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Process Capability

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‼ Content• Definition: Process Capability• Where Capability Analysis can we used• Process capability study• Why should I know the capability of my process• Why should I know the capability of my supplier process• Definition of Capability Indices• Process control Vs Process capability• How to calculate capability indices• Relation between capability indices value and sigma value• Need for calculating Process capability• Difference between Cp and Pp• Uses of Cp and Pp• Difference between Cpk and Ppk • Uses of Cpk and Ppk• Can Cpk or Ppk be Negative? What does a negative Cpk or Ppk indicates ?

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Definition:- Process Capability “ Process Capability is the measured, inherent variation of the product turned out by a process”.

In the Definition of Process Capability 1.) PROCESS REFERS to some unique combination of machines, tools, methods, materials & people engaged in production. It is often feasible & illuminating to separate & quantify the effect of the variables entering this combination.2.) CAPABILITY REFERS to an ability, based on tested performance, to achieve measurable results.3.) MEASURABLE CAPABILITY REFERS to the fact that process capability is quantified from data that , in turn, are the results of measurement of work performed by the process.4.) INHERENT CAPABILITY REFERS to the product uniformity resulting from a process that is in a state of statistical control “instantaneous reproducibility” is a synonym for inherent capability.5.) PRODUCT is measured because product variation is the end result.

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‼ Examples Where Capability analysis can be used :

• Process that is not centered

• Process with large variability

• One-sided specifications

• Setting/confirming customer specifications

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‼ Process Capability Study

• Process capability study is a scientific and a systematic procedure that uses control charts to detect and eliminate the unnatural causes of variation until a state of statistical control is reached.

• When the study is completed, you will identify the natural variability of the process.

The objective is to get as close to the theoretical best that your process can achieve by eliminating special causes of variation, so that only common (natural) causes are acting on the process, and then to reduce these to a minimum, whenever possible.

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‼ Why Should I Know the Capability of My Process

• It allow one to summarize process capability in terms of meaningful percentages and metrics.

• To predict the extent to which the process will able to hold tolerances or customer requirements. Based on the law of probability ,you can compute how often the process will meet the specifications or the expectations of your customer.

• It helps you choose from among competing processes, the most appropriate one for meeting customers expectations.

• Knowing the capability of your processes, you can specify better the quality performance requirements for new machines, parts and processes.

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‼ Why Should I Know the Capability of My Supplier’s Process

To set realistic cost effective part specifications based upon the customer's needs and the costs associated by the supplier at meeting those needs.

To understand hidden supplier costs

To be pro-active.

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‼ Definition of Capability Indices

• A process capability index is a numerical summary that compares the behavior of a product or process characteristic to engineering specification.

• These measure are also often called capability or performance indices or ratios

• A capability index relates the voice of the customer (specification limits) to the voice of the process.

• A Large value of the index indicates that the current process is capable of producing parts that, in all like hood, will meet or exceed the customer’s requirements.

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Process control Process Capability

Out of Control(Special Causes Present)

In Control(Special Causes Eliminated)

TIME (continued below)

In Control but not Capable(Variation from Common Causes Excessive)

In Control and Capable(Variation from Common Causes Reduced)

TIME (continued from above)

Lower Spec LimitUpper Spec Limit

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It is the ratio of the specification

width to 6 x process standard deviation

‼ How to Calculate Capability Indices

Cp, Pp is a measure of a process’s ability to meet a specification (or it is a measure of a group of items’ nearness to the target value).

Cp = USL-LSL 6sP

Pp = USL-LSL 6sT

Cp, Pp compares specification range (tolerance) to process width regardless of where the process is centred.

The formula for calculating Cp, Pp is as follows:

(Upper specification limit-Lower specification limit)

6ϭCp=

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Cpk, Ppk measure how close the process centre is to the nearest customer spec.

It is (difference between the process average and the nearest specification)(3 x the process standard deviation).

• The Cpu index is the position of the total process variation (6ϭ)in relation to the upper specification limit.

• The CPU index is the position of the total process variation (6ϭ) in relation to the lower specification limit. Cpu and Cpl are defined with the following equations:

X

USLLSL

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Cpk = min {Cpkl, Cpku}Cpkl -LSL 3sP

Cpku USL- 3sP

Ppkl -LSL 3sT

Ppku USL- 3sT

Ppk = min {Ppkl, Ppku}

Cpu = Cpl = Cpk = Cp

=

=

=

=

Only when the process is centered about the target Value.

Cpkl = (Process Mean – LSL)/(3*Standard Deviation)Cpku = (USL – Process Mean)/(3*Standard Deviation)

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Cp Cpk Pp Ppk Sigma

Red (Bad) < 1.00 < 1.00 < 1.33 < 1.33 < 4.5

Yellow (OK) 1.00 - 1.33 1.00 - 1.33 1.33 - 1.67 1.33 - 1.67 4.5 - 5.5

Green (Good) > 1.33 > 1.33 > 1.67 > 1.67 > 5.5

(Cpk x 3) +1.5 = sigma

‼ Relation between Capability Indices Values and Sigma Value

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• The automotive industry standard QS-9000 mandate the use of capability indices, but state the capability requirements in an overly complex and confusing way.

( Automotive industry action group (AIAG),1995 state, in part :

“Ongoing process performance requirements are defined by the customer. If no such requirements have been established ,the following default values apply:

• For stable processes and normally distributed data, a Cpk value ≥ 1.33 should be achieved.

• For chronically unstable processes with output meeting specification and a predictable pattern, a Ppk Value ≥ 1.67 should be achieved

‼ Need for Calculating Process Capability

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Results Interpretation

Pp and Ppk > 1.67The process probably meets customer requirements. After approval, begin production and follow the approves control plan.

1.33 ≤ Ppk ≤ 1.67The process may not meet customer requirements .after part approval, begin production with additional attentions to the characteristics until an ongoing Cpk ≥ 1.33 is achieved.

The process is substandard for meeting customer requirements .process improvement must be given high priority and documented in a corrective action plan. Inspection or testing is required until an ongoing Cpk of 1.33 is demonstrated.

Ppk < 1.33

Continue…

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‼ Difference Between Cp and Pp

• The Biggest difference between Cp and Pp is how the standard deviation is determined, Pp we Use sampling and have to calculate an estimated standard deviation of the sample.

• In Cp we are assuming a stable process and will likely have enough data to calculate a true standard deviation.

‼ Uses for Cp & Pp

•Used to see if a process is capable.

•Neither are concerned with centering. Cp or Pp takes into account dispersion, NOT centering. Since Cp does not consider process centering so it cannot be used to determine if a process is acceptable.

•Cp & Pp are NOT concerned with the control of a process. The term “control” infers an element of time and Cp or Pp is merely a snapshot of the process variation at a given point in time.

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•Both indices are larger-is-better quality characteristics•Can never be 0.

•If Cp or Pp >1, Tolerance is > spread, Process has potential to be capable (depending on centering).

• A CP of >1 doesn’t mean quality One could have a Cp of 2 and be producing 100% defects, because the process was not centered within the specification limits.

•If Cp or Pp <1 process spread is > tolerance, and the variation will never fit and the process will never be capable.

•A Cp of < 1 does NOT indicate a process is out of control. “Control” is controlling variation over a period of time

•If 0< CP <1, then the specifications are that percentage of the process.• Ex. Cp 0.70 = 70%. A Cp of 0.70 means the specifications are 70% of the process.

 

Continue…

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‼ Difference Between Cpk and Ppk

• Cpk and Ppk are ways to measure the capability of a process because they are monitoring indices for process centering.

‼ Uses for Cpk & Ppk: Is The Process Acceptable?

• Cpk or Ppk takes into account centering and thus can be use to determine if a process is acceptable.

• Ways to measure the capability of a process.

• Reflect the actual performance of the process.

• Both Cpk and Ppk can be a negative numbers. It means that, on average, the process is not meeting customer requirements.

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‼ When to use Cp, Cpk, Pp, and Ppk

New process or process not under statistical control

Existing process under statistical

controlMeasure of spread

‘Fit’Pp Cp

Measure of Centering Ppk Cpk

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‼ Can Cpk or Ppk be Negative? What does a negative Cpk or Ppk Indicate?

• Yes, it is possible for Cpk and Ppk to be negative. Let’s look at the equation – for simplicity we will use the Ppk.

• It is impossible to have a standard deviation be negative so that would mean that x(bar) was larger that the Specification Limit.

• In other words, the process average is out of specification.

• This could be an indication that the process mean has drifted over either the upper specification or the lower one.

• This is not good because it means that the process is not meeting customer requirements.