Process Variability - Buisness Management - Lecture Slides, Slides of Business Administration

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Process Variability and

Capability

Designed Size

Theoretical Basis of

Control Charts

95.5 % of values

within 2σ

Theoretical Basis of Control Charts

99.7 % of values

within 3σ

Kurtosis

 Amount of peakedness

or flatness

Kurtosis < 0 Kurtosis > 0 Kurtosis = 0

Sub-groups with different variances

Heteroskedasticity

Process Capability and 6σ

 A “capable” process has UTL and LTL 3 or more

standard deviations away from the mean, or 3σ.

 99.7% (or more) of product is acceptable to

customers

LTL UTL

3 σ 6 σ

LTL UTL

Process Capability

LTL UTL

LTL UTL

Capable Not Capable LTL UTL LTL UTL

Process Capability

Process

•  Specs: 1.5 +/- 0.
  •  LTL = 1.5 – 0.01 = 1.
  •  UTL = 1.5 + 0.01 = 1.
•  Mean: 1.505 Std. Dev. = 0.
  •  LCL = 1.505 - 3*0.002 = 1.
  •  UCL = 1.505 + 0.006 = 1. - 1.
    • 1.49 1. - 1. - 1. Specs

Capability Index

 Capability Index (C pk ) will tell the position of the control limits relative to the design specifications.  C pk ≥ 1.0, process is capable  C pk < 1.0, process is not capable

Process Capability

 Tells how well parts produced fit into specs

 For our example:

 C

pk

= min[ 0.015/0.006, 0.005/0.006]

 C

pk

= min[2.5,0.833] = 0.833 < 1 Process not capable

Process Capability: Re-centered

 If process were properly centered  Specs: 1.5 +/- 0.

 LTL = 1.5 – 0.01 = 1.

 UTL = 1.5 + 0.01 = 1.

 Mean: 1.5 Std. Dev. = 0.

 LCL = 1.5 - 3*0.002 = 1.

 UCL = 1.5 + 0.006 = 1.

Process Specs

What if Not Capable?

 We can’t sell everything we

make to these people

 Find less choosy customers?  Measure & sort all for them?

 Shifting the Mean

 Not trivial, may be easy  Adjust a setting?

 Reducing variability – Hard!

 Process varies over time  Find and get rid of variability  Training workers, new equip?

LTL UTL

LTL UTL

Summary

 All processes exhibit variability

 Reviewed some basic statistical concepts

 Defined process capability measurement, Cpk  Difficulties of making a process capable