In this lecture we look at task grouping and interval determination and phasing for the grouped tasks. We also look at the issue of how tasks are worded to avoid ambiguity and provide clarity for the people interpreting the requirements to carry out the tasks. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 1ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 2We have now looked at some basic techniques to calculate a cost rate for each task and to determine an optimum interval. Our methods placed no restriction on what the intervals could be and so it is likely that if you employed these methods for 100s or 1000s of tasks you would end up with a wide distribution of intervals. The tasks all require some level of access to the system being maintained and need to be scheduled to create sensible work packages for the people carrying out the tasks. So whether tasks are grouped or not there will be a need to rationalise the number of permissible task intervals to achieve a practical program of work. I have listed three basic steps 1. Grouping tasks whereappropriate 2. Setting permissible intervals and assigning these to the grouped and remaining standalone tasks. 3. Determining the phase relationship between the cycles for the different tasks ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 3The first step is task grouping There are many factors that may influence whether or how tasks should be grouped. The sub-system the tasks are directed at and the optimum task interval we have calculated play a large role in determining what tasks can be grouped together. Tasks we choose to group will normally be directed at one sub-system and need to have similar intervals if we are not to severely compromise the optimum intervals we calculated. Some other considerations are listed belowthese. •We would normally only group tasks that have the same lead trade •We need to ensure the grouped tasks are achievable in a normal working shift •We may choose to group some tasks such as lubrication across multiple sub-systems. •We generally would only group tasks requiring the same level of system isolation. •The same goes for special set-up requirements. I am thinking here of things such as Confined space Working at heights Gas or other hazardous environment The Position the equipment has to be in to carry out the task The final point I have listed is the level of maintenance. I explain what I mean by this on the next slide. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 4I have listed three levels of maintenance Operational Intermediate level and Deep level If you group tasks that require different levels for their execution they will have to be carried out at the deepest level which may not be a good use of time and resource. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 5On this slide I have suggested that the additional data fields could be tabulated in the manner we used for the FMECA. Our end point for the first step is determining what tasks can be grouped and assigning these to a package or task list. I realise that this could be an oversimplification as the way individual tasks are handled in the MMS is dependent on the design of the system. Some systems may permit a dynamic package where individual tasks can have different intervals and the task package differs each time it is scheduled. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 6We have looked at criteria for grouping tasks. The 2nd step in establishing an efficient schedule of preventive tasks involves determining allowable task intervals and assigning an interval value to each package of grouped tasks and any remaining stand-alone tasks. We only consider here the tasks that require a system shut-down. Tasks that can be completed with the system in operation can be scheduled at nearly any interval. Determining the range of allowable intervals needs to be done in conjunction with the 1st step of grouping tasks. We want to be able to assign an interval to each package that is close to the mean of the individual tasks included in the package. This will be easier to achieve if the original grouping is done with some idea of how many intervals we will allow. The starting point is in deciding the shortest interval that will be allowed. This sets the interval at which the system must be stopped and all tasks must then be set to occur at a multiple of this interval. The first consideration is whether there is time at regular intervals when the system is not required by the operators. If there is it is preferable that the shortest task interval is set by these non-operating windows. If you can’t do this, the savings generated by the preventive maintenance tasks must bear the cost of stopping the system. If the periods when the system is not required or is at very low demand are very frequent the base interval may actually be set as a multiple of the interval between these periods. When we calculated the cost rate for each individual task there was a term for the cost of preventive renewal. (Cm) Generally this cannot include the loss of contribution margin associated with stopping the system on a planned basis because the number of tasks sharing this loss will not be known. The cost rate for shutting the system down at a particular interval needs to be added to the cost rates for component renewal to determine an optimum system shutdown interval. We will look at a simple example of this in these notes. However on a large scale determining an optimum system shutdown interval by consideration of the cost rate for each task in the program would be very difficult. In general this will not be practical and the exercise simplifies to one of determining the maximum system shutdown interval that will still allow the majority of tasks to be completed within a suitable tolerance band. This may be governed by a few high criticality tasks on a short interval or a large number of high frequency tasks of lower criticality that in summation have high consequence One approach to this is to prepare a histogram of proposed task intervals and starting at the most frequent consider the level of uncertainty in the interval calculation. We want to gauge the tolerance band for the most frequent tasks and from this the maximum interval that can be selected that will still allow the majority of these tasks to be completed within their tolerance band. Another consideration is the Volume of work. – the annual predicted maintenance workload and how many trades people is it practical to employ on any one stoppage. This may dictate the minimum number of stoppages required per year to actually complete the planned workload. Allowing a task to take any multiple of the base can create scheduling issues and for this reason consideration also has to be given to what multiples of the base interval will be permitted. We will look at this after the next class exercise ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 7This diagram from the UKMOD Standard shows an initial distribution of the cumulative task duration at each of the proposed intervals with the tasks separated by maintenance level. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 8This slide shows the rationale proposed by the UKMOD standard for grouping tasks with different proposed intervals into a single package. They start with the tasks requiring deep level system access. The interval for tasks with economic consequences can be reduced or increased to achieve a minimum cost overall schedule but the intervals of tasks with safety consequences can only be reduced. They use the same approach for the tasks requiring lower levels of system access but seek to synchronise these with the deep level package intervals. Their diagram here is a simplification. It shows a single cluster of task intervals. If this cluster defines the lowest package interval then we need to ensure that other tasks requiring deep level access can be satisfactorily grouped at an interval that is a multiple of this package interval. For fixed plant the main difference between a deep level and an intermediate level of maintenance will be the duration of system outage required. In this case it is more likely that you would start with packaging the intermediate level tasks. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 9I have included this slide which is part of diagram from Tony Kelly’s book because Kelly provides a different perspective to the standards focussing on military hardware. Tony Kelly firstly identifies the tasks that can be done with the system on-line and then those that can be done in windows when the system is not needed and finally those where the system is shutdown specifically to carry out the work. You can obtain more detail on each of these process steps in the E-reading extract from his book. His bottom up approach is similar to the MILSTD approach to packaging but his top down approach covers factors relevant to industrial plant and not covered in the MILSTDs. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 10When we calculate the cost rate for each individual task there is a term for the cost of preventive renewal. (Cm) Generally this cannot include the loss of contribution margin associated with stopping the system on a planned basis because the number of tasks sharing this loss will not be known. The cost rate for shutting the system down at a particular interval needs to be added to the cost rates for component renewal to determine an optimum system shutdown interval. In this simple example it is assumed that planned system stoppage cost is the same regardless of the number of tasks undertaken in the stoppage. The cost variable Cm is taken to be the renewal cost for the component and the system outage cost is added separately. Cf is calculated as the sum of the cost of an unplanned system stoppage and the cost of the component renewal. It is assumed that these tasks can only be done with the system stopped. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 11The cost rates for the age renewals and condition based renewals have been calculated and are shown in the table on this slide and the next slide. The reliability of the first 4 components assumed Weibull distributions with the parameters shown below. Weibull Parameters Comp 1 Comp 2 Comp 3 Comp 4 Shape 3.50 3.40 3.50 3.40 Scale 8.00 13.00 8.00 18.00 Location 3.30 5.02 12.00 35.00 Mean 10.5 16.7 19.2 51.2 ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 12ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 13This table shows the calculation of the total cost associated with each of a range of potential shutdown intervals starting with 1 week and extending to 15 weeks. The proposed interval for each task is based on the optimum interval for each task. If the proposed system outage interval is greater than the task optimum the task interval is set to the system outage interval. If the optimum is less than the proposed system outage interval the task interval is set at (Optimum interval / system outage interval) rounded to the nearest integer and multiplied by the system outage interval. For example the optimum interval for task 1 is 6 weeks. If the system is shutdown every 4 weeks the task interval is set at 6/4 =1.5 which rounded to 2 multiplied by 4 equals 8 weeks. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 14The result is hardly surprising and it indicates that focussing on the few high criticality tasks on a short interval is all that is needed. In this case just considering the planned system costs with task 1 would have given the same answer. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 15The individual task intervals must be a multiple of the base interval. We look here at what this means for the cycle time for the whole program. In the example I give where you have intervals given by base multipliers of 5,6,7,and 9 compared to 4,6,and 8. 5,6,7,9, LCM=630 4,6,8, LCM = 24 In the first case if the base was 2 weeks and intervals of 10, 12 14 and 18 were allowed the overall time before the cycle repeated would be 1260 weeks (more than 24 years) compared to 48 weeks for cycle repeat with the second example. So a fairly small adjustment to allowable intervals can have a significant effect on the program cycle time and can greatly simplify the scheduling pattern. This in turn makes it easier to adjust task phasing and control peak labour demand. Wikipedia gives a simple method for calculating LCM by dividing by primes. Refer Wikipedia – Least Common Multiple lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b. Since it is a multiple, it can be divided by a and b without a remainder A method using a table This method works for any number of factors. You begin by listing all of the numbers vertically in a table like this (We can try 4, 7, 12, 21, and 42): 47 12 21 42 The process begins by dividing all of the factors by 2. If any of them divide evenly, write 2 at the top of the table and the result of division by 2 of each factor in the space to the right of each factor and below the 2. If they do not divide evenly, just rewrite the number again. If 2 does not divide evenly into any of the numbers, try 3. Now, multiply the numbers on the top and you have the LCM. In this case, it is 2 × 2 × 3 × 7 = 84. This is a variation on Euclid's algorithm, as common factors are essentially divided out along the way of dividing all of the numbers at once by each successive factor. You will get to the LCM the quickest if you use prime numbers and start from the lowest prime, 2. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 16 x 2 2 3 7 4 2 1 1 1 7 7 7 7 1 12 6 3 1 1 21 21 21 7 1 42 21 21 7 1Once you have the base interval you can work backwards from the longest interval to calculate allowable task intervals. You do this by finding the integer factors of the longest interval that are multiples of the base. Note the longest interval probably has the greatest level of uncertainty in terms of the reliability estimates used in its calculation so it may be possible to adjust this to ensure a reasonable range of other intervals ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 17ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 18Finally the 3rd step in our process. Setting the phase relationship between the cycles for each package to smooth the labour demand. Our ability to do this depends in part on the intervals that we have allowed for each package. The key is that a task that occurs at an interval that is an integer multiple of that of another task will stay out of phase with that tasks if it they are started out of phase. I have illustrated this on the next slide. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 19In this example we have a base interval of 4 weeks and allowable task intervals of 4, 8, 12, 24, 48 and 96 weeks. The program cycle is determined by the lowest common multiple of the package intervals which is 96 weeks. If each successive package interval in the cycle is an integer multiple of the previous intervals then the packages can be scheduled to stay out of phase. Compare the second program with first. 24, 48 and 96 week interval packages can be kept out of phase with each other and with 8 and 12 week interval packages. 12 week packages cannot be kept out of phase with 8 week. It is possible to divide the longer interval packages and schedule them apart. Eg Two 8 week packages could be created with one scheduled every 4 weeks. Adjusting the phase timing of each package can have significant effect on labour demand smoothing. In the example above offsetting the packages reduced the std deviation on the number of packages scheduled each outage from 1.33 to 0.45. This advantage may be discounted if you want the packages to coincide. For instance the 12 and 24 week packages might both have the same special set up requirements and are better coincided. There is no single answer for the best program. There are also other issues to consider such as when tasks are triggered by different measures of usage (eg weeks versus hours of operation) Note if you are referring to MILSTD2173 in their terminology this example would have a Phase Cycle 96 weeks Phase Interval 4 weeks And it would be a 24 phase program ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 20The second part of this lecture is on task description. First point is that we want to avoid ambiguity. Hopefully from the analysis we have conducted we have a clear intention for the task. We need to word the task in a manner that the intention is accurately conveyed ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 21The standard gives definitions of key terms. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 22In this example the words check and inspect appear to be used interchangeably. The instructions are also vague. The use of the word “etcetera” is not helpful. It makes the tasks open ended. They appear to have been developed without any knowledge of likely failure modes. They would sit better with a general inspection rather that an inspection associated with condition based renewal. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 23ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 24I explore here what it means to conclude the condition of an item is OK on an inspection. This assumes the system has regular shutdowns in which repairs can occur on a planned basis. It also assumes that the inspection warning time is greater than the interval between repair windows. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 25This table gives a suggestion for a standard response for a condition check. ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 26ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 27ENGG960 P. Gordon, R. Dwight & K. El-Akruti UOW 28