Venkateswaran K

1 variance test is used to compare variance of sample to a known population, with the assumption that sample is drawn from a normally distributed population. This analyses the difference between an observed process std deviation and a specified std deviation. It determines whether the population variance differs from hypothesized value specified in the test
 
Example 1:
Let us take a Timber company ships its high quality products through sea to high priced markets of European countries.
The quality analyst at the receiving country wants to determine whether the variance of the moisture content in the shipment
Has increased from that of the specified value. If the variance is greater than maximum acceptable variance , analyst uses the confidence interval to determine how is the difference and whether this difference  has practical significance.   
A test of single variance can be left tailed or Right tailed. Here in this case Let us assume if the moisture content variance specified is 0.1 gm/cc, it means our Null hypothesis is the population variance = specified variance and Alternate hypothesis is that population variance should be less than specified .
Here the word “Less” indicates that it is left tailed test.
 
Example 2:
If the doctor wants to know the variation of Diastolic (low) Blood pressure levels in patients is more than 60mm /hg.
In this case the word “more” indicates that it is right tailed test.
 
The following Data considerations need to be satisfied when applying the chi – square test:
1> The sample must be randomly drawn from the population
2>The data needs to be ensured for normal distribution
3> Each observation should be independent from all other observations.
 
How to derive the Test statistic for 1 variance? is given below:
 

 

The Laney’s P chart is based on the working principle of a p chart used for attribute data– the difference being that it adjusts for very large sample sizes(usually > 5000), to provide an accurate assessment of control points than in a p chart.
 
It is difficult to assess the statistical control of the proportion due to the over dispersion of results, with a normal p chart. Points on a p chart are shown out of control due to over dispersion. Laney’s sigma Z is a measure of over dispersion. While attribute p chart shows points out of control ,applying same data to plot Laney’s p chart shows points in control.
 
The advantage of the p chart is that it gives us the proportion defective in y axis & np chart gives us the whole number of defective in y axis.
while Laney's p chart has the advantage of using varying control limits - it avoids the variation due to over dispersion, in case of higher sample size ( of more than 5000).
 
The disadvantage of p chart is that its predictions may not be accurate if the population has varying sub groups. Hence under such specific conditions of sample size more than 5000 with varying sub groups Laney's P chart is used.
 
Let us take example of our central Govt planning to set up Temporary health care bedded hospitals in Tier 1 towns to tackle the pandemic. And let us say the each Tier 1 city has population varying between 5000 ~ 35000 , out of which % proportion of the people who are attacked by the COVID need hospitalization in let us say 10 such cities is the vital input to the govt to plan the priority. In this case use of p chart would give us over dispersion of results.so the statistical dept shall use Laney's p chart to calculate the proportion using varying control limits and also addressing the variation of the large sample using the Laney's sigma which is not expressed as binomial as in a normal p chart. In this way the govt can really find the tier 1 cities for which the number of persons to be treated exceeds the broader control limits set by Laney's p chart. This is very useful to disregard the variation due to over dispersion or under dispersion .

 

 

Problem Definition Tree:
 
 
CTQ Drill down or Problem Definition Tree diagram relates high level focal points(Resultant output)to project objective(factors)
 The measure of those items linked to the CTQ are called Project Y.
 
The following situations mandates the Problem definition Tree to be applied:
 
1.When Project Indication is vague without knowing which parameter need to be improved.
2.When parameters of Big Ys are defined from customer perspective rather than process control perspective.
3.When dimensions of the Big Ys are aimed at abstract terms and not in tangible terms.
 
 
In General ,The following rules can be applied while splitting the Big Ys to Project Y :
 
1st Rule – Boxes in a split should not overlap. Need to respect the parent dictionary and divide it into subgroups
2nd rule – Need to ensure that sub groups selected must encompass the whole dictionary .
3rd Rule – Boxes or sub groups must be able to provide us with details and data needed for running experiments.
 
The Black belt should finalize the last unbreakable activity or component which can contribute to the Big Y and select this item as Project Y. This is the actionable item which need to be acted upon to improve the Project Y and thus the Big Y to solve
 
 
Let us take example of OEE Overall Equipment efficiency not achieved the Target for may '23( Big Y) and drill down to find the project Y - which contributes the highest , so that action can be initiated immediately .
 
The injection  molding machine shop OEE is 84% , which is average of 3 machines OEE #1,#2,#3.However target is 90%.
In this Example - the black belt has to stop here and take a call, after he had broken down the Big Y to actionable items or factor KPIs, at the activities contributing to availability loss of M/C #2 - out of the which Top 3 activity can be taken as Project Ys .Thus we have divided our Big Y of OEE Target not achieved problem into many Project Ys and Black Belt can stop here as below to finalize projects for further working by small work groups on each .
Here Changeover Time is the 1st actionable item to be worked on followed by Breakdown time reduction & material shortage issue reduction. Once all these Project Ys are addressed , eventually the Big Y ( OEE of molding) would be achieved. Problem definition Tree clearly gives us direction, focus.
 
1.Change over time - 45%
2.Breakdown Time - 22%
3.Raw material shortage time - 18%
 

 
The General criteria/steps to be used while splitting boxes.
1.Use Logic to make splits ( using creative & alternate searches)
2.Never move to next level until , all important in the family is identified.
3.Make Broad splits first and detailed splits later - Avoid going into the factor x , until the detailed split of Ys 
4.FInally use facts and physical laws of logical correlation to make decision vis cause/effect matrix.