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Process Capability Studies. Before performing a process capability study the process must be stable. The natural behavior of a process is termed its process capability. Once the process capability study is completed, process improvement studies can start (PDSA) cycle.

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process capability studies
Process Capability Studies
  • Before performing a process capability study the process must be stable.
  • The natural behavior of a process is termed its process capability.
  • Once the process capability study is completed, process improvement studies can start (PDSA) cycle.
  • For attributes, process capability studies are carried out with control charts and rational subgrouping as discussed previously.
  • We will concentrate on Variables process capability studies
slide2
Natural Limits - indicate what a process is capable of producing. That is they provide an indication of the variability that is inherent in the process.
  • They are calculated as follows:

Upper Natural Limit (UNL) = process centerline + 3(process standard deviation)

Lower Natural Limit (LNL) = process centerline - 3(process standard deviation)

Note: it is assumed that the measurements follow a normal distribution

slide3
Example
  • A process is stable, centered, and distributed normally with an average of 30 lbs. And an average range of 4.8 lbs. Find the natural limits(assume n = 5):
process capability indices
Process capability indices
  • Process capability indices are used to state a process’s ability to meet specifications in one summary statistic.
  • Assumptions:
    • Process is stable
    • Variables data
    • Process is normally distributed
  • Cp : Used to summarize the processes ability to meet a two sided specification limit.
    • It is assumed that the process average (x bar bar) is centered on nominal
slide5
CPU: Used to summarize a process’s ability to meet a one sided upper specification limit.
  • CPL: Used to summarize a process’s capability to meet a one sided lower specification limit.
slide6
Cpk Used to summarize a process’s ability to meet a two-sided specification without assuming the process is centered on nominal.
  • Note:
    • If a process is unstable process capability studies are meaningless
    • If a process is not normally distributed, out-of-spec fraction can be incorrectly calculated.
slide7
Example (Problem 2 chapter 11)

The ABC Co. produces steel tubes. The steel tube process is a stable cut-to-length operation that generates tubes that are distributed normally with a mean of 12.00 inches and a standard deviation of 0.10 inch.

The LMN Co. wishes to but tubes from the ABC Co. The LMN Co. requires steel tubes 11.95 inches long with a tolerance of ± .30 inches.

Compute Cp, CPU, CPL and Cpk