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I have the utilization rates of several machines for each week over a year. These differ per week because of the occurrence of machine failures and changes of orders. Meaning that one week a machine could be a bottleneck and the other week not. I want to rank these machines based on the utilization and so determine their criticality. However if I calculate the mean utilization, information gets lost. The same is when I count the events the utilization is bigger than a threshold. For example;

  • machine A has a utilization of 50% and 14 weeks the utilization > 90%
  • machine B has a utilization of 70% and 7 weeks the utilization > 90%
  • machine C has a utilization of 89% and 6 weeks the utilization > 90%

In my opinion machine A is more critical than machine B. So ranking based on a threshold value seems reasonable. However, when comparing machine B and C this is not that clear. Does anyone know a statistical/mathematical method to get a good comparison?

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  • $\begingroup$ could you please clarify your data. For Machine A, is the overall utilization 50% (average over a long time period) & at 14 weeks or over a 14 week period it has > 90% utilization? $\endgroup$
    – Fred
    Jun 3 '15 at 9:57
  • $\begingroup$ Yes. The average utilization over 52 weeks is 50% and of the 52 weeks, 14 weeks have a utilization > 90%. $\endgroup$
    – user78820
    Jun 3 '15 at 10:05
  • $\begingroup$ I don't know if you have the data for your machines, but machine availability with the utilization gave give greater understanding of an individual machine's utilization. If a machine has a high availability but a low utilization then you can ask why. Is it because of no operators, scheduled maintenance, unschedued maint., lack of maint personnel, breakdown, delay in getting parts, different production/processing rates for machines that rely on each other. $\endgroup$
    – Fred
    Jun 3 '15 at 12:00
  • $\begingroup$ Thanks! The reason why I want a ranking: a company has circa 200 machines, with in total 10.000 parts. For each machine needs to be determined how many spare-parts should be on stock such that costs are minimized (holding cost, downtime costs, replenishment costs). To focus in the first place on the most critical machines I need a ranking. Critical means for which machine no availability of parts has the biggest impact. (I know this is part dependent, but that will be analysed on machine level). Thus the cause of a high utilization (breakdowns, processing rates etc.) are not relevant. $\endgroup$
    – user78820
    Jun 3 '15 at 12:18
  • $\begingroup$ However incidents like a power failure, do, but these are taken into consideration. $\endgroup$
    – user78820
    Jun 3 '15 at 12:19
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I don't know of any mathematical or statistical techniques that would help you analyse machine utlization data.

From the additional information you've given in the comments, my understanding is that your aim is the minimize the cost of keeping spare parts for the machines based on machine usage.

The critical factor is going to be the duration of usage for each machine.

Using your example data, you are correct in surmising that Machine A is the critical machine because it was heavily used for 14 weeks of the year, whereas the other two machines were only heavily used for 7 and 6 weeks.

I think your ranking should be based on the expected periods of heavy utilization, with machines being used for the longest period being the critical ones for which spare parts are kept. The overall utilization for the year is irrelevant for your study.

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Measuring utilization by itself is masking some of the information you're attempting to glean from this environment.

From your description, there are at least three cases where a machine may not be put to use:

  1. Machine is broken
  2. Change order has been placed, waiting on re-tooling or equivalent
  3. No work for machine to produce

In addition to tracking overall utilization, I would recommend tracking outages based upon their categories. It's not enough to say "Machine A had a 50% utilization rate" because you don't know why the machine was sitting idle for half of the time.

In other words, tracking utilization is merely tracking the symptoms of the problems within your overall process. Tracking outages will allow you to identify what the problems actually are and address those. For example, by knowing outage rates then you may see that change orders are causing more down time than machine breakages. Or you may see that the machines break too often and are impacting overall productivity.

But you won't be able to glean those insights until you track the individual outage causes.

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  • $\begingroup$ Thanks, but I don't need to have insight in the cause of the utilization. Spare-parts have as function to facilitate the maintenance activities. If a part is critical (i.e. a failed part causes downtime) it needs to be available. The company has currently more than sufficient parts and wants to reduce that amount. However it's impossible to analyse 10.000 parts for criticality. Therefore i have to start my analysis on machine level. Thus i want to select the most critical machine based on several factors; demand of parts, downtime costs and utilization. $\endgroup$
    – user78820
    Jun 4 '15 at 8:19
  • $\begingroup$ If a spare-part is not available, the consequences are more severe for delivery performance of the company, if this is the case for a machine with a high utilization than with a low. Hence I need a ranking of machines to focus on the most critical machine. $\endgroup$
    – user78820
    Jun 4 '15 at 8:19
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Simplest way to study machine utilization is the chart the trends. I used excel to generate three sets of data to approximately match data as specified by the question

  • machine A has a utilization of 50% and 14 weeks the utilization > 90%
  • machine B has a utilization of 70% and 7 weeks the utilization > 90%
  • machine C has a utilization of 89% and 6 weeks the utilization > 90%

Below is trend graph for the set of random data

enter image description here

Following are statistical information for the above set of random data.

  • The averages for random A,B and C data set are: 55,67, and 84
  • The median for random A, B, and C data set are: 60, 72, and 88
  • The standard deviation for random A, B, and C data set are: 28, 32, and 17

Looking at the trend Machine A a drop in utilization as highlighted by Root Cause 1. This type of information can help as drive an investigation. Example:

  • An obvious question would was preventive maintenance (PM) performed around week 13
  • Was there a change in operator at week 13 on machine A
  • Does the machine utilization track power outage

Beside standard deviation, averages and trend analysis, histograms, control charts and bar graph are two other simple but powerful statistical tools that you might want to consider.

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  • $\begingroup$ Thanks, but I don't need to have insight in the cause of the utilization. Spare-parts have as function to facilitate the maintenance activities. If a part is critical (i.e. a failed part causes downtime) it needs to be available. The company has currently more than sufficient parts and wants to reduce that amount. However it's impossible to analyse 10.000 parts for criticality. Therefore i have to start my analysis on machine level. Thus i want to select the most critical machine based on several factors; demand of parts, downtime costs and utilization. $\endgroup$
    – user78820
    Jun 4 '15 at 8:22
  • $\begingroup$ If a spare-part is not available, the consequences are more severe for delivery performance of the company, if this is the case for a machine with a high utilization than with a low. Hence I need a ranking of machines to focus on the most critical machine. $\endgroup$
    – user78820
    Jun 4 '15 at 8:22
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The problem is a multi-criteria decision analysis (MCDA), as I want to rank the machines based on several (available) criteria. With initially the following criteria: downtime costs and utilization. However with utilization there was the following problem: if the events are counted that surpasses a threshold or the average utilization is used, both situations would lead to loss of information. As it is an MCDA, both criteria can be added, thus the criteria are now:

  1. downtime costs per time unit
  2. average utilization per time span
  3. number of events the utilization that surpasses a threshold (e.g. 95%)

As these factors are not directly commensurable and differ in importance, a weighted method is needed. To select the appropriate method 7 guidelines are used (Guitouni and Martel, 1998);

  • Guideline G1: Determine the stakeholders of the decision process. If there are many decision makers (judges), one should think about group decision making methods or group decision support systems (GDSS).
  • Guideline G2: Consider the Decision Maker (DM) `cognition' (DM way of thinking) when choosing a particular preference elucidation mode. If he is more comfortable with pairwise comparisons, why using tradeoffs and vice versa?
  • Guideline G3: Determine the decision problematic pursued by the DM. If the DM wants to get an alternatives ranking, then a ranking method is appropriate, and so on.
  • Guideline G4: Choose the Multi Criteria Analysis Problem (MCAP) that can handle properly the input information available and for which the DM can easily provide the required information; the quality and the quantities of the information are major factors in the choice of the method.
  • Guideline G5: The compensation degree of the MCAP method is an important aspect to consider and to explain to the DM. If he refuses any compensation, then many MCAP will not be considered.
  • Guideline G6: The fundamental hypothesis of the method are to be met (verified), otherwise one should choose another method.
  • Guideline G7: The decision support system coming with the method is an important aspect to be considered when the time comes to choose a MCDA method.

Based on all guidelines except guideline G6, this results in the following suitable methods: Analytic Hierarchy Process (AHP) or Promethee II. However, AHP has the assumption that inner and outer criteria are independent. A correlation test showed that there exists significant correlation between criteria 2 and 3, thus the criteria are not independent. Promethee II is therefore the appropriate method for ranking the machines given my situation.

Guitouni, A., Martel, J.-M., 1998. Tentative guidelines to help choosing an appropriate MCDA method. Eur. J. Oper. Res. 109, 501–521.

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