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**Global Business Management Group**

Statistical Process Control INTRODUCTION

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**Why we use control charts ?**

Global Business Management Group Statistical Process Control What is SPC ? What is VSC ? Why we use control charts ? Plotting of control chart ...

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**Statistical Process Control**

Global Business Management Group Global Business Management Group Statistical Process Control The Arithmetic mean : Most of the time when we refer to the average of something we are talking about arithmetic mean only. To find out the arithmetic mean , we sum the values and divide by the number of observation. Advantages : it's a good measure of central tendency.It easily understood by most people Disadvantages :- Although the mean is reliable in that it reflects all the values in the data set, it may also be affected by extreme values that are not representative of the rest of the data.

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**Global Business Management Group**

Statistical Process Control The Median : The median is a single value from the data set that measures the central item in the set of numbers.Half of the item lie above this point and the other half lie below it. We can find median even when our data are qualitative descriptions. For example we have five runs of the printing press the results of which must be rated according to the sharpness of the image. Extremely sharp, very sharp, sharp slightly blurred, and very blurred.

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**Global Business Management Group**

Statistical Process Control Mode :- The mode is a value that is repeated most often in the data set. Infect it is the value with highest frequency.

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**Statistical Process Control**

Global Business Management Group Statistical Process Control Average Income Country X Country Y 10,000 Rs/Month 11000 Rs/Month Which country is ECONOMICALLY more stable ???

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**Global Business Management Group**

Statistical Process Control Country X Country Y Avg Std dev

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**Measure of SPREAD sigma Statistical Process Control**

Global Business Management Group Statistical Process Control Standard Deviation is the sigma Measure of SPREAD

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**Global Business Management Group**

Statistical Process Control (sigma) = √ (x-x ) + (x-x ) + … (x-x ) (n - 1) _ 1 2 n 2 2 2

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**Statistical Process Control**

Global Business Management Group Statistical Process Control Plot HISTOGRAM for following DATA

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**Normal Distribution Curve**

Global Business Management Group Statistical Process Control Normal Distribution Curve

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**Global Business Management Group**

Statistical Process Control Properties of a normal model curve :- It is symmetrical , unimodel and bell shaped. The values of mean , median and mode are identical. It is uniquely determined by the two parameters , namely mean and standard deviation. In the family of normal curves smaller the standard deviation , higher will be the peak. If the original observations follow a normal model with mean mu and std dev sigma then the averages of random sample of size n drawn from this distribution will also follow a normal distribution. The mean of the new model is same as the original model I.e mu but the standard deviation gets reduced to (sigma)/root "n"

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**Global Business Management Group**

Statistical Process Control 99.73% +/-3 sigma 95.45% +/- 2 sigma 68.26% +/- 1 sigma 2.14% 13.6% 34.13% 34.13% 13.6% 2.14%

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**Global Business Management Group**

Statistical Process Control Description of a NORMAL DISTRIBUTION LOCATION: The central tendency it is usually expressed as the AVERAGE SPREAD: The dispersion it is usually expressed as SIGMA

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**Global Business Management Group**

Statistical Process Control A Process Control System THE PROCESS INFORMATION ABOUT PROCESS ACTION ON THE PROCESS Local Action - Special cause Action on the System - Common cause ACTION ON THE OUTPUT

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**DEMING’s Funnel Experiment**

Global Business Management Group Statistical Process Control DEMING’s Funnel Experiment

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**Variation :- Common cause and Special Cause**

Global Business Management Group Statistical Process Control Variation :- Common cause and Special Cause In order to effectively use of process control measurement data, it is important to understand the concept of variation. No two characteristic or products are exactly alike, because any process contain many source of variability. Some source of variation in the process cause short-term, piece to piece difference's - e.g., backlash and clearance with in a machine and its fixturing. Other sources of variation end to cause changes in the output only over along period of time, either gradually as with tool or machine wear, step with procedural changes, or irregularly, as with environmental changes such as power surge. Therefore the time period and condition over a which measure are made will effect the amount of the total variation that will be present. Common cause refer to the many sources of variation within a process that has a stable and repeatable distribution over a time. This is called “STATE of STATISTICAL CONTROL” . Common cause behave like a stable system of chance cause. If only common cause of variation are present and do not change, the output of a process is predictable. The change in the process due to the SPECIAL cause can either be detrimental or beneficial. When detrimental, they need to be identified and removed. When beneficial, they should be identified and made a permanent part of the process.

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**Global Business Management Group**

Statistical Process Control SPECIAL CAUSE LOCAL ACTION COMON CAUSE ACTION on SYSTEM

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**Global Business Management Group**

Statistical Process Control CONTROL CHART When you need to discover how much variability in a process is due to unique events/individual actions in order to determine whether a PROCESS IS IN STATISTICAL CONTROL Variable Data Attribute Data p Chart np Chart c Chart u chart X bar - R chart X-s Chart X- Mr Chart

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**X R Statistical Process Control = X+X+X+…X n R+R+R+…R = n**

Global Business Management Group Statistical Process Control X = X+X+X+…X n n R+R+R+…R R = n n Upper Control Limit UCL = X + A R 2 Lower Control Limit LCL = X - A R 2 Center Line for Average Chart is X double bar and Center line for Range chart is R bar

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**Statistical Process Control**

Global Business Management Group Statistical Process Control The p Chart = Proportion Defective p = Number of rejects in a subgroup Number inspected in subgroup p = Total Number of rejects Total Number inspected _

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**INTERPRETING CONTROL CHARTS**

Global Business Management Group Statistical Process Control INTERPRETING CONTROL CHARTS

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**Global Business Management Group**

Statistical Process Control COMMON QUESTION TO ASK WHEN INVESTIGATING AN OUT OF CONTROL PROCESS

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**Process Capability Cpk = Cp = Statistical Process Control**

Global Business Management Group Statistical Process Control Process Capability Tolerance band 6 * Cp = (USL-X d bar), (X d bar - LSL) Cpk = Min of 3* 3*

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