Sector Private Care
5. Contact Centre Model Methodology
5.6 Model data
In this section we present the data used for the model and describe the process for
collecting data and fitting probability distributions for the various activities in the model.
164 5.6.1 Call durations
There are two types of call handlers with social services skills, agents and advisors. Agents and advisors take broadly the same types of calls but advisors are generally more skilled and experienced. As mentioned previously, there is one fundamental difference between their roles: agents cannot deal with complicated children‘s calls (Children‘s call type 3).
The call time data were collected manually by the researcher, by direct observation in the contact centre during the study. A total of 467 calls were observed and the durations recorded. Inspection of these data revealed an apparent difference between agents and advisors in terms of the time they spent dealing with different call types. A chi-square test was carried out to test whether this was statistically significant. The hypothesis was that if there was a significant difference between the two call-handler types then they would be treated separately in the modelling. If there was not a significant difference, then a further decision would be made about the possibility of modelling only one staff type.
The t-test is used to test whether there is a statistically significant difference between the means of the two populations. The t-statistic is calculated as follows:
2 2 2 1
2 1
2 1
- x t x
n S n
S
where x is the sample mean, S is the standard deviation and n is the sample size. The degrees of freedom are calculated as follows:
(n1+n2) – 2
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where n1 is the total number of values in the first population, and n2 is the total number of values in the second population. The critical value is read from the t-distribution table using the relevant number of degrees of freedom. If the test statistic is greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis. A two-tail test was carried out, as we were testing only whether the two populations differ and not the direction of the difference. A t-test is appropriate in this case as both sample sizes were greater than 30.
The t-test was carried out a) for the call itself, b) for the ―wrap time‖ and c) for the total call duration. The wrap time is the time spent on administrative activities relating to the call but performed after the call itself is terminated, enabling the call handler to finish the case. The t-test was carried out for Call Type 1, Call Type 2 and Adult Service Call Type 3.
Children‘s Services call type 3 could not be compared as the processes are different. An independent samples t-test was carried out and equal variances were not assumed. For each test the following hypotheses were tested:
Null hypothesis (Ho): There is no difference between the mean length of time an agent and advisor take to deal with calls, and any observed difference in the sample is simply due to chance.
Alternative hypothesis (H1): There is a difference between the mean length of time an agent and advisor take to deal with calls received, and the observed difference in the sample is not due to chance.
The first test was carried out for the call duration on all the calls received. The data are summarised in Table 5.4.
166 Staff
Type
Number of calls in sample
Mean (Seconds)
Standard Deviation
Standard Deviation Squared
Agent 258 356.907 343.33 117873.99
Advisors 209 337.2919 296.63 87988.18
Table 5.4: Data for t-test for all calls received call durations
The test statistic is 0.662 and there are 465 degrees of freedom. As this value is less than the critical value of 1.96 the null hypothesis cannot be rejected at the 5% level of
significance, in other words we can be 95% certain that we have not made a Type 1 error and rejected the null hypothesis when in fact it is true. Identical tests were carried out for the wrap up time and the total call duration. The test was carried for Call Type 1, Call Type 2 and Adult Service Call Type 3. Full details of all the tests can be found in Appendix A6 and are summarised in Table 5.6.
The second test used was the chi-square test, which tests whether paired samples come from the same distribution or not. The test checks whether there is a significant difference between the call times for agents and advisors, and a comparison is made between the
―observed‖ and ―expected‖ data.
Null hypothesis (Ho): There is no significant difference in the distributions of call durations between agents and advisors.
Alternative hypothesis (H1): There is a statistically different difference in the distributions of call durations between agents and advisors.
For this test the agents‘ call total were taken to be the ―observed‖ data and the advisor call data were taken to be the ―expected‖ data. The observed data for each test were the
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numbers of calls observed for each grouped value of the call time for agents and advisors.
From this the expected call data were generated. The null hypothesis will be true if the differences between the observed and expected call frequencies are similar, as tested using the Chi-square test statistic.
The test statistic χ2 is calculated as follows:
cells
2 2
expected expected)
-(observed
The expected frequencies are calculated by multiplying the column total by the row total and dividing by the grand total. The degrees of freedom is calculated by the following formula
(r – 1)(c – 1)
where r is the number of rows and c is the number of columns. The χ2 value calculated above is then compared with the critical value from the chi-square table. If the test statistic is greater than the critical value then we reject the null hypothesis and accept the alternative hypothesis. The χ2 test was carried out at both the 1% and 5% levels of confidence.
The first test was carried out for the call duration on all the calls received. The data are summarised in Table 5.5, which shows the expected and observed call count proportions for all calls in the sample.
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Call count proportions Observed Expected Call Times Agent Advisor
0:00-0:59 11.24 10.05
1:00-1:59 13.95 11.00
2:00-2:59 10.08 12.92
3:00-3:59 10.85 13.40
4:00-4:59 6.98 9.57
5:00-5:59 7.36 8.61
6:00-6:59 8.91 5.26
7:00-7:59 8.14 7.66
8:00-8:59 5.81 3.35
9:00-9:59 2.71 3.83
10:00-11:59 1.94 4.31
12:00-12:59 3.10 2.87
13:00-15:59 2.71 3.35
16:00 + 6.20 3.83
Table 5.5: The expected and observed call count proportions
The test statistic for the data is 10.539 and there are 13 degrees of freedom. The test
statistic is less than the critical value (22.36) at the 5% level. We accept the null hypothesis and conclude that there is no statistically significant difference in call times between agent and advisors. To be more conclusive, the test was applied to the wrap and total call
durations of the same data. An investigation into the three call types used for the t-test was also carried out. Identical tests were carried out for the wrap up time and the total call duration, for Call Type 1, Call Type 2 and Adult Service Call Type 3. The tests results can be found in Appendix A7 and are summarised in Table 5.6.
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Table 5.6 summarises the results from all the statistical tests. There is no statistically significant difference between agent and advisors when looking at the total set of calls.
However, differences appear when looking at the three individual call types: there are statistically significant differences in all three call types.
All Calls Talk Duration Wrap Duration Total Duration
T-Test None None None
Chi-Square None None None
NFA/ Signposting/ Information Talk Duration Wrap Duration Total Duration
T-Test None Significant (5%) Significant (1%)
Chi-Square Significant (1%) Significant (5%) Significant (1%)
Passed to key team or key worker Talk Duration Wrap Duration Total Duration
T-Test Significant (1%) Significant (1%) Significant (1%)
Chi-Square Significant (5%) Significant (1%) Significant (1%)
Passed to PAT Talk Duration Wrap Duration Total Duration
T-Test Significant (5%) Significant (5%) Significant (1%)
Chi-Square Significant (1%) Significant (1%) Significant (1%)
Table 5.6: Summary of the results from the T-Tests and Chi-Square Tests
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As a result of the significant differences in the three call types as well as the difference in the process of dealing with Children‘s complex calls, it was decided to model two staff types in the simulation model.
5.6.2 Staffing data
A variety of sources were used to create a staff roster that could be used in the model. We were given access to the paper records of the real-life staff roster. As well as this, data were provided showing how many staff members were logged onto the system to handle social service calls in fifteen minute segments. Unfortunately this did not have the agent/advisor split. Moreover there were discrepancies between the paper and the electronic records. This issue was discussed with the operations manager of Hantsdirect, and it was considered that the number logged into the system was more accurate than the paper records. To overcome the issue of not knowing how many agents and advisors there were, the paper staff roster was used. The ratio of agents and advisors per fifteen minute segment was used to calculate the likely number of agents and advisors logged onto the system.
The final staff roster used in the model was based on two weeks‘ data. One week was taken from June 2009 and the other from July 2009. These two weeks were considered by the Hantsdirect staff to be representative of two typical working weeks. The average number of staff in each fifteen minute slot was calculated and used to create the final staff roster. This was validated with two senior members of staff at Hantsdirect and was considered as acceptable for modelling purposes. The final staff profiles that are used in the simulation model can be found in Appendix A8.
An additional advisor was used in the model, to reflect the real-life situation in which one extra advisor is rostered to deal with other forms of contact such as emails and faxes. When there are no other forms of contact to deal with, this additional advisor is able to take calls.
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From direct observations in the contact centre, it was clear that staff are not available 100%
of the time. There are other factors which reduce the availability of call handlers to answer calls. Following discussions with Hantsdirect, the staff availability was set to 80% for both agents and advisors. The staff availability within the Simul8 model was therefore set to 80%.
5.6.3 Call arrival rates
Three weeks‘ data were provided by the Operations Manager of the contact centre. These data were produced by the call centre software. From these, two ―typical‖ working weeks were chosen by the Operations Manager. One week was taken from June 2009 and the other from July 2009. Call arrivals were provided in fifteen minute blocks for each day of the week. However, after discussion with the Operations Manager and the Project Manager, it became apparent that the reported split of calls between Adult and Children‘s was
incorrect. The current process for identifying the type of call on entry into the system was not accurate. Following discussion with the Project Manager a solution was determined.
Call arrivals for Adult and Children‘s Service would be combined. On the basis of a previous study carried out by the Project Manager and his team, it was decided to assume that 45% of calls are for Adult Services and 55% of calls are for Children‘s Services.
Assumption ten: 45% of calls are for Adult Services and 55% for Children‟s Services.
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The total number of calls by day of week is given in Table 5.7.
Adult Service Calls Children‘s Service Calls
Monday 377 458
Tuesday 312 382
Wednesday 279 344
Thursday 294 364
Friday 253 308
Table 5.7: Call counts by day
Monday is clearly the busiest day and the number of calls decreases thereafter on a day-by-day basis. Not only is there a difference in the total number of calls, but the distribution of calls throughout the day is also different for each day of the week. This is shown
graphically in Appendix A9. There is significant variation between each day. These
differences are accounted for in the model. It was decided that the arrivals in the simulation model would follow an exponential distribution, as this is a good model for events which occur at random and independently of each other, and is commonly used to model arrival rates. This allows for each run of the model to include variability in the number of arrivals as expected with the real world system. The mean inter-arrival times for Adult and
Children‘s calls used in the model can be found in Tables 5.8 and 5.9. The mean inter-arrival time is altered every fifteen minutes in the model, to reflect the time-dependence of the real-world data
Assumption eleven: Call arrivals follow an exponential distribution.
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Table 5.8: Adult Services Calls: mean inter-arrival times