# Help with Homework Problem

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• #249474

Karthik Dharmalingam
Participant

Scenario: A BPO company which takes care of the back office operations of one of the major Insurance billing office. Internally quality Team (BPO Team) audits are considered as the process SLA (service level agreement) and target is 98%. Internal Quality Team picks random sample and perform 10% sampling and share the quality accuracy to internal stakeholders and to the Clients. In turn, Clients pick some random samples from the audits done internally to check the sanity of the internal audit process, this is called Audit the Auditor (ATA) but ATA accuracy is not a SLA metric.

Typical situation:

• Total claim processed: 1000 claims
• Internal audit sample size: 100 claims (10% sample size)
• Defect observed by Internal audit Team (BPO) : 10
• Quality score : 10/100 = 90% (Defective Unit methodology)
• Client picks samples from internally audited population: 10
• Client identified error : 1
• Final accuracy by the Clients : 10 (internally identified errors by BPO) + 1 (error identified by the Client) / 100 = 11/100
• Accuracy: 89%

Clarification:

– Option A: Should we add the client identified error to the overall SLA, as the error was missed by the  internal audit Team (Defect leaked through internal QC Team) and report the SLA score as 89%

or

– Option B: the additional 1 error identified by the Client must be treated as an error for Internal QC Team and not to the process SLA.

Which one is more appropriate?

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#249476

Robert Butler
Participant

If you are going to re-sample the internal audit sample then the short answer is the sample size is no longer 100 it is 110 and 11/110 = 90%. Another way to look at this is you have a sample of 100 – you find 10 defects in that sample.  You dump everything back in the bin and run a re-sample of the same population taking 10 samples and finding 1 defect. Given what you found with 100 samples this is not surprising and your re-sampling is just a short hand confirmation of what you found with the larger sample.

If the people you are talking to insist on only adding an additional found defect to the original defect count and do not take into account the fact of all of the sample in the re-sample then why stop there?  Let’s see, I take the 100 samples and I re-test the 100 samples 10 times. The chances are I’ll get 10 defects each time I do this -therefore, at the end of 10 sample/re-sample cycles I’ll probably have 100 defects which when I add them together will give me 100/100 = 0% accuracy.

1
#249641

MBBinWI
Participant

@Karthikdharmalingam – What is being identified is a measurement system error.  In this situation, each internal audit sample that is taken and subsequently subject to the ATA, this can be used to identify a confidence interval on the data provided by the internal audits.

1
#249723

Karthik Dharmalingam
Participant

Thanks Robert. with 11/110, score is same as the score reported by a BPO first time, does it mean the additional error identified by the Client should be added to the SLA or seen as a measurement system error and not to the SLA?

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#249724

Karthik Dharmalingam
Participant

Thanks for your inputs, I didn’t get it. you mean to say, the additional error identified by the Clients must be seen as a measurement system error and check the internal sampling method?

0
#249757

Robert Butler
Participant

I might be missing something but my understanding of the scenario you described is as follows:

a. Quality team takes a 10% sample of the total output.  With a total output of 1000 this becomes a sample of 100.

b. Quality team does a 100% inspection of the 100 samples and finds 10 defects in that sample.  Therefore, their claim, based on the examination of the 100 samples, is the  quality score is 10/100 = 90%.  This value, as I understand your post, is the SLA.

The second crew takes the same batch of 100 samples, pulls 10 samples from this group and finds 1 defect.  From your post I understand this to be the ATA.

1. The ATA defect cannot be viewed as an additional defect to add to the 10 found during the 100% check (the SLA) because the first group did a 100% inspection and found a grand total of 10 defects. Therefore all the second group did was find one of the original defects in their 10 sample sub-sample of the 100 and confirm, via the smaller sample, what was found with the complete inspection of the larger sample.

What I don’t follow is the reasoning concerning the way the ATA sub-sample is taken and assessed.  After all, there is a chance of pulling 10 samples from the original 100 and finding no defects and there is also the chance of pulling 10 samples and finding you have drawn the original 10 defects.

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#249782

Fausto Galetto
Participant

@Karthikdharmalingam

In order to provide you with a sensible solution you have to answer to these questions:

1.       The sample S1 (sample size 100) is 10% of the “population”? It seems so from your writing…

2.       The sample S2 (sample size 10) is 10% of the SAMPLE S1? It seems so from your writing…

3.       IF NOT specify clearly