Considering six sigma in a TPM schedule

The best and recommended way to establish the frequency of preventive maintenance of a machine is to study first its mean time between failure, MTBF.  The frequency of maintenance should ideally be less than the determined MTBF. For instance if a machine fails every 20 days on the average, it would be recommended to set a preventive maintenance frequency at 15 days.

How do we determine the number of days ahead for maintenance schedule before failure? MTBF is surely a Total Productive Maintenance,TPM,  indicator but because it calculates a mean than in a six sigma environment it must also calculate the standard deviation associated with the mean, so that we can speak of central tendency of failures.  So if we operate our TPM management within the quantitative culture of six sigma, the MTBF indicator would be replace by a CTBF, central tendency of failures, indicator and it would be expressed as: central tendency of failures of 20 days with 2.23 days deviation. Therefore establishing how many days ahead of the mean time between failure to set the frequency of maintenance depends on the variation in time of the failure, that is the standard deviation of failures.  We calculate first the coefficient of variation which is standard deviation divided by mean and thus set this percentage below the mean as the calculated frequency of maintenance. Again if our MTBF is 20 days, with a standard deviation of 2.236 days, the coefficient of variation would then be 11.18% and maintenance should be scheduled by calculation every 17 days, ideally every 15 days to use multiple or submultiple of months.

However many times our MTBF calculations falls in the hours or event minutes range,  mean time between failures of 6 hours for instance. So how do we set a maintenance schedule below 6 hours? It wouldn’t make any sense. When that happens it is because the definition of MTBF depends on the definition of what is considered a failure in your system. In general failures are considered to be those conditions which place the system completely out of service and into a need of repair. There is a difference between failures with loss of function and failures with reduced function. Failures which occur that can be left or maintained in an unrepaired condition (failures with reduced function), and do not place the system out of service, are not considered failures under this definition of MTBF according to “Defining failure: what is MTTR, MTTF, MTBF” by Stephen Foskett, which makes complete sense.  

If the system fails and can be repaired, thus there exist as well a second indicator in TPM which is defined as MTTR, mean time to repair, or combined with six sigma culture, CTTR central tendency of repairs. This is particularly important in identifying the types of stoppage, failure mode, to consider in defining the maintenance scope. The first question is: does the failure or stoppage affect or not the process cycle efficiency and/or productivity. As a product goes under several processes in the value stream before it is ready for delivery, it is fundamental to identify the bottleneck process in the value stream, because if MTTR or CTTR is below the bottleneck time than the failure mode does not necessarily affect. Therefore in recording failures time and mode, it is critical to record as well their impact (affect or not affect) which means that prior to this there exist a value stream where process cycle time are shown and bottleneck known.


Once impact is recorded by failure mode it is then easy to seek correlation between failure modes and impact (affect/not affect) by running a Chi square hypothesis test to determine dependence or independence between modes and impact.

• If independent it means that it does not matter if the failure mode affect or not it must be considered in the maintenance program as it is unpredictable: in that occurrence it may no affect but in the next it may. Therefore it is a topic that must be included in the activities to perform during the next maintenance and at every maintenance schedule.

• If dependent, one more test must be perform.  The Cramer's contingency coefficient which is a method to provide an easier measure of strength of association. This means that failure modes with a high Cramer coefficient that do not affect productivity and/or process cycle efficiency may not have a short to medium rate of frequency of maintenance. Notice that it is not said that they should be ignored. Not at all. A failure is a failure and as such must  e treated in a preventive way. What is said is that for those not affecting the frequency of maintenance can be much higher.  

In summary when a lean six sigma is in effect, as far as TPM is concerned:

1. MTBF and MTTR should be replaced by CTBF and CTTR, respectively central tendency between failures or simply central tendency of failures and central tendency to repair or simple central tendency of repairs.
2. In collecting data for those indicators, it is critical to identify if the failure mode has an impact or not on productivity and/or process cycle efficiency.
3. To state if there is impact or no impact per failure mode, it is fundamental to have a prior value stream map with identified bottleneck process
4. To determine if failure modes are correlated to impact, it is necessary to run a chi square test and Cramer coefficient in case of dependence
5. Failure modes independent of their impact shall undergo a schedule calculated to be below MTBF
6. Impact dependent of the failure modes required the calculation of their strength of association, and if high then failure modes can undergo a longer time period on the schedule.

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