Topic 3 - Process Capabilities

Requirements for process capabilities analysis

- Process is in statistical control - process is stable - data is normally distributed - calibration is done

Cp

- assumes that the process mean is at the true center of the specification band - it measures potential capability (the best at which process/service can achieve)

Major uses of data from a process capability

- examine if level of quality is maintained or improved - assist in product design, selection and modification -establish interval btw sampling for process monitoring - specifying performance requirements for new equipment or processes - selecting and controlling of vendors - reducing the variability

Process capability index (Cpk)

- is the actual process capability - a statistical tool, to measure the ABILITY of a process to produce output within customer's specification limits. - it measures producer's capability to produce a product within customer's tolerance range - to estimate how close your product is to a given target (Specification Limits), assuming performance is consistent (in statistical control) over time

Interpretation of Cp and Cpk

- the larger the process capability index (Cp or Cpk), the better is the quality Cp value does not change as the process center changes

Specification limits (USL, LSL)

- the values between which products or services should operate. - Are determined by engineers, developers, designers, managers, clients, etc

Process Capability

- to evaluate the variation of the process with respect to process specifications. - refers to the uniformity of the process - spread of the process = dispersion = 6σ - used when a process is under statistical control. Process capability uses the process sigma value determined from either the Average, Range ot Sigma control charts

Steps taken to enhance the process capabilities. If Cpk and/or Cp < 1.33

1. Reduce the standard deviation (variability) 2. Check the specifications 3. Investigate using 5M, 1E

Steps taken to enhance the process capabilities. If Cpk<Cp:

1. Shift process mean to the true centre 2. Reduce the standard deviation (variability)

Capable process

A process where almost all the measurements fall inside the specification limits

Control limits

Are functions of the natural variability

Best Cpk value

Cpk of at least 1.33 (4 sigma) or higher to satisfy most customers

Variability in the process

Is a measure of the uniformity of output

Out-of control

Many in-control processes make products that are out of specification. As the specifications are smaller than the natural tolerance limits. refers to process is not in statistical control, therefore the process is not stable. At this condition, the process capability cannot be calculated

Relationship between control limits and specification limits

No mathematical relationship

Natural tolerance limits

Represent the natural variability of the process (usually set at 3σ from the mean)

Cp formula

USL-LSL/6σ

Process Capability analysis

an engineering study to estimate process capability

Cpk = Cp = 1

indicate a process is perfectly centered, and the mean (process average) is 3 standard deviations away from the upper limit and the lower limit

Cpk = or >1.33

indicates that the process is capable and meets specification limits. Any value less than this may mean variation is too wide compared to the specification or the process average is away from the target.

Cpk = Cp

indicates that the process is centered at the center of the specifications limits

Cpk = 0,

indicates that the process mean is equal to one of the specification limits values, i.e. the center line of the process is on either the USL or LSL lines.

Cpk < 0

means that the mean of the process is outside the customer specification limits; the process will produce output that is outside the customer specification limits.

Process Capability indices

to compare the output of a stable process to the specifications limit to make a statement about how well the process meets specification.

Process control

to evaluate the variation of the process over a period of time, with the goal to reduce or eliminate the variation in the process.

Z formula

z = (x - μ)/σ

Cpk formula

𝑚𝑖𝑛[(𝜇−𝐿S𝐿)/3𝜎, (𝑈S𝐿−𝜇)/3𝜎]