1. ## Process Capability

I am not sure if I am calculating the process capability index correctly. Here is what I have so far.

Day No. Defective Bills
1 10
2 9
3 13
4 10
5 15
6 10
7 14
8 13
9 14
10 14
11 12
12 13
13 14
14 13
15 12
16 12
17 14
18 16
19 14
20 10
Mean = 12.60
SD = 1.93
LSL = 6.81
USL = 18.39

I need help in finding the process capability for this set of data and I am not sure if I am using the right standard deviation.

I appreciate any help.

Thank You!

2. First test the following stuff.
1) Normality assumption
2) Test process is n statistical control ( No Trends or Cycles or Seasonality)

After that you can use I MR chart(individual and moving range chart) for calculating Process capability

[ If you wanted to complicate this, Use c chart for estimating variance. Since it is a discrete variable. ].

3. First, you have discrete count data. So, a standard capability study would not apply. The standard deviation would not be useful, except as a crude approximation, trying to model a discrete distribution with a normal distribution.

Unfortunately, I would also reject that it is Poisson distributed, using a Poisson test (p-value 0.003).

In this case, you can say that the mean number of defects is 12.6.
You can also say that the lowest observed was 9.00, and the highest was 16.00. You can also use percentiles.

No matter how you analyze it, you are a long way from Six Sigma.

4. Thats what I assumed but I also thought to use an estimated standard deviation such as Sd/C4 referring to tables with a sample size or (n=20) but I do not think that is right either.

Thank you much for your help!

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