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Analysis of repair strategies for automatic assembly systems.


The quality of products manufactured by automatic assembly systems (AASs) are subject to the accuracy of the operations of workstations and the quality of assembly components. A finished product may not comply to the specification due to defective components or inaccurate assembly operations. To ensure that a finished product conforms to the manufacturing specifications, repair and inspections stations are installed to detect and repair defective products. When a defective product is detected, it can be repaired or reworked on line and sent back to the inspection station again until all the manufacturing specifications are met [ILLUSTRATION FOR FIGURE 1 OMITTED]. Alternatively, the defective product can be sent to the next downstream station after it is repaired and on reinspection will be processed again [ILLUSTRATION FOR FIGURE 2 OMITTED]. Although online repair and reinspection is generally preferable to rework and off-line inspection, the feedback situation sometimes is unfeasible from a material handling viewpoint[1]. Additionally, with a high defective rate, the online inspection station can become the bottleneck which can significantly lower productivity of the whole system. Since repairing a product may require very costly automatic machines, predictive models for estimating the performance of AASs with different repair strategies are very valuable for design engineers to perform cost-benefit analysis of automation. In particular, these models can be beneficial to manufacturing plants in Hong Kong or some other South-east Asia countries which are upgrading the quality of their products by automation.

We are interested in the closed-loop repair and inspection systems, where a finite number of pallets are installed to circulate between the workstations. Both online and offline inspection strategies will be investigated. Other factors considered in this paper which affect the throughput of the systems include: the buffer units installed between two adjacent workstations, the repair time of jammed workstations, the defect rate of assembly components, the number of the repair loops inserted and the number of pallets circulating in the assembly system.

In this paper, an example is given in which a repair and inspection station is installed at the end of the assembly system in order to study the effect of different repairing strategies.

A discrete event simulation model was built for the study and is described in the following section. The factorial experiments were carried out to analyse the performance of the system as a function of the various factors mentioned. The technique used in our study has been described previously by Buzacott and Hanifin[2] and Law[3,4] who analysed the effects of different parameters by applying experimental design techniques to simulation results. Some preliminary studies of the performance characteristics of AAS with repair loops have been presented by the authors[5,6]. However, the results are limited to the applications on AASs with online repair loops only. This paper extends those results to systems with offline repair systems and provides a deeper understanding of the effects of significant design factors on the performance of automatic assembly systems with repair loops. Predictive equations for both online and offline strategy are developed.

Model description

A discrete event simulation model written in Pascal was developed to study the behaviour of the system under various configurations (i.e. two different repair strategies at different levels of the design factors). In the system under investigation, workstations are arranged in series with the inspection workstation attached at the end of it. However, additional inspection systems can be installed when more inspection operations are required to test the quality of a product. If an online repair station is installed, products which do not pass the inspection test will be sent to the repair station as many times as necessary until the quality of the products conform to the manufacturing specifications. However, if offline repair strategy is applied, products which do not pass the inspection test will be sent offline for repairing and inspection. Once, the products have met the manufacturing specifications, they will be sent to the next downstream station without going back to the inspection station again. Thus, the quality of the products must have been met before leaving the system. Figures 1 and 2 show the structure of the systems under investigation.

Performance characteristics

Under normal operation, each station can be in one of the four following states:

(1) Idle - when no pallet is available for immediate processing.

(2) Jammed - when defective assemblies (components) are encountered.

(3) Force down - when the downstream buffer units are full and consequently a completed assembly cannot be released.

(4) Busy - when the station is processing a normal (non-defective) assembly.

These four states can be classified into two types, namely, productive and non-productive states. States 1 through 3 are classified as non-productive since a workstation cannot operate on any normal assemblies when it is in one of these three states. Therefore, the productivity of the system increases or decreases as the duration a workstation is in productive or non-productive state(s) increases or decreases.


The following assumptions are given:

* Priorities. When a repair station returns a pallet with a fixed product back to the main stream, it may happen that a pallet arrives at the same inspection station simultaneously. Under this condition, priority will be given to the pallet from the repair station.

* Process characteristics of the workstations. The assembly system is balanced. That is, every workstation shares the same mean processing time and distribution.

* Breakdown characteristics of the workstations. The only cause of breakdown of a workstation is the jamming of a defective assembly, and the probability of encountering a defective assembly is the same for all the workstations.

* Repair characteristics of workstations. The repair time of workstations follows a geometric distribution and it takes at least one unit time to clear the defective assembly which causes the jamming of a workstation.

* Transport time for the pallets. The unit transport time is defined as the time required for a free running assembly to travel one buffer space and it is constant.

* System capacity. There are sufficient spaces for the last workstation to release its final product. Also, assemblies are always available to feed the workstations. Consequently, the last station will never be blocked and the first station will never be starved.

The experiment

Input parameter

To study the performance characteristics of the system, a full [2.sup.7] factorial statistical experimental design[7] was used to analyse the simulation results based on the following seven control variables:

R = average time to clear a jam (repair time); D = percentage of defective assemblies encountered; S = processing time of each station; B = buffer size; P = pallet ratio; L = type of repair strategy; N = total number of repair stations.

The length of each run was 22,000 time units. Data collected from the first 2,000 time units were discarded to establish the steady state of the system. Each of the 128 conditions was replicated five times. Different random seeds were used for different experimental conditions and each replication.


Two different levels for each factor were chosen carefully to represent typical system operating conditions. For instance, the buffer size was set equal to two or five. These two levels were chosen to represent the range of the buffer size in a typical automatic assembly system. The high and low levels of each factor chosen are summarized in Table I.


Since the total simulation time is 20,000 and the process time is five, the maximum output is equal to 20,000/(5 + 1) = 3,333 products, which is the total steady state simulation time/(processing time of station 1 + 1 unit time for transferring the pallet out of the station). This theoretical output will be considered as a base line result to be compared with the results obtained by using different combinations of levels according to the [2.sup.7] factorial design.
Table I. Values of the high/low levels

             p(a)   D(b)   B(c)   R(c)   S(c)     L       N

Low          0.25     1      2      5      5    online    1
High         0.75    10      5     25     10    offline   2

Note: a = total buffer size; b = percentage; c = time units


By making use of the Yates' algorithm[4], the estimated main effect and the interaction effects were obtained. The order of significance based on the absolute effect on the number of total products produced within the designed region is summarized in Table II.

The statistical results indicate that the main effects of the factors S, P, D, B, R chosen within the design region are significant at the 99 per cent level of confidence. In other words, all these factors mentioned can impose statistically significant impact on the productivity of the system.
Table II. Summary of importance of effects within the design

                Single repair loop        Double repair loop
              Estimated    Order of     Estimated     Order of
Factors       effects     importance     effects     importance

S               -434           1            445           1
P                311           2            274           2
D               -211           3           -230           3
B                200           4            183           4
R               -178           5           -181           5
PB              -165           6           -143           6
PS              -123           7           -111           7
RD              -102           8           -101           8
N                 23           -             34           -
L                  7           -              9           -

In terms of total products produced, the duration of the processing cycle of the system appears to be the most significant factor among the seven chosen factors. By changing this factor from five unit time to ten unit time, the total products produced is decreased by more than 13 per cent. However, the number of repair loops installed (N) and the repair strategy used (L) do not appear to have a significant impact on the productivity.

One of the main difficulties in analysing the productivity of an automatic assembly system is due to the interaction of different factors. Table II shows that P x B, P x S and D x R can significantly affect the productivity of an automatic assembly system. This suggests that these factors involved are highly interactive; thus one must be cautious not to interpret them individually or separately. We will discuss these effects later.

So far, we have only analysed the impact of each factor based on its absolute impact on the productivity. However, it is also essential to know the rate of change in productivity with respect to each factor in order to select the best system configuration. Table III shows the percentage of change in the number of completed products per unit change of each factor. In terms of the rate of change in productivity, S (process time) is the most important factor (Table III). More importantly, it shows that the decreasing rate in productivity with respect to defective percentage depends on repair strategy.


Experiment with factor levels

In the previous section, we can only conclude whether a factor has a statistically significant impact. To get further insights into the behaviour of the systems, more levels of each factor have to be chosen within the previous design region for analysis. In particular, we are interested in determining whether the response (productivity) is linearly or non-linearly dependent on the factors. Also, we want to know the relationships between the repair strategies and the factors under investigation.

Three additional levels were chosen for both factor R and D to study their behaviour in detail since they are the factors that are interactive and can behave differently under different repair strategies (Tables II and III). One additional level is chosen for the rest of the factors for further investigation. Levels chosen for each factor are summarized in Table IV.
Table IV. Summary of levels of different factors

Factor        (+)      (0)      (-)

R(a)           5       10        15      20     25
D(b)           1        3         5       7      9
S(a)           5        7        10       -      -
B              2        4         6       -      -
P             0.25     0.5       0.75     -      -


a = time unites
b = percentage

Effect of service time

Service time is defined as the processing time for an assembly at a station. In our system, every pallet must pass through all workstations and an inspection station. If defects are found on a product, the pallet carrying the defective product will be sent to the repair station. As the service time at each station increases, pallets will have to stay at the workstations longer and hence reduce the overall productivity. Figure 3 shows that the productivity decreases linearly as the service time increases. However, it shows no significant impact on productivity when different repair strategies are used.

Effect of the repair time

Similarly, productivity appears to decrease linearly as the repair time increases [ILLUSTRATION FOR FIGURE 4 OMITTED]. This again can be explained. As the jam time increases, more assemblies will be accumulated at the downstream buffer units and in turn increase the forced down occurrences. Hence, the time for a workstation to be in a non-productive state increases and significantly decreases the overall productivity. Unlike the previous case, the two repair strategies do not appear to have different effects on productivity as repair time increases.

Effect of defective assemblies

Productivity appears to decrease linearly as the percentage of defective assemblies increases. This phenomenon is quite consistent with our intuition. As the defective assemblies increase, the chance of accumulating assemblies at the buffer units also increases. Hence, the occurrence of force down increases and decreases the overall productivity [ILLUSTRATION FOR FIGURE 5 OMITTED]. Additionally, the decreasing rate of productivity of online repair strategy is relatively greater than that of offline repair strategy. The difference in productivity of the repair strategies increases as the defective percentage increases. The rate of change in productivity with respect to defective percentage for online and offline are -4.42 per cent and -2.86 per cent respectively when two repair loops are installed. In other words, offline repair strategy may be worth using when a high defective percentage in assemblies is encountered.

Effect of pallet ratio

Pallet ratio is defined as:

[the total number of pallets/(total buffer units + total number of workstations)].

The relationship between the pallet ratio and the productivity of the system appears to be a convex function. In other words, the productivity increases as pallet ratio increases and decreases after the peak productivity point has been reached [ILLUSTRATION FOR FIGURE 6 OMITTED].

The effect of the pallet ratio is particular important to closed-loop automatic assembly systems. If too few pallets circulate within the system, workstations will have a high percentage of starving time even if the occurrences of force downs can be reduced. On the other hand, if too many pallets are installed, the probability of encountering force downs can be significantly increased even if the starving time may be reduced. Since the cost of pallets is not trivial and the total number of pallets installed can significantly affect the overall performance of the system, it is very critical for an engineer to have a good estimation for the optimal number of pallets.

Figure 6 shows that the impact of pallet ratio on productivity behaves consistently no matter if online or offline repair strategy is used. However, it appears that the offline repair strategy is slightly more productive when high pallet ratio is used. In other words, it may be more beneficial to apply offline repair strategy when a high pallet ratio number is used.

Effect of the buffer size

The function of the buffer units is to reduce the occurrences of force down. In other words, they help to decouple the workstations. From the experimental results, it suggests that the productivity increases as more buffer units are installed. However, the marginal effectiveness diminishes when their size increases [ILLUSTRATION FOR FIGURE 7 OMITTED].

This phenomenon can also be explained. As more buffer units are installed among the workstations, the force down occurrences can be reduced. However, when the number of the buffer units installed between two workstations exceed the total number of the pallets (the saturation point), force downs can no longer happen. Hence, adding more buffer units cannot further improve the productivity. Moreover, increasing buffer units means increasing transport time of pallets and, consequently, decreasing the efficiency of the system.

Effect of the repair loops

Our analysis suggests that productivity remains the same as the number of repair loops is increased from one to two [ILLUSTRATION FOR FIGURE 4 OMITTED]. However, more detailed study on the effect of repair loops under different industrial environments has been done by the authors[5,6].

Interaction effects

From the simulation results, three important interactive effects have been identified. They are: P x B, P x S and D x R. In this section, we will discuss why these factors are interactive.

Interaction between pallet ratio and buffer size

When the pallet ratio is at high levels (0.5 and 0.75), a jamming at any station can cause the whole system to be forced down in a very short time. That is, the buffer units cannot decouple the jamming effect of a station and hence does not improve the overall productivity of a system. However, when the pallet ratio is at 0.25, a station can perform normally even when a downstream station is jammed if sufficient buffer units are installed to decouple the jamming effect. Under this condition, the duration of a station in normal state can be increased. Thus, the productivity can be improved significantly by adding more buffer units. Figure 8 shows that when the pallet ratio is at levels 0.5 and 0.75, productivity remains almost the same. However, when the pallet ratio is at 0.25, productivity increases as the buffer size increases.

Interaction between pallet ratio and service time

When the pallet number increases up to the optimal range, the utilization rates of each station are near their maximum and hence adding more pallets will not further improve the productivity. However, when the pallet ratio is below the optimal range, an increase in the pallet number can significantly reduce the idle time of each station and, thus, the productivity can be improved significantly.

From Figure 9, it appears that there is no significant improvement in productivity when the pallet ratio is increased from 0.5 to 0.75 for both a low level and a high level service time. However, when the pallet ratio is increased from 0.25 to 0.5, the productivity increases significantly. Also, it shows that the increase in productivity at a low level service time is more significant than that at a high level service time.

Interaction between defective percentage and repair time

When a defective assembly is encountered by a station or detected by an inspection station, it takes time to clear an assembly or repair a defective product. So, the longer the jam time, the less productive is the station. Therefore, the impact of the defective percentage is closely related to the mean time to clear a jam or the mean repair time.

Figure 10 shows that productivity is significantly affected by the mean repair time at any given defect percentage level.

The regression model

In the previous sections, we explored the impact and the properties of different factors to get some general insights into the system.

In this section, we present a predictive model that can estimate the productivity of the system. The aim of the model is to assist the engineers to get an approximation about the total products that can be produced by the system within our design region.

The statistical analysis system (SAS)[6] was used to obtain a regression model. The five major factors identified from the previous sections were considered as the independent variables while the total products produced was considered as the dependent variable. The following regression model was obtained with the stepwise approach:

Total products = 740 - 99S - 335RD + 7,633P + 219B - 4,020/[P.sup.2] - 292PB -184PS (the coefficient of determination, R-squared, was 0.961).

The regression equations suggested that the interaction effect of repair time and defect percentage is more important than the individual main effects. Therefore, these two factors should be considered simultaneously. The relationship of buffer size and productivity is also significant. The pallet ratio, which relates to the productivity in a convex form (as shown in the equation), also plays an important role in the equation.

With the equation, the engineer can attain a better quantitative sense about the impact of each factor. Additionally, it shows that interaction effects are important considerations.


From the above study, we observed that R, D and S have a linear effect on productivity while B and P have a non-linear effect. The following observations were also made:

* Service time, pallet ration, defect percentage, buffer size and repair time are important factors that can affect the performance of AASs with repair loops and should be examined carefully during system design. However, the repair strategy does not show significant impact on the performance of the system within our design region, though the offline repair strategy appears to perform better when the defect percentage of assemblies increases. Since the installation cost of an offline repair station may be relatively more expensive than an online repair station, design engineers should consider using online repair strategy when the defective percentage is at low level (less than 10 per cent).

* The effect of buffer units tends to plateau as buffer size increases. Therefore, buffer units should not be added without careful examination of their effectiveness.

* The pallet ratio must be chosen carefully since adding two many or too few pallets can cause a significant decrease in productivity.

* The jam rate and repair time both can linearly affect productivity.

* The number of repair stations can have a direct impact on the efficiency of the system. However additional inspection and repair stations installed may potentially improve the quality of the products.


1. Buzacott, J.A. and Shanthikumar, J.G., Stochastic Models of Manufacturing Systems, Prentice-Hall, Englewood Cliffs, NJ, 1993, pp. 530-37.

2. Buzacott, J.A. and Hanifin, L.E., "Models of automatic transfer lines with inventory banks: a review and comparison", AIIE Transactions, Vol. 10 No. 2, 1987, pp. 197-207.

3. Law, S.S., "A factorial analysis of automatic transfer line system", International Journal of Production Research, Vol. 21, 1983, pp. 827-35.

4. Law, S.S., "A statistical analysis of system parameters in automatic transfer lines", International Journal of Production Research, Vol. 19, 1981, pp. 709-24.

5. Leung, W.K. and Sanders, J.L., "Simulation analysis of the performance of tunnel-gates stations for free-transfer assembly system", International Journal of Production Research, Vol. 5 No. 3, 1986, pp. 191-202.

6. Lai, K.K., Lam, K. and Leung, W.K., "Factorial experiments in the analysis of automatic assembly systems", Journal of Applied Statistics, Vol. 21 No. 5, 1994, pp. 383-94.

7. Box, G.E.P., Hunter, W.G. and Hunter, J.S., Statistics for Experimenters: An Introduction to Design, Data Analysis and Model Building, John Wiley & Sons, New York, NY, 1978.

Further reading

Boothroyd, G. and Murch, C.L.E., Automatic Assembly, Marcel Dekker, New York, NY, 1982.
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Author:Leung, W.K.; Lai, K.K.
Publication:International Journal of Quality & Reliability Management
Date:Jun 1, 1996
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