Patterns of Variation

Question 1

Variation

Answer 1

• Lack of consistency
• It can introduce waste and errors into the process

Question 2

Why measure Variation?

Answer 2

• Reliability - we want our customers to know that they’ll always get a certain level of quality for us. Also, we’ll often have a Service Level Agreement or similar in place. Consequently, every product needs to fit specific parameters.
• Cost - Variation costs money. So to lower costs, we need to keep levels low

Question 3

Discrepancies occur when:

Answer 3

• There is wear and tear in machines
• Someone changes a process
• A measurement mistake is made
• Material quality or makeup varies
• The environment changes
• A person’s work quality is unpredictable

Question 4

Six Elements in any Process

Answer 4

1. Method
2. Mother Nature, or Environmental
3. Man or people
4. Measurement
5. Machine
6. Materials

Question 5

Process Spread vs Centering

Answer 5

Question 6

Types of Variation

Answer 6

• Common Cause
• Special Cause

Question 7

Common Cause Variation

Answer 7

• Happens in standard operating condition.
• Think about a factory. Fluctuations might occur due to:
  
  • Temperature
  • Humidity
  • Metal quality
  • Machine wear and tear
• Common cause variation has a trend that you can chart.
  
  • In the factory, product differences might be caused by air humidity. You can chart those differences over time then compare that chart to weather bureau humidity data

Question 8

Special Cause Variation

Answer 8

• Occurs in non-standard operating conditions.
  
  • Factory example, disparities could occur if:
    
    • a substandard metal was delivered
    • one of the machines broke down
    • a worker forgot the process and made a lot of unusual mistakes
  • This type of variation does not have a trend that can be charted.
    
    • Instead, you’ll see a departure from a trend

Question 9

Why is it important to differentiate Common and Special Cause Variations?

Answer 9

• Different factors affect them
• We should use different methods to counter each
• The wrong change can cause even more discrepancies

Question 10

How to identify Common Cause Variation?

Answer 10

• Run Charts
  
  1. Mark your median measurement
  2. Chart the measurements from your process over time
  3. Identify runs.
     
     1. These are consecutive data points that don’t cross the median marked earlier. They show common cause variation

Question 11

How to identify Special Cause Variation?

Answer 11

• Control Charts
  
  1. Mark your average measurement
  2. Mark your control limits.
     
     1. These are 3 standard deviations above and below the average
  3. Identify data points that fall outside the limits marked earlier.
     
     1. In other words, above the upper control limit or below the lower control limit. These show special cause variation

Question 12

Variation Formula

Answer 12

Variation = SD²

Variation is the square of a sample’s standard deviation

Question 13

How to find the cause of Variation?

Answer 13

Multi-Vari Chart

Question 14

How to Counter Variation

Answer 14

• Counter Common Cause Variation using long term process changes
• Counter Special Cause Variation using exigency plans
  
  • Extra or replacement processes

Question 15

Combining Variation

Answer 15

• Rather than finding variation in a single sample, you might need to figure out combined variance in a data set.
  
  • For example, a set of two different products. For this you’ll need the variance sum law
    
    • First, look at whether the products have any common production processes
    • Second, calculate the combined variance using one of the below formulas:
      
      • No shared processes formula
      • Shared processes formula

Question 16

No Shared Processes Formula

Answer 16

The two products don’t share any production processes? Great! Then you can use the simplest version of the variance sum law.

Variance(X + Y) = Variance(X) + Variance(Y) Variance(X - Y) = Variance(X) + Variance(Y)

Question 17

Shared Processes Formula

Answer 17

The two processes do share some or all production processes? That’s OK, you’ll just need the dependent form of the variance sum law instead.

Variance(X + Y) = Variance(X) + Variance(Y) + Covariance(X,Y) Variance(X - Y) = Variance(X) + Variance(Y) - Covariance(X,Y)

Calculate covariance using the following formula.

Cov(X,Y) = Σ ((X-μ) * (Y-ν)) / n-1

where:

• μ is the mean value of X.
• ν is the mean value of Y.
• n = the number of items in the data set.