Process Capability Analysis (Ppk / Cpk)

Overview

Process capability analysis evaluates whether a manufacturing process is capable of consistently producing products within the specified tolerance limits. Unlike machine capability studies (MFU), which only examine short-term machine capability, process capability analysis considers all influences that occur over a longer production period.

my8data distinguishes between two groups of process capability indices:

When to use which index?

• Cp/Cpk: Suitable for evaluating short-term process capability. These indices show the process potential when only inherent variation is considered.
• Pp/Ppk: Suitable for evaluating long-term process performance. These indices reflect actual process performance, including all influencing factors such as tool wear, material batches, temperature changes, etc.

Info: In an ideal, stable process, Cp and Pp should be close to each other. A significant difference between Cp and Pp indicates systematic influences that affect the process over time (e.g., drift, shift changes).

Typical Requirements

Warning: The threshold values mentioned here are industry-standard guidelines. Specific requirements are determined by your customer's specifications or applicable standards.

Data Entry and Specifications

Data Structure

For process capability analysis, you need measurement data collected over a representative production period. The data should reflect the typical variations of the process (different shifts, material batches, environmental conditions, etc.).

Recommended Data Quantities

Specification Limits

Enter the specification limits as you would for an MFU:

• USL (Upper Specification Limit): The maximum allowable measurement value
• LSL (Lower Specification Limit): The minimum allowable measurement value
• Target Value (optional): The desired nominal value

Subgroup Formation

The formation of subgroups is critical for distinguishing between short-term and long-term variation:

• Within a subgroup: Parts manufactured under conditions as similar as possible (short time period, same tool, same operator)
• Between subgroups: Time intervals that capture typical process variations

Tip: A best practice approach is to collect 5 consecutive parts per hour or per shift over a period of at least 20 production cycles. This ensures that both short-term and long-term variation is captured.

Input Formats

my8data supports data entry in the following formats:

Indices Cp, Cpk, Pp, Ppk

Cp — Process Capability Index (short-term)

The Cp value describes the ratio of tolerance width to short-term process variation. It shows the potential of the process without considering the location of the mean.

Formula:

Cp = (USL - LSL) / (6 * σ_within)

The variation σ_within is estimated from the variation within subgroups (e.g., via R̄/d₂ or s̄/c₄).

Cpk — Critical Process Capability Index (short-term)

The Cpk value additionally considers the location of the process mean relative to the specification limits.

Formula:

Cpk = min((USL - x̄) / (3 * σ_within), (x̄ - LSL) / (3 * σ_within))

Pp — Process Performance Index (long-term)

The Pp value has the same structure as Cp but uses the overall standard deviation of all measurements instead of the variation within subgroups.

Formula:

Pp = (USL - LSL) / (6 * σ_overall)

Ppk — Critical Process Performance Index (long-term)

The Ppk value considers the location of the mean analogously to Cpk, but is based on the overall standard deviation.

Formula:

Ppk = min((USL - x̄) / (3 * σ_overall), (x̄ - LSL) / (3 * σ_overall))

Relationship of the Indices

Info: The ratio of Pp/Ppk to Cp/Cpk provides insight into process stability. The quotient Cp/Pp is sometimes referred to as an instability index. A value close to 1.0 indicates a stable process.

Assessment Table

Warning: A non-capable process (Cpk or Ppk < 1.00) means that process variation is greater than the tolerance width. In this case, parts outside the specification will be produced with high probability. Immediate corrective action is necessary.

Control Charts

Purpose of Control Charts

Control charts are an essential part of process capability analysis. They serve to visualize the process over time and to determine whether the process is statistically controlled (in control).

Info: The calculation of Cp/Cpk assumes that the process is statistically controlled. If the control chart shows systematic patterns or rule violations, the calculated capability indices are not meaningful. Stabilize the process first before evaluating capability.

Available Control Charts

my8data automatically creates the following control charts as part of process capability analysis:

Elements of the Control Chart

Each control chart contains the following lines:

• UCL (Upper Control Limit): Upper statistical limit at x̄ + 3σ
• CL (Center Line): Process mean
• LCL (Lower Control Limit): Lower statistical limit at x̄ - 3σ

Tip: Do not confuse control limits (UCL/LCL) with specification limits (USL/LSL). Control limits are calculated from the data and show the natural variation of the process. Specification limits are specified by the customer or drawing.

Interpretation

Warning: Before interpreting process capability indices, always check the control charts first. A process that is not statistically controlled does not provide reliable Cp/Cpk or Pp/Ppk values.