Process Capability Analysis Overview

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Questions and Answers

What does the Process Capability index (Cpk) measure?

  • The total variation in the output of a process.
  • The average output of a process over time.
  • The probability of a process producing defective items.
  • The consistency of a process in meeting customer specification limits. (correct)

What are the two components compared in calculating the Cpk value?

  • Process mean and specification limits. (correct)
  • Range and standard deviation of the process.
  • Mean and median of the data set.
  • Standard deviation and control limits.

Which situation indicates that a process is considered capable?

  • Variation of the process exceeds the specification limits.
  • All measurements fall outside specification limits.
  • Most measurements fall inside specification limits. (correct)
  • Control limits exceed the specification limits.

What is a key difference between Cp and Cpk?

<p>Cp measures the overall process variation, while Cpk accounts for process mean shift. (A)</p> Signup and view all the answers

What does a higher Cpk value indicate?

<p>Higher probability of meeting specifications. (B)</p> Signup and view all the answers

How is process variation represented in terms of sigma?

<p>Process spread is equal to 6σ. (C)</p> Signup and view all the answers

What significant factor is assumed when calculating Cpk?

<p>The population of data values is normally distributed. (B)</p> Signup and view all the answers

What does the rejection percentage analysis evaluate?

<p>The effectiveness of a process in producing acceptable products. (C)</p> Signup and view all the answers

What does a higher Cpk value indicate about a process?

<p>The process has a higher capability to meet specifications. (B)</p> Signup and view all the answers

Which of the following values of Cpk indicates a process that has a high percentage of rejects?

<p>0.67 (C)</p> Signup and view all the answers

How is Cpk calculated for a process with an upper specification limit (USL) of 18, lower specification limit (LSL) of 0, mean (μ) of 12, and standard deviation (σ) of 3?

<p>min[(18-12)/3, (12-0)/3] (A)</p> Signup and view all the answers

If a process is centered in its specification limits, which relationship between Cp and Cpk is true?

<p>Cp = Cpk (A)</p> Signup and view all the answers

Which situation would likely result in a higher percentage of rejects?

<p>Cpk of 0.67 (C)</p> Signup and view all the answers

In which case is the process spread greater than the specification limits?

<p>Case 3-L (C)</p> Signup and view all the answers

What will be the effect of increasing the standard deviation while keeping the mean constant in a process?

<p>Cpk will decrease. (B)</p> Signup and view all the answers

If the USL is 16 and LSL is 0, what is the Cp for a process with a mean (μ) of 8 and standard deviation (σ) of 4?

<p>0.67 (C)</p> Signup and view all the answers

Which condition must be met for the process capability index (Cpk) to be accurately calculated?

<p>The process must be in statistical control. (C)</p> Signup and view all the answers

In the Cpk calculation, which of the following values are used?

<p>The upper and lower specification limits and the mean. (A)</p> Signup and view all the answers

How does a higher standard deviation affect the capability of a process?

<p>It limits the process ability to meet specification limits. (A)</p> Signup and view all the answers

What does a Cpk value of 1.33 indicate about the process capability?

<p>The process is highly capable. (D)</p> Signup and view all the answers

If the process spread (6σ) is greater than the difference between USL and LSL, what can be inferred?

<p>The process needs improvement. (B)</p> Signup and view all the answers

What is indicated by a percentage of rejects of 0.0064%?

<p>A process that produces few non-conforming products. (A)</p> Signup and view all the answers

What happens to the process capability index if the mean moves closer to the upper specification limit?

<p>Cpk will decrease. (A)</p> Signup and view all the answers

When comparing Cp and Cpk, which statement is true?

<p>Cp measures potential capability, while Cpk measures actual performance. (C)</p> Signup and view all the answers

Flashcards

Process Capability Index

A measure of a process's ability to meet the specification limits. It's calculated when the process is stable.

Stable Process

A process that is in statistical control and predictable; variations are due to common causes, not special causes.

Specification Limits (USL and LSL)

The maximum (USL) and minimum (LSL) acceptable values for a product or process characteristic.

Cpk

A capability index that estimates the probability that a product or process characteristic will fall within the specification limits.

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Process Standard Deviation (σ)

A measure of the variability or spread of the process outputs. The smaller σ, the better.

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Out-of-Control Process

A process that is not stable and has variations due to special causes; process capability cannot be calculated.

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Normal Distribution

A common bell-shaped distribution used to model many natural phenomena, including stable processes.

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Capable Process

A process where almost all measurements fall within the specification limits.

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Cpk Definition

A process capability index measuring a process's ability to produce products within specification limits.

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Higher Cpk Value

Indicates a better process capability, producing fewer products outside the specification limits.

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Cpk = Cp

Indicates the process is centered within the specification limits.

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Process Spread (6σ)

Total variability of a process, measured as six standard deviations from the mean.

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Cpk Calculation

Calculated as the minimum of two values: [ (USL-µ)/3σ ] and [ (µ-LSL)/3σ ]. USL = Upper Specification Limit, LSL=Lower Specification Limit, µ = Process Mean, σ = Standard Deviation.

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Process Capability (Cp)

Describes the process's potential to produce within specification limits, independent of the process mean's location (centering).

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Process Control

Evaluating a process's variation over time to reduce or eliminate it.

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Process Capability

Evaluating a process's variation in relation to customer requirements (specifications).

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Process Capability Index (Cpk)

A statistical tool measuring how well a process produces output within customer specifications.

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Cpk Value

A higher Cpk value indicates a better process capability, producing fewer products outside the specifications.

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Study Notes

Process Capabilities

  • Process capability refers to the uniformity of the process.
  • Process capability analysis is an engineering study to estimate the capability of a process.
  • Variability in a process measures the uniformity of output.
  • Process control evaluates process variation over time to reduce or eliminate variation.
  • Process capability evaluates how well a process meets specifications.
  • Generally, process capability is used when a process is under statistical control.
  • Control limits are functions of natural process variability.
  • Natural tolerance limits usually represent 3σ from the mean.
  • Specification limits are determined by engineers, developers, designers, managers, clients, etc.
  • There is no mathematical relationship between control limits and specification limits.
  • Process capability indices (Cp & Cpk) are used to compare process variability to specifications.
  • Process sigma value is used to determine process capability.

Process Capability Indices (Cp & Cpk)

  • Cp assumes the process mean is at the center of the specification band. It measures potential capability.
  • Cpk measures the actual process capability.
  • Cpk considers the actual process mean position within the specification limits.
  • Cpk = min[(USL–µ)/3σ, (µ–LSL)/3σ]
  • Cp = (USL-LSL)/6σ

Major Uses of Process Capability Analysis

  • Examine if the level of quality is maintained or improved.
  • Assist in product design, selection, and modification.
  • Establish an interval between sampling for process monitoring.
  • Specifying performance requirements for new equipment or processes.
  • Select and control vendors.
  • Reduce process variability.
  • Process capability = Spread of the process = Dispersion = 6σ

When to Perform Process Capability Analysis

  • Process is in statistical control: σ and μ (or X) are constant.
  • Process is stable.
  • Data is normally distributed.
  • Calibration is done.

Interpreting Cp and Cpk

  • Larger Cp or Cpk values indicate better process quality.
  • Cp values do not change based on the process center.
  • Cpk equals Cp only when the process is centered.
  • Cpk < Cp indicates the process is not centered.
  • Cpk of 1.33 or larger is generally accepted as acceptable, indicating the process meets specification limits.

Steps to Enhance Process Capability

  • If Cpk < Cp, shift the process mean (µ) to the true center.
  • If Cpk and/or Cp < 1.33, reduce process variability (σ) and check the specifications.

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