mail2payan

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Hello All,

This time am uploading a SIX SIGMA template, which may help you people in some way.

If you like it, please do give me some feedback.

Enjoy.....:SugarwareZ-135:
 

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yummy1984

Par 100 posts (V.I.P)
Six Sigma stands for Six Standard Deviations (Sigma is the Greek letter used to represent standard deviation in statistics) from mean. Six Sigma methodology provides the techniques and tools to improve the capability and reduce the defects in any process.

It was started in Motorola, in its manufacturing division, where millions of parts are made using the same process repeatedly. Eventually Six Sigma evolved and applied to other non manufacturing processes. Today you can apply Six Sigma to many fields such as Services, Medical and Insurance Procedures, Call Centers.

Six Sigma methodology improves any existing business process by constantly reviewing and re-tuning the process. To achieve this, Six Sigma uses a methodology known as DMAIC (Define opportunities, Measure performance, Analyze opportunity, Improve performance, Control performance).

Six Sigma methodology can also be used to create a brand new business process from ground up using DFSS (Design For Six Sigma) principles. Six Sigma Strives for perfection. It allows for only 3.4 defects per million opportunities for each product or service transaction. Six Sigma relies heavily on statistical techniques to reduce defects and measure quality.

Six Sigma experts (Green Belts and Black Belts) evaluate a business process and determine ways to improve upon the existing process. Six Sigma experts can also design a brand new business process using DFSS (Design For Six Sigma) principles. Typically its easier to define a new process with DFSS principles than refining an existing process to reduce the defects.

Six Sigma incorporates the basic principles and techniques used in Business, Statistics, and Engineering. These three form the core elements of Six Sigma. Six Sigma improves the process performance, decreases variation and maintains consistent quality of the process output. This leads to defect reduction and improvement in profits, product quality and customer satisfaction.

Six Sigma methodology is also used in many Business Process Management initiatives these days. These Business Process Management initiatives are not necessarily related to manufacturing. Many of the BPM's that use Six Sigma in today's world include call centers, customer support, supply chain management and project management.

Six Sigma Engineering
A Six Sigma Engineer develops efficient and cost effective processes to improve the quality and reduce the number of defects per million parts in a Manufacturing/Production environment.
Six Sigma Engineers determine and fine tune manufacturing process. Once a process is improved, they go back and re-tune the process and reduce the defects. This cycle is continued till they reach 3.4 or less defects per million parts.
Six Sigma is all about knowledge sharing. If a company has more than one manufacturing unit/plant, its more than likely that one of the plants produces better quality than others. The Six Sigma team should visit this higher quality plant and learn why its performing better than others and implement the techniques learned across all other units.
Research/Design department within a company can use the above techniques to learn from another R&D departments in the same company or affiliate companies and implement those techniques.
Motorola developed a five phase approach to the Six Sigma process called DMAIC.
DMAIC
• Define opportunities
• Measure performance
• Analyze opportunity
• Improve performance
• Control performance

Six Sigma Statistics
Six Sigma uses a variety of statistics to determine the best practices for any given process.
Statisticians and Six Sigma consultants study the existing processes and determine the methods that produce the best overall results.
Combinations of these methods will be tested and upon determining that a given combination can improve the process, it will be implemented.
Six Sigma stands for "Six Standard deviations from the arithmetic mean".
Six Sigma statistically ensures that 99.9997% of all products produced in a process are of acceptable quality.
Six Sigma allows only 3.4 defects per million opportunities.
If a given process fails to meet this criteria, it is re-analyzed, altered and tested to find out if there are any improvements.
If no improvement is found, the process is re-analyzed, altered and tested again.
This cycle is repeated until you see an improvement.

Once an improvement is found, its documented and the knowledge is spread across other units in the company so they can implement this new process and reduce their defects per million opportunities.
Sigma Confidence Intervals
Confidence intervals are very important to Six Sigma methodology.
To understand Confidence Intervals better, consider this scenario:
Acme Nelson, a leading market research firm conducts a survey among voters in USA asking them whom would they vote if elections were to be held today. The answer was a big surprise! In addition to Democrats and Republicans, there is this surprise independent candidate, John Doe who is expected to secure 22% of the vote.
We asked Acme, how sure are you? In other words how accurate is this prediction?
Their answer: "Well, we are 95% confident that John Doe will get 22% (plus or minus 2%) vote"
In the statistical world, they are saying that John Doe will get a vote between 20% to 24% (also known as Confidence Range) with a probability of 95% (Confidence Level).
Definition of Confidence Interval
According to University of Glasgow Department of Statistics, Confidence Interval is defined as:
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter. Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter.
In our Acme Nelson survey example
• The confidence interval is the range 20 to 24
• The confidence level is 95%
• The confidence limits are 20 (lower limit) and 24 (upper limit)
• The unknown population parameter is the 'percentage of the total vote' John Doe is expected to Get
The width of the confidence interval, in our case 24-20=4 is a measure that is directly proportional to the precision.
Consider this scenario..
What if Acme Nelson's survey predicted that John Doe will get 22% plus or minus 20% vote. In other words Acme is saying John Doe will get between 2% and 42% of the vote.
How good is this number? Even a monkey can predict that. This is a very wide confidence range and in order to reduce the Confidence Interval, Acme needs to collect more samples.
Confidence Limits
Confidence limits are the lower and upper boundaries of a confidence interval.
In our Acme example, the limits were 20 and 24.
Confidence Level
The confidence level is the probability value attached to a given confidence interval. It can be expressed as a percentage (in our example it is 95%) or a number (0.95).
Confidence Interval for a Mean
A confidence interval for a mean is a range of values within which the mean (unknown population parameter) may lie.
Examples of Confidence Interval for a Mean
• A Web master who wishes to estimate her mean daily hits on a certain webpage.
• An environmental health and safety officer who wants to estimate the mean monthly spills.
Confidence Interval for the Difference Between Two Means
A confidence interval for the difference between two means specifies a range of values within which the difference between the means of the two populations may lie.
Examples of Confidence Interval for the Difference Between Two Means
• A Web master who wishes to estimate her difference in mean daily visitors between two websites.
• An environmental health and safety officer who wants to estimate the difference in mean monthly spills between two production sites.
Confidence Intervals Summary
Confidence intervals are very crucial to Six Sigma. Confidence intervals provide crucial information as they give us a range of possible values and attach a confidence level to the interval.
Confidence Intervals in Six Sigma
When we calculate a statistic for example, a mean, a variance, a proportion, or a correlation coefficient, there is no reason to expect that such point estimate would be exactly equal to the true population value, even with increasing sample sizes. There are always sampling inaccuracies, or error.
In most Six Sigma projects, there are at least some descriptive statistics calculated from sample data. In truth, it cannot be said that such data are the same as the population's true mean, variance, or proportion value. There are many situations in which it is preferable instead to express an interval in which we would expect to find the true population value.
This interval is called an interval estimate. A confidence interval is an interval, calculated from the sample data that is very likely to cover the unknown mean, variance, or proportion.
For example, after a process improvement a sampling has shown that its yield has improved from 78% to 83%. But, what is the interval in which the population's yield lies? If the lower end of the interval is 78% or less, you cannot say with any statistical certainty that there has been a significant improvement to the process.
There is an error of estimation, or margin of error, or standard error, between the sample statistic and the population value of that statistic. The confidence interval defines that margin of error.
The next page shows a decision tree for selecting which formula to use for each situation. For example, if you are dealing with a sample mean and you do not know the population's true variance (standard deviation squared) or the sample size is less than 30, than you use the t Distribution confidence interval. Each of these applications will be shown in turn.
Decision Tree for selecting What Formula to use:

Six Sigma Z Confidence Intervals for Means
Z Confidence Interval for Means applies to a mean from a normal distribution of variable data. Use the normal distribution for the confidence interval for a mean if the sample size n is relatively large (≥ 30), and σ is known.
The confidence interval (C.I.) includes the shaded area under the curve in between the critical values, excluding the tail areas (the α risk). The entire curve represents the most likely distribution of population means, given the sample's size, mean, and the population's standard deviation.





Here we are making an assumption that the underlying data we are working with is distributed like the bell curve shown.

The most common confidence interval used in industry is probably the 95% confidence interval. If we were to use its formula on many sets of data from the population, then 95% of the intervals would contain the unknown population mean that we are trying to estimate. And 5% of the intervals would not contain the population mean. 2.5% of the time, the interval would be low, and 2.5% of the time, the interval would be too high.

The probability is 95% that the interval contains the population parameter. The 95% value is the confidence coefficient, or the degree of confidence. The end points of the interval are called the confidence limits. In the graphic on the previous page, the endpoints are defined by

Example - Z Confidence Interval for Means

Calculate a 95% C.I. on the mean for a sample (n = 35) with an x-bar of 15.6" and a known σ of 2.3 "



This interval represents the most likely distribution of population means, given the sample's size, mean, and the population's standard deviation. 95% of the time, the population's mean will fall in this interval.
Six Sigma t Confidence Interval for Means
Use the t distribution for the confidence interval for a mean if the sample size n is relatively small (< 30), and/or σ is not known.
The confidence interval (C.I.) includes the shaded area under the curve in between the critical values, excluding the tail areas (the α risk). The entire curve represents the most likely distribution of population means, given the sample's size, mean, and standard deviation.




Six Sigma t Confidence Interval for a Variance
Use the c2 (chi-squared) distribution for the confidence interval for the variance

The confidence interval (C.I.) includes the area under the curve in between the critical values, excluding the tail areas (the α risk). The entire curve represents the most likely distribution of population variances (sigma squared), given the sample's size and variation.



Six Sigma t Confidence Interval for a Variance Example

Calculate a 95% C.I. on variance for a sample (n = 35) with an S of 2.3"


This interval represents the most likely distribution of population variances, given the sample's size and variance. 95% of the time, the population's variance will fall in this interval
Z Confidence Intervals for Proportions
This Z Confidence Interval for Proportions applies to an average proportion (which is from a binomial distribution).



Example - Z Confidence Interval for Proportions

DPO, DPMO, PPM, DPU Definitions - Six Sigma Defect Metrics

What Is DPO? What Is DPMO?

A unit of product can be defective if it contains one or more defects. A unit of product can have more than one opportunity to have a defect.
• Determine all the possible opportunities for problems
• Pare the list down by excluding rare events, grouping similar defect types, and avoiding the trivial
• Define opportunities consistently between different locations

Proportion Defective (p):
p = Number Of Defective Units / Total Number of Product Units

Yield ( Y1st-pass or Yfinal or RTY)
Y = 1 - p
The Yield proportion can converted to a sigma value using the Z tables

Defects Per Unit - DPU, or u in SPC

DPU = Number Of Defects / Total Number Of Product Units

The probability of getting 'r' defects in a sample having a given dpu rate can be predicted with the Poisson Distribution

Defects Per Opportunity - DPO

DPO = no. of defects / (no. of units X no. of defect opportunities per unit)

Defects Per Million Opportunities (DPMO, or PPM)
DPMO = dpo x 1,000,000
Defects Per Million Opportunities or DPMO can be then converted to sigma & equivalent Cp values (see sigma table)
Six Sigma Capability Improvement
Defect Based Six Sigma Metrics - Example
If there are 9 defects among 150 invoices, and there are 8 opportunities for errors for every invoice, what is the dpmo?

dpu = no. of defects / total no. of product units = 9/150 = .06 dpu

dpo = no. of defects / (no. of units X no. of defect oppurtunities per unit)
= 9/(150 X 8) = .0075 dpo
dmpo = dpo x 1,000,000 = .0075 X 1,000,000 = 7,500 dpmo

What are the equivalent Sigma and CP values? See Sigma Table.

Converting Yield to sigma & Cp Metrics - Example
Given: a proportion defective of 1%

• Yield = 1 - p = .990
• Z Table value for .990 = 2.32σ
• Estimate process capability by adding 1.5 σ to reflect the 'real-world' shift in the process mean

2.32σ + 1.5σ = 3.82σ

• This σ value can be converted to an equivalent CP by dividing it by 3σ :

CP = 3.82σ/3σ = 1.27

Note: Cpk cannot be estimated by this method

Six Sigma Capability Improvement

Sigma Table
Yield dpmo Sigma (σ) Cp Equiv. COPQ (Cost of Poor Quality)
.840 160,000 2.50 0.83 40%
.870 130,000 2.63 0.88
.900 100,000 2.78 0.93
.930 70,000 2.97 0.99
.935 65,000 3.01 1.00
.940 60,000 3.05 1.02
.945 55,000 3.10 1.03 30%
.950 50,000 3.14 1.05
.955 45,000 3.20 1.06
.960 40,000 3.25 1.08
.965 35,000 3.31 1.10
.970 30,000 3.38 1.13
.975 25,000 3.46 1.15
.980 20,000 3.55 1.18 20%
.985 15,000 3.67 1.22
.990 10,000 3.82 1.27
.995 5,000 4.07 1.36
.998 2,000 4.37 1.46
.999 1,000 4.60 1.53 10%
.9995 500 4.79 1.60
.99975 250 4.98 1.66 5%
.9999 100 5.22 1.74
.99998 20 5.61 1.87
.9999966 3.4 6.00 2.00
 

amitjangid

Par 100 posts (V.I.P)
dear dear what is this its dammn confusing and it sems very hard to understand but lets see how it works bye tc
 

singhal_amit

Par 100 posts (V.I.P)
Thanx alot buddy... i was thinking to join a separate course for Six Sigma.. This would help me alot in understanding this topic....
 

rakesh1988

New member
WOW~!!!!! nice work dude!!! SUPER COOL
also thanks a loooooooooooooooot to Yamini Bhaskar :)
super duper info........
helped me a lot B-)
 
Hello All,

This time am uploading a SIX SIGMA template, which may help you people in some way.

If you like it, please do give me some feedback.

Enjoy.....:SugarwareZ-135:

Hey payan, thanks for sharing the presentation on six sigma and i am sure it would be useful for many people as i read your presentation and i got some important and nice points on six sigma. Well, i am also uploading a document on six sigma which may help others.
 

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