# Process Capability Analysis and Process Analytical Technology

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Process Capability Analysis and Process Analytical Technology
Presented by: Steven Walfish President, Statistical Outsourcing Services [email protected] http://www.statisticaloutsourcingservices.com

Agenda
• Introduction to Capability – What is capability – Histograms – Normal Distribution
• Capability Indices – Cp – Cpk – Pp – Ppk
• Calculating Sigma – Relating capability to percent nonconforming
• Capability with attribute data – Defects per Million Opportunities (DPMO)
• Process Analytical Technology (PAT)

What is Capability?
• Process capability compares the output of an in-control process to the specification limits.
• The comparison is made by forming the ratio of the spread between the process specifications (the specification "width") to the spread of the process values, as measured by process standard deviation.
• A capable process is one where almost all the measurements fall inside the specification limits.

Graphical Representation

LSL
Mean = 75 SD = 0.3 USL = 73 USL = 77 6S = 1.8

USL
6S on each side of the mean to the specification limit.

73.2

73.8

74.4

75.0

75.6

76.2

76.8

Histogram

73.66 40 30 20

74.11

74.41

74.71

75.31 75.61

±1S (68.3%)

75.91

±2S (95.4%)

±3S (99.7%)

76.36

±4.5S (99.9993%)

10

Frequency

0

74.0

74.4

74.8

75.2

75.6

76.0

76.4

Examples of Capability
• Some examples of where capability analysis can be used:
• Process that is not centered • Process with large variability • One-sided specifications • Setting/confirming customer specifications

Percent Out of Specifications
• Based on the normal distribution, the percent of product that would fall out of specification can be calculated.
• This is best explained using an example.
• Assume we have a process with mean = 50, standard deviation = 4, USL = 58 and LSL = 46.
• We divide this problem into two parts. First the percent out of specification on the high end (greater than the USL) and then the percent out on the low end (less than the LSL).

The Normal Distribution

• The normal distribution is:

Z = USL − X ; X − LSL

S

S

• Z is the number of standard deviations that the specification is from the mean.

• Normal probability tables give you the percent of the distribution that would exceed the specification limit for a given z value

• Remember that 68.3% of the data is within ±1S (therefore 31.7% is outside of ±1S).

Out of Specification Calculations

Z = USL − X ; X − LSL

S

S

Z = 58 − 50 ; 50 − 46

4

4

Z = 2 for the upper specifcation and 1for the lower specification • A z = 2 is 2.28% out of specification; z=1 is 15.9%.

• The total percent expected to be out of specification would be 18.1%

• We will discuss summary statistics for this later.

Estimating Sigma
• There are several methods for estimating sigma (S) used in capability analysis.
• Control charts
– Rbar – Sbar – Moving Range – MSSD
• Pooled standard deviation • Total standard deviation (Long-Term) 