Monitoring Belt Conveyor Performed by CUSUM Control Method

J. Bhattacharya, India

Courtesy : Trans Tech Publications - Bulk Solids Handling Journal

1. Introduction

CUSUM control chart, a popular quality control tool can be effectively used in monitoring in-service reliability of a belt conveyor. One of the established criteria of determining operational or in-service reliability is to obtain time between failures (TBF) or the mean time between failures (MTBF). MTBF is the mean of samples of time between start of operation to the stop in the event of a failure for each specified component of an equipment. Obviously, the increase in TBF or MTBF means that the system performance is improving or vice-versa.

2. CUSUM Control Scheme

The basic approach in this form of scheme is to compare a charted quantity with a reference or pre-defined value. The reference value will usually be the nominal, or target value for the quantity [1, 2], if the ith measurement of the quantity is denoted xi and the reference value as T, they are subtracted, giving (xi - T). The cumulating sum, CUSUM is then calculated by adding this value to the sum of all the previous values, i.e.

(xi - T)

Then if xi is actually close to T, the CUSUM will tend to remain close to zero. But if it is different the CUSUM will rapidly rise from zero or go below if that is the arrangement between xi and T. A similar CUSUM model can be effectively used to study the in-service reliability estimates of a belt conveyor.

2.1 Methodology

It is desirable in the beginning to determine the number of possible failures in a belt conveying system. It is a general practice to describe each task resulting from any belt conveyor break-down in action codes. The action codes specify the basic operations for the repair and not the overall maintenance tasks that were carried out along with the action code failure. Consequently more than one action code may be required to describe an individual maintenance task. But to demonstrate the aspects of CUSUM all tasks leading to a single repair were recorded in one action code, e.g., each maintenance task of removal, refitting, clearing or oiling of one unified component was recorded in a single code.

The total time required to complete each maintenance task was also calculated by summing up the time consumed in each task. An example sheet of types of failures encountered in belt conveying system may be observed in Table 1. It must also be appreciated, however, that the action codes available to the maintainer may run into numbers totaling several thousands but cannot be provided with accurate descriptions [3].

This model here is dependent on the assumption that a repair is made only at a failure of a certain part, not to an event or fault initiation. For example, squeaking of the belt conveyor may lead to a replacement but shall not be considered to be a reliability significant failure as it may be ignored at first.

Table 1: Location of various types of faults in a belt conveying system in the study period

3. Reliability Significant Failures

All the appropriate listing of failures and repairs were made in the data base from job reports. Failures having discernible repair times were codified. by the action codes. Depending upon the operational experience of a mine maintenance information compiled during this period, principal types of repair work necessary for certain type of failures were identified and depending upon that the mean time to repair has been codified into a reliability significant factor. So in principle the reliability significant factor becomes an indicator of how much repair time should be presumed should there be any particular failure. Failures involving exceptionally long repair time will have significant factor as unity and other failures will be graded relatively to lesser fractions according to their mean time of repair. The total number of reliability significant failures occurring in a particular period is thus estimated by multiplying the appropriate significant factor by the number of action code entries of each type occurring in that period and summing overall relevant action code failures' significant factors. So in real terms all the major and minor failures including renewals occurring in a specified period of time will be converted into a number of reliability significant failures of unity. The significant factors, then estimated are capable of predicting number of reliability significant failures in the unit of failures having significant factor as unity. Now the predicted value of reliability significant failures can be compared with the actual value of significant failures that would be obtained after the repair has already been done. This will be possible by rating the reported repair time against unity or as reported in the case where against a reported active repair time significant factors are assigned. Proceeding as in the case of prediction, actual significant failures can also be calculated. Tables 2 and 3 enumerate the procedures for calculation of actual and predicted values from a set of failure data against action code entries.

Table 2: Determination of reliability significant failures
Table 3: Belt conveying system failure data for the month

4. Reliability Estimation by CUSUM Plot

A CUSUM plot of MTBF against operational time was drawn for each subsystem using the results of the detailed reliability analysis of the trial. The CUSUM plot was centered on target MTBFs estimated from the overall run time and the total number of reliability significant failures occurring in the trial (Table 4). From earlier discussions the actual CUSUM ordinate plotted in Fig. 1 is given by

Table 4: Determination of overall MTBF of the belt conveying system
(Tj - Nj . average MTBF)

Tj = total run time during jth month
Nj = number of reliability significant failures occurring during jth month
Average MTBF = Overall average MTBF.

Similarly the predicted CUSUM ordinate will be prepared based on MTBF values calculated from the maintenance data. The CUSUM ordinates are plotted in such a case as follows:

[Tj - (
nij . ki) . average MTBF]

Tj = total run time during jth month
Nj = number of entries of action code i during jth month
ki = reliability significant factor for action code type i
Average MTBF = Overall average MTBF.
The actual and predicted CUSUM ordinates are both given in Fig. 1 for the corresponding values in Table 5 for the period extending seven months.

Fig. 1: Belt conveyor system CUSUM analysis ---- predicted CUSUM line; ____ actual CUSUM line
Table 5: Belt conveying system failure data and reliability evaluation

5. Observations and Discussion

Observing the actual and the predicted values in the CUSUM plots certain points can be brought to notice.

  • The up slopes of the plot represent an improvement in the performance of the equipment whereas the down slopes represent the degradation in the performance.

  • The slopes of the predicted and actual CUSUM lines in most of the places nearly look the same but the values have difference in co-ordinates. This is due to certain errors creeping into fixing the ratings and overall MTBF values, possibly in both the predicted and actual cases.

  • It may be observed from Table 5 that the actual and predicted numbers of significant failures are nearly the same but they show considerable differences in CUSUM values as in Table 5. This is due to CUSUM technique itself where the difference is summed up continuously.

6. Decision Criteria for CUSUM Chart

Although the CUSUM chart gives a much clearer indication of changes than a conventional control chart, there is still a need for objective decision criteria where the slope of the chart needs to be monitored rather than the vertical position of plotted points. The most widely used method is known as the '5-10-10' mask [2], where H in Fig. 2 is set at five times standard deviations of the plotted CUSUM value, and the slope of the sides of the mask is set at 0.5 standard deviations per plotting interval, i.e., calendar months here. Thus, at a position ten plotting intervals to the left of the 'vertex' of the mask, the sides of the mask are [5 + (0.5 x 10)] = 10 standards deviations either side of the central line. The details of the mask are given in Fig. 2. In use, the vertex of the mask is placed on the last plotted point, with the central line horizontal. If any of the previous plot intersects the sides of the mask, this calls for an immediate treatment, if required. This is illustrated in Fig. 3.

Fig. 2: General form of decision mask
Fig. 3: Use of decision mask; (a) no decision; (b) upward change; (c) downward change [2]

7. Conclusions

The proposed CUSUM chart technique offers certain advantages:

  • The procedure is simple and Can be easily understood by persons with little background in mathematics.

  • While the management should have the objective of keeping the CUSUM co-ordinates above or equal to zero CUSUM line the negative values would represent at the end of a period how much more has to be achieved to attain a desired level of performance.

  • The most important aspect in the technique is to fix the proper rating against the correct description of a breakdown leading to repair or renewal. Obviously, it will take rigorous cross-checking of the results obtained in the initial trials through reiterative measures. A software support will be necessary if manual handling of data becomes difficult.

  • Last but not least, the CUSUM chart is an illustrative technique which displays the status of performance of the equipment in a period of time. Thus, it can be used as a tool in overall decision making related to performance, effectiveness of repair, spare quality and inventory etc.


  1. BISSEL, A.F.: CUSUM Techniques for Quality Control; Institute of Statisticians, London, 1984.

  2. BS 5703: Guide to Data Analysis and Quality Control Using COSUM; Part 1-4, 1980-82, BSI, U.K.

  3. ENGLISH, C.: In-Service Reliability estimates from Maintenance Data; Reliability Engineering and Systems Safety, Vol. 21 (1988), pp. 163-173.

Dr. Jayanta Bhattacharya
Indian Institute of Technology, Dept. of Mining Engineering,
Kharagpur 721302, West Bengal, India.
Tel.: +91 32 22 44 83
Fax: +91 32 22 23 03