Table 3-1.3 Hazard rates—elements A to F. Note: Data for weeks 11-44 and 55-99
Figure3-1.13 Hazard rate—element A.
Figure 3-1.14 Hazard rate—element B.
Figure3-1.15 Hazard rate—element C
Figure 3-1.16 Hazard rate—element D.
Figure 3-1.17 Hazard rate—element E.
Figure 3-2.18 Hazard rate—element F.
*Note: In Tables 3-1.1, 3-1.2, and 3-1.3, we have shown only a part of the data set. The data for weeks 11–44 and 55–90 have been omitted to improve readability.
AN EXAMPLE TO SHOW THE EFFECT OF THE SHAPE FACTOR
In Appendix 3-1, we derived the