Introduction

The spread of mass production in the previous century has necessitated the implementation of statistical methods in order to verify and control manufacturing processes. The
statistical measurement of processes provides key inputs for engineers and decision makers, that’s why Statistical Process Control (SPC) has been
elaborated during the previous decades.

In the quality management literature, the measurement and evaluation of machines and processes are called
capability studies.

Measuring the capability of machines and processes have several benefits:

- Verification of a new or modified machine / process, before serial production (to check if it is capable).
- Continuous verification of existing processes (to check if we are on the right track from capability standpoint).
- Serves as a leading indicator, forecasts trends, and provides hints where we need to intervene, what machines / processes we need to improve.
- Verification of improvements, if they are efficient enough to improve our processes.

Source: qMindset.com

Key Features

We distinguish between machine and process capability studies. Both rest on the same methodological basis,
however the intentions are different. On top of that, we also need to differentiate short-term and long-term studies.

In order to understand capability, we have to interpret some basic terms.

Capability Studies | ||

Capability study | Machine | Process |

Time-frame | Short-term (e.g. one continuous production run) | Long-term (e.g. continuous measurement of process capability in serial production) |

Aim | To reveal the machine-specific effects on the production | To discover all process-affecting factors and coefficients, that have impact on the capability of the manufacturing process |

Used for... | New machine setup and optimization | New process setup, process optimization, Statistical Process Control (SPC) |

What does an inaccurate number mean? | Your machine itself is generating unacceptable variation and it’s incapable to produce in range. | Your process is incapable due to an affecting factor (machine, material, environment, etc.) |

Influencing factors | Machine (+measurement) |
Machine Men Method Material Environment (+measurement) |

Number of values taken | min. 50 units (100 units preferred) min. 25 units if C _{mk} ≥ 2.0 |
min. 125 units (hundreds or thousands of units preferred) |

Acceptable if... | C_{mk} ≥ 1.67 |
C_{pk} ≥ 1.33 |

Used indices | C_{m} and C_{mk} |
C_{p} and C_{pk} and P_{p} and P_{pk} |

Important: as we calculate the mean of random samples, instead of calculating the mean of the whole
population, we have to use n-1 (degrees of freedom) in the denominator during the calculation of variance and standard deviation.

We have to note, that stability or capability by itself is not enough. The process needs to have both to
produce proper characteristics consistently. Features of a stable and capable process:

- Mean is at the nominal specification, with very low variance.
- No typical trend is visible (no systematic variation in the means).
- Sample variation and the variation of the total population are not different significantly.

Let’s take some examples (see chart):

Drunken bowman: he shots on the target randomly, the variation of his shots is high, and on top of that,
the location of the shots is incorrect, as he barely hits the board. He is neither capable, nor stable.

Lucky drunken bowman: although the variation of his shots is still high, somehow he hits the board every
time. He is capable, but not stable.

Skilled bowman with wrong glasses: his skill is superb, his hits are very near to each other, but because
of the distorting lens in his glasses, the shots systematically go to the upper right side of the board. He is stable, but not capable.

Robin Hood: with his perfect skill, he is able to systematically find the middle of the target. His shots
have very low variance, and the mean is exactly in the middle. He is both stable and capable.

The machine capability study is an evaluation that represents only the internal production capabilities and
characteristics of the machine (cycle time, tooling, voltage, current, etc.) without deeply considering the external influencing factors (warm-up,
environmental temperature, personnel, etc.). The intention of this short-term study is to analyze the influence of the machine-specific impacts
on the manufacturing process.

For the calculation of machine capability, we use two major indices: C_{m} and C_{mk}. Both represent the
capability of a machine, but in different ways.

Machine capability (C_{m}) is the relation between the spread of the machine and the tolerance range (e.g.
C_{m} = Tolerance / Spread). By other words, C_{m} indicates the number of times the width of the spread fits into the complete tolerance range.
It does not take into account where our distribution of data is located to the mean or upper- and lower specification limits, so even if
some of your values are near to USL or LSL, the C_{m} number remains the same.

Statistical software are calculating the spread (and pull a distribution curve over the spread) by
using the quantiles of the distribution, however a manual method is much easier and still usable. Instead of using quantiles, we simply
use the standard deviation (sigma) of the data set. By this method our formulae is the following:

C_{m} = (USL – LSL) / 6 * Ϭ, or T / 6 * Ϭ

Important: the higher your machine variation is (sigma), the lower your C_{m} will be. The higher the C_{m} is,
the more stable your process will be (from machine side).

The machine capability index (C_{mk}) not only represents the correlation between the spread and the tolerance
range, but also takes the location of the distribution into account.

C_{mk} = min [ (USL - μ) / 3 * Ϭ ; (μ - LSL) / 3 * Ϭ ]

Important: the higher your machine variation is (sigma), the lower your C_{mk} will be. On top of that, the
higher the offset is, the lower your C_{mk} will be. Offset means the distance between the middle of the tolerance range and the process mean.

The process capability study is a long-term evaluation of a process that takes all influencing factors
into account, for example:

- Machine (cycle time, adjusted parameters, warm-up time, etc.)
- Material (raw material, sub-assembly, etc.)
- Man (different operators in different shifts, different handling, etc.)
- Method (various pre-processing of part before the studied process, etc.)
- Environment (humidity, temperature, etc.).

All of these influencing factors affect the variation and stability of the process. Combining this
information with a larger sample size (long-term study), the process capability study provides a comprehensive evaluation about what we
can expect from our analyzed process.

Before calculating the process capability indices (C_{p}, C_{pk}), we should perform a study of process stability, to check the variances (sigma, means,
distribution, etc.) in sub-groups, and between sub-groups by doing F-test or
ANOVA (analysis of variances). This pre-analysis already gives us hints about the stability of the process, and we can see if there is an
external factor, which takes a higher impact on our production process. Note: the calculation of C_{m} is similar to C_{p} (so as with C_{mk} and C_{pk}) as the mathematical
background is the same, the differences are discussed in the 'Capability Studies' table in the beginning of the section.

Process capability (C_{p}) is the relation between the spread of the process and the tolerance range (e.g. C_{p}
= Tolerance / Spread). By other words, C_{p} indicates the number of times the width of the spread fits into the complete tolerance range. It does
not take into account where our distribution of data is located to the mean or upper- and lower specification limits, so even if some of your
values are near to USL or LSL, the C_{m} number remains the same.

Statistical software are calculating the spread by using the quantiles of the distribution, however a
manual method is much easier and still usable. Instead of using quantiles, we simply use the standard deviation (sigma) of the data set. By
this method our formulae is the following:

C_{p} = (USL – LSL) / 6 * Ϭ, or T / 6 * Ϭ

Important: the higher your process variation is (sigma), the lower your C_{p} will be. The higher the C_{p} is,
the more stable your process will be.

Process capability index (C_{pk}) not only represents the correlation between the spread and the tolerance
range, but also takes the location of the distribution into account.

C_{pk} = min [ (USL - μ) / 3 * Ϭ ; (μ - LSL) / 3 * Ϭ ]

Important: the higher your machine variation is (sigma), the lower your C_{pk} will be. On top of that, the
higher the offset is, the lower your C_{pk} will be. Offset means the distance between the middle of the tolerance range and the process mean.

By using a statistical software, it is very easy to calculate the Cp and Cpk values of a population (traditional spreadsheets are also usable). On top
of that, such a software supports to visualize the results and the histogram, so it helps to see through the process capability.

Having a low C_{pk} in our manufacturing affect scrap rate and defect cost. Even with a 4 sigma capable
process (which is equal to C_{pk} = 1.33), the measured characteristic will be out of the specification (tolerance range) on 63 ppm of the
products.

To keep a consistently reliable manufacturing chain, the continuous abatement of process capability
must be considered as well. What does it mean?

The variance of every process increases over time (as a Murphy law) that must be kept in bay. If a machine and a process is designed to be capable for a
6 sigma production, it does not mean, that the system will be able to keep this 6 sigma level on the long-term. Based on statistics, this shift
of process capability is estimated to 1.0 - 1.5 sigma, so a process with 6 sigma will be resulting defects on a 4.5 – 5.0 sigma level over years (see short-term and long-term adjusted sigma table).

While C_{p} and C_{pk} indices are calculated within sub-groups (e.g. consecutive measurements in one shift), P_{p}
and P_{pk} are calculated by considering an unstable process with a systematic variation (e.g. shift-to-shift or batch-to-batch process variation).
Process performance indices calculate with the overall standard deviation (sigma) of the whole data set.

Source: qMindset.com

Hints

It is very important to note, that the capability of the measuring device critically affect both machine
and process capability. Before doing a machine- or process capability study, always perform an MSA or GRR% evaluation. If the chosen device is
not capable to measure the given characteristics (due to low GRR% or low "ndc" number), it mustn’t be used, as it misleads us, resulting
unreliable C_{m}, C_{mk}, C_{p} and C_{pk} values. On top of that, your sample size has a major impact on the confidence level of the study: the higher
the sample size, the more it represents the whole manufacturing population (leads to more reliable process capability study).

It is crucial to determine the right technology and the right machine for the given process. If this is
not done right during the APQP framework, the machine capability will be low even after all possible improvements, resulting high scrap rates.
To avoid this upfront, the DMADV SixSigma methodology (Define, Measure, Analyze, Design, and Verify) is highly advised.

It may happen, that the given tolerance ranges are set much stricter, than really needed. To change the
specification, an engineering change procedure (e.g. engineering change request) must be started, with the approval of internal engineering,
and the release of the customer.

Several statistical software help us by choosing the right distribution model that fits to our process.
Otherwise it would be very difficult, and would take a long time to calculate manually. Some examples for typical distributions in a
manufacturing environment:

Source: qMindset.com

Summary

- Capability studies are analysis procedures, which are performed to measure the capability of a process or machine.
- The machine capability study is a short-term evaluation that represents only the internal production capabilities and characteristics of the machine, without deeply considering the external influencing factors.
- The process capability study is a long-term evaluation of a process that takes all influencing factors into account (man, machine, material, method, and environment).
- Capability studies give the basis of Statistical Process Control (SPC).
- Machine capability indices are C
_{m}and C_{mk}. - Process capability indices are C
_{p}and C_{pk}. - Process performance indices are P
_{p}and P_{pk}.

Source: qMindset.com

Relevant Topics

Process Control and Analysis

Measurement System Analysis (MSA)

Process Control and Analysis

Measurement Capability (C_{g}, C_{gk})

Process Control and Analysis

Gage Repeatability and Reproducibility (GR&R)

Process Control and Analysis

Attributive Repeatability and Reproducibility (R&R)

Process Control and Analysis

Attribute Agreement Analysis (AAA)

Process Control and Analysis

Statistical Process Control (SPC)

Process Control and Analysis

T-test

Process Control and Analysis

F-test

Process Control and Analysis

Analysis of Variance (ANOVA)

Process Control and Analysis

First Pass Yield (FPY) and Rolled Throughput Yield (RTY)

Process Control and Analysis

Internal Reject Rate (IRR)

Process Control and Analysis

Overall Equipment Effectiveness (OEE)

Process Control and Analysis

End of Line Test (EOL)

Audits and Release

Production Part Approval Process (PPAP)

Project Planning and Elaboration

Advanced Product Quality Planning (APQP)

Project Planning and Elaboration

Special Characteristics (SC)

Process Improvement and Problem Solving

6 Sigma / DMAIC

Fact sheet

Information about the capability studies of machines and processes.

Topic / Article: Machine- and Process Capability

Term Category: Process Control and Analysis

Business Sector: All

Timing: During process trials and serial production

Files, Attachments: None

Topic / Article: Machine- and Process Capability

Term Category: Process Control and Analysis

Business Sector: All

Timing: During process trials and serial production

Files, Attachments: None

Term Up-to-date

Knowledge Base Tags

Find all the major quality tags you are looking for (in alphabetical order).
AAA
APQP
AQL
Attributive R&R
CAPA
Containment Action
Cost of Quality
CP
CQM
CSL
DV Test
EOL
Failure Statistics
FTA
Fish-Bone (Ishikawa)
5 Whys
FMEA
FPY and RTY
F-test
Global 8D
Golden Sample
GR&R
Incoming Quality Inspection
IRR
ISIR
ISO 9000 Family
ISO 9000:2015
ISO 9001:2008
ISO 9001:2015
ISO 9004:2009
ISO/TS 16949:2009
IATF 16949:2016
Kick-Off Meeting
Limit Sample
LL
Machine- and Process Capability
Measurement Capability (C_{g}, C_{gk})
MSA
OEE
One-way ANOVA
Pareto Analysis
PDCA
PEP
Poka-Yoke
PPAP
Problem Solving
Process Audit
Product Audit
PSW
QA
QAM
QC
QFD
QI
QM
QMS
QP
Quality Basics
Quality Claim Management
Quality Review / Milestone
Ramp-Up Quality Assurance Plan
RE
Root Cause
Run at Rate
Sampling Test
6 Sigma / DMAIC
SC
SOP
SPC
SQM
Supplier Development
Trial Run
T-test
VDA Quality Standards