# How to Get Expected Defectives in Minitab Binomial Capability Analysis

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- This topic has 6 replies, 3 voices, and was last updated 1 month ago by leavor.

- AuthorPosts
- August 12, 2020 at 5:25 am #249351
I use minitab’s binomial capability analysis, and use the constant 200 in the Sample size.

**Minitab Result:**Binomial Plot can be used to determine whether the data conforms to the binomial distribution.

It can be seen that the number of observed defects on the X axis is the category of the number of Unanswered Calls.

However, I don’t know how to calculate the expected number of defects on the Y axis.

I would like to know the specific calculation steps for the expected number of defects, thank you very much.The data used is in the attachment.

0August 12, 2020 at 12:39 pm #249357

Katie BarryKeymaster@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@leavor Minitab has excellent technical support. Have you checked with them directly? I have notified them of this post in the meantime.

0August 12, 2020 at 6:57 pm #249358

MinitabUser1829Participant@MinitabUser1829**Include @MinitabUser1829 in your post and this person will**

be notified via email.I have attached a document which gives the method for computing Expected Defectives. An example is provided. The screenshots are from an older version of Minitab, but the method is the same as what is in Minitab 19.

###### Attachments:

- Instructions.docxYou must be signed in to download files.

0August 12, 2020 at 11:17 pm #249363Thank you for your help!

I have drawn Binomial Plot according to the provided help document

I am using Python and my code is as follows:

# -*- coding: utf-8 -*-

“””

Created on Thu Aug 13 11:20:54 2020

@author: leavor

“””

import pandas as pd

from collections import Counter

from scipy.stats import binom

from matplotlib import pyplot as plt

data = pd.Series([12,10,15,11,10,14,15,13,11,14,11,13,13,12,11,11,15,10,11,15,12,13,

12,13,14,12,13,13,10,12],name=’Defectives’)#Defectives

sampleSize = 20#sample size const

N = len(data)#N

collec = Counter(data)

key = list(collec.keys())#Observed Defectives

freq = list(collec.values())#Frequency

df = pd.DataFrame({‘OD’:key,’Freq’:freq})

df = df.sort_values(by=’OD’)

tmp = pd.Series([1]).append(df[‘Freq’])

df[‘Indicator’] = tmp.cumsum().iloc[:-1].values#Indicator

df[‘Rank’] = (2*df[‘Indicator’]+df[‘Freq’]-1)/2#Rank

df[‘ECDF’] = (df[‘Rank’]-0.375)/(N+0.25)#ECDF

p = data.sum()/(N*sampleSize)#AverageProportion

df[‘ED’] = binom.ppf(df[‘ECDF’],sampleSize,p)#expected defectives

plt.scatter(df[‘OD’],df[‘ED’])

plt.plot(df[‘OD’],df[‘OD’],color=’r’,linewidth=0.8)

plt.xlabel(‘Observed Defectives’)

plt.xlabel(‘Expected Defectives’)

plt.title(‘Binomial Plot’)0August 12, 2020 at 11:33 pm #249365I tried to extend this method to the Poisson distribution, but encountered difficulties.

I don’t know the ECDF of Poisson calculation formula, and I don’t see the formula in the minitab supporting document.

@MinitabUser1829,Can you provide a Poisson Plot method, thank you very much!0August 13, 2020 at 12:06 pm #249376

MinitabUser1829Participant@MinitabUser1829**Include @MinitabUser1829 in your post and this person will**

be notified via email.You can use the same steps as outlined in the document I attached before, with 2 changes:

- For step 5, calculate the average number of defects.
- For step 6, use
**Calc > Probability Distributions > Poisson**. For the*Mean*, enter the number computed from step 5.

0August 13, 2020 at 11:23 pm #249390I’ve got it, thank you very much!

0 - Instructions.docx
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