Consideration of faults not yet occurred 

 

Sudden Death

If specimens are removed from the service life test, before they have failed, then these random tests will be considered incomplete. In this situation it is clearly incorrect to input the "service lives" into the statistics in the same way as would be done had they have failed. In the same way, if they are simply omitted from the entire Equation, then important information which could have been evaluated has not been included. The information that has been gained from this test shows that a certain number of samples reached a certain service life without becoming faulty. The use of such information is called "Sudden Death Testing".

In laboratory tests it is possible to test a number of specimens at the same time on the same apparatus. If one specimen becomes faulty then the others are usually still in working order. The parts which are not faulty still appear in the evaluation, although they were not left to run to the end of their service life. Assume, for example, that the following tests were carried out using three specimens at the same time, all within the same test apparatus. The resulting service lives are shown in Table 1.

Lifetime

Faulty Parts

Part without faults

10

1

2

14

1

2

16

1

2

18

1

2

 

After this the service lives are entered in chronological order, in order to obtain the so-called mid-range or medium (see Table 2).

i

Lifetime

Faulty

1

10

Yes

2

10

No

3

10

No

4

14

Yes

5

14

No

6

14

No

7

16

Yes

8

16

No

9

16

No

10

18

Yes

11

18

No

12

18

No

 

The first faulty part receives the rank number 1. The next two values shall not appear directly in the Weibull diagram, but they will indirectly influence the frequency value of the resulting evaluation. The fault at 14h shall not be ranked number 2, but instead shall be given larger value with a delta value. This is calculated using Equation 18.



The term nNext refers to the quantity of the samples including those which have failed. The calculation required with n = 12 is D = (12+1-1)/(1+9) = 1.2 and  
Rank(i) = Rank(I-1) +
D = 2.2. If the next sample is also faulty then the next rank value takes the previous value plus the then current delta. In this example the next fault will lie at 16h D = (12+1-2.2)/(1+6) = 1.54 and
Rank(i) =  Rank(I-1) +
D = 3.74 etc. The frequency can be calculated using Equation 4 Section “The Weibull Diagram”.



The sudden death method results in a steeper rise on the chart because the observations only include the pure faults (with n = 12). If the results were to include all samples individually tested and all of the faults, then the result would basically be that of the Sudden Death method. The advantage is the considerably shortened test phase. The same method clearly applies for faults in the field in which a certain "vehicle group" (random tests) is observed. In the case of field data certain problems do occur in the area of prognosis.

 

The concrete calculation steps are shown as a flow-chart in the template Weibull_Sudden_Death.vxg.

                    

 

 

Prognosis of faults not yet occurred

In general there tends to be a relatively large variation on the results in field fault calculations with long service lives. This has the following cause : when one examines for example the frequency of a certain fault on the Weibull chart with a service life of X, then a certain sector of the total production will not have reached this service life and will therefore not be included as faulty. A correct summary as to the frequency of this fault at service life X can only be achieved if all of the parts produced have reached this service life. The analysis gets progressively more accurate as the period of time between the construction of the part and the analysis becomes greater. The reason for this is simply that all parts have reached a certain service life. It is however also necessary to obtain the earliest possible prognosis on the field data. This means that it is necessary to devise a method in which a prognosis of faults which have not yet occurred is included. These parts are known as "prognosis parts". The following description details a process in which these "prognosis parts" are defined.

 

It is assumed that the prognosis parts have the same fault likelihood as those parts which have failed before them. If the statistical number of kilometres covered (distribution of service life) is known, then it is relatively easy to calculate the failure probability of the prognosis parts.

 

The service life distribution can be ascertained using the faulty parts if the registration date; date of fault; and service life are known. This can also be ascertained through inquiries. The service life distribution shows how great the percentage of vehicles is which have not reached a certain service life. They are appropriately standardised using service life / month although it can be adapted and re-calculated using any other time span line. In practice it is necessary to observe that this service life distribution is not constant. There is, for example, very little mileage available during the first stages of production vehicle sales although at a later stage this is taken simply from year to year. Furthermore it is necessary to note that the same part reappears in different vehicle types and as part replacements as well as having greatly differing mileage (e.g. taxis drive great distances in their service lifetime) and driving in various countries. Appropriately the service life distribution is set out in two sections. For example :

 

Service life distribution after 1 month :

X1      10.0%             720 km

X2      63.2%             2160 km

X3      90.0%             3700 km

 

At the first "support point X1" 10% of vehicles have not reached the 720 km point. At X2 63.2% have not reached 2160 km etc.

 

This means that for every service life taken, it is possible to calculate the number of vehicles that have not reached this point. Mathematically speaking the reverse function of the Weibull is necessary at this point (see attachment). Using this and the production figures it is possible to calculate the number of prognosis parts.

The prognosis parts are then used to ascertain the percentile for each service life during which there have been faults registered, this is shown on the service life distribution diagram. Using the production figures, only the exact figure is calculated. This is only relevant for the first value (prognosis part at 2000 km). The prognosis parts which follow can now be calculated using the next number of vehicles which have not yet reached the relevant service life, excluding the previous prognosis parts and faulty parts. In this case a negative number of prognosis parts may be the result and this should be replaced with 0.

 

Now a "corrected" failure frequency can be taken from the prognosis parts. This is calculated with Equation 19 for the corrected failure-frequency sum

 



and with Equation 20 for the prognosis parts frequency sum

 

The start value for the beginning of the calculation for i = 0 shall be set to 0. In the case of the example shown above, the corrected failure frequency and/or prognosis line, as shown in Diagram 6, is the result as calculated with a production quantity of 999 units. It is especially noticeable that the corrected failure frequency first becomes useful once the service life is longer. The reason for this is that very few vehicles have reached this point in the service life. The implementation period which equals the observation period has a particular influence on the corrected failure frequency. As already mentioned, the further the observation period lies in the past or if this period is very long, the line of the corrected failure frequencies will always be close to the line of concrete failures. In this case, the corresponding service life of all vehicles has already elapsed and no new prognosis parts arise. Analysis of components should also only be conducted within a closely delimited production period (max. 3 months) as the observation period applies only to one "point" (mean value between the components produced first and last).

In the case of a large number of failures, it is of advantage to form classes referred to the distance covered (mileage). As a result, progression of failures in the Weibull chart is, in the majority of cases, a straight line.

 

A kinked progression (shallow start) occurs over the service life also for the prognosis line. This may be attributed to the fact that the failures occur outside the warranty period and are therefore no longer contained here, is referred to as expired data although there are in reality "failures". As a rule, this statement can be made when the "kink" occurs above 40000 km. In this case, it is very probable that the warranty period has elapsed. If the kink is below 40000 km, it must be assumed that only a certain "assembly" or a limited production batch is affected and thus, despite the higher kilometre reading (mileage), no further failures are to be expected.

 

 

The concrete calculation steps are shown as a flow-chart in the template Weibull_Prognosis.vxg



Determining service life distribution form "defective parts"

 

As described in the introduction, the service life distribution can also be determined from the defective parts data. For this purpose, the following data are required for each defective part:

 

-          Vehicle registration

-          Repair data

-          Kilometre reading (mileage)

 

The "operating time" of the component is determined from the difference from the repair date and vehicle registration. These data are entered in a table together with the distance covered, i.e. kilometre reading (mileage). As service life distribution can be determined only for the same operating periods, the data are immediately standardised to one month, i.e. the service life is divided by the time in operation.

The point of intersection of the adjustment line produced from these data at 10 %, 63.2 % and 90 % frequency (probability) provides the required kilometre values at these points. For this purpose, perpendiculars are drawn at the corresponding frequencies. The determined values can now be adopted directly in the actual Weibull evaluation.

 

See also general basics