13-Process Capability Training

8/14/2019 13-Process Capability Training

http://slidepdf.com/reader/full/13-process-capability-training 1/43

1

Supplier Quality Assurance and Management Department

Process Capability

1, Jatco Requirements

2, Cmk, Cpk, Ppk Explanation

3, Control Charts and Capability Ratio`s



2


SPC Jatco Requirements

When calculating process capability Jatco requires a 90%

confidence level.

Achievement target

Control MethodPpK Cpk

Confidence

Level

Characteristics of

Critical Parts 1.67 or higher 1.67 or higher

90%

SPCSpecial

Characteristic (S

Characteristic)1.67 or higher 1.67 or higher

Characteristic in QA

List1.67 or higher 1.33 or higher SPC

GeneralCharacteristics

1.33 or higher 1.33 or higher Check sheet,etc.



3


Process Capability

Capability Studies

A process capability study is performed for a new orchanged production process (including assembly) in order

to verify the (preliminary) process capability or

performance and to obtain additional inputs for controlling

the process.



4


Process Capability

Machine Capability Study

The machine capability study is a short-term study withthe sole aim of discovering the machine-specific effects

on the production process.

Process Capability Study

The process capability study is a longer-term study. In

addition to variation arising from the machine, all other

external factors that influence the production process overa longer operating time must be taken into account.



5


Process Capability

Stable Process

A stable (in statistical control) process is only subject torandom influences. In particular, the location and

variation of the product characteristic are stable over time.

Quality-Capable Process

A process is quality-capable when it can meet all the

specified requirements without exception.



6


Process Capability

Capability Indices Cmk, Cpk and Performance Index

Ppk The term Cpk must only be used for a stable process. A process

is stable if the following synonymous statements apply to it:

•Mean and variance are constant.•No systematic variations of the mean such as trend, batch-to-

batch variation, etc., occur.

•There is no significant difference between sample variation

and total variation.•Every sample represents the location and variation of the total

process.



7


Process Capability

If the process is not stable, one speaks of “process

performance”, and the index is called the process

performance index, Ppk .

This applies to all processes with systematic variation of

the mean such as trend or batch-to-batch variation.

It is, therefore, the process behaviour which determineswhether the index is named Cpk or Ppk .



8


Process Capability

In a machine capability study (“initial process study” or

“short term study” ), the index is always called Cmk , Cmk is understood to be an index for a short-term

capability study.

Only when sufficient data has been collected over a longer

term (e.g., as the result of a process capability study, pre-

production run with at least 125 values or evaluation of

several control charts) it is possible to calculate anddistinguish between Cpk and Ppk on the basis of the

process behaviour.



9


Process Capability

Flow Chart for Machine and Process Capability Study



10


Process Capability

Flow Chart for Machine Capability Manual Calculation Procedure

If no special software is available, m C and Cmkalso can be calculated as follows. The

mean x and the overall standard deviation s total

are calculated from the n measured values x i :



11


Process Capability

As specified at least fifty ( n = 50 ) parts should be manufactured

for a machine capability study, but use of one hundred ( n =100 )

parts is preferred. In practice, capability studies often incur high

costs due to expensive measurements. In such cases, the

following, two-stage procedure may be used to minimize cost:

Machine Capability Study with Reduced Expense

1. Of the 50 parts produced consecutively, begin the study by

measuring only every second part, i.e., parts 2, 4, 6, ..., 50. This

step yields 25 measured values per characteristic. The machine isconsidered capable if the capability index calculated from the 25

values is Cmk ≥ 2.0 .



12


Process Capability


2. If 1.67 < Cmk < 2.0 , the

remaining 25 parts must also

be measured. These results

are combined with the

original 25 measurementsand the capability index is

re-calculated. The machine

is considered capable if a

capability index Cmk ≥1.67is achieved using all 50

values.

Simplified Machine Capability

Manuafcture 50 parts in sequance and

number them in the order they where

manufactured.

Measure every 2nd part

i.e. parts # 2,4,6,.....50

Document the measurements and

Measure the parts # 1,3,5,....49 and add

the measurement values to the excisting

documented results (# 2,4,6,....50)

Cmk ≥1.67 Machine is

capable

Problem

analysis make

improvements

Cmk ≥ 2.0

yes

yesno



13


Process Capability


In special cases, it may be unavoidable to reduce the sample size

even further (regardless of the capability requirement). This may be

the case if the measurement procedure is very expensive or the test

is destructive.

Naturally, the smaller the sample size, the less accurate theconclusions (larger confidence interval of the characteristic

calculated from the sample). The Jatco SQA engineer must be

consulted before the sample size is reduced.

In such cases, the machine or process parameters should be given priority instead of the product parameters.



14


Process Capability


The process capability study is a long-term study that is conducted

over an extended operating time and includes sources of variation

external to a machine.

These sources are typically summarized under the headings of Man,

Machine, Material, Method and Environment.



15


Process Capability


A process capability study includes the following steps:

Select parts from series production in “rational” samples (not

sorted); at least 25 subgroups should be evaluated. The preferred

sample size is n = 5. Overall, at least 125 parts should be

examined.

•Measure part characteristics and record the results along with

production sequence.

•Statistical evaluation of the data: Evaluate temporal stability and

statistical distribution.

Calculate capability indices.



16


Process Capability


Note: In special cases, use of fewer than 125 parts may be

unavoidable due to time or cost of making the necessary

measurements, or if the test is destructive.

Smaller sample sizes lead to larger confidence intervals of the

characteristic(s) being studied. In turn, this reduces the accuracy

of the conclusions that may be drawn from the data.

The Jatco SQA Engineer must be consulted before the sample

size is reduced.



17


Process Capability


The random samples shall be taken from on-going production understandard production conditions (i.e. with machine broken in and

cycle time and machine adjusting parameter values as in standard

production) at regular intervals in the same size each time.

In this case, in contrast to the MCS, all effects that result from

changes in machine parameter values, tooling changes and machine

malfunctions shall be taken into consideration.

However, the measurements that are necessary for machine setup or

for a corrective measure are not taken into consideration in the PCS



18


Process Capability


When taking random samples, the measurement of the parts should be carried out as promptly as possible. However, if an

accumulation of several random samples before the measurement

recording cannot be prevented, an assignment of the parts to the

random samples in their time sequence is to be made possible.In contrast, the sampling sequence of the individual parts of a

random sample does not have to be considered.

The form of sampling sometimes carried out in practice, in which

each nth part, e.g. each 10th part, is taken from the on-going

standard production, is not suitable for the process capability

investigation.



19


Process Capability


The random sample size n must be at least 3 (recommended

size n = 5)

The random sample quantity m must be at least 6

The total random sample size should generally be m× n>125.



20


Process Capability


If this random sample size is difficult to obtain for economicor technical reasons, a smaller one is also permissible. Then

the corresponding higher limit values calculated using a 90%

confidence level using the equation below must be complied

with.

However, the effective total random sample size (without

outliers) must be at least 30.



21


Process Capability


The random sample frequency must be high enough so that at least

once, a sampling of the specified size n is carried out within a time

interval in which no systematic influences on the process are

expected, i.e. at least one random sample per

– shift and employee

– change of the machine parameter values

– tool life and

– material batch



22


Process Capability


The testing period, over which the sampling of the m random

samples extends, must contain at least the following influences

(recommended period 1 to 2 weeks):

– 3 changes of shift

– 3 changes of employees

– a change of the tooling or change of the machine parameter

values and

– a change of the material batch



23


Process Capability


Studying the Process Stability

For the stability test, “control limits” based on the normal

distribution are calculated for the means and the standard deviations

If the control limits for the means are exceeded, this shows that the process is not stable and that its position has changed systematically.

i.e. Make a control chart with the data and confirm stability.

If the process can be shown as stable then use Cp/Cpk if the process

cannot be shown to be stable then use Pp/Ppk .



24


Process Capability


Studying the Statistical Distribution A qualitative evaluation can be made and a distribution assigned

using graphic representations such as an individual value plot, a

histogram, probability plots etc. Calculating the shape parameters

(skewness, kurtosis) or performing distribution tests can act as

quantitative methods.



25


Process Capability


Calculating Process Capability Indices

If no special software is available, capability and performance

values can also be calculated as follows.

Normal distribution:

Estimating the process average.

Total Mean ( Mean of the sample means) Mean of a sample with size n (e.g. n=5)



26


Process Capability


Estimating the standard deviation of the process.



27


Process Capability


If the Process Cannot be Shown to be Stable: From the n measured values x i , the total mean x and the overall

standard deviation s total are calculated:

and with T = USL - LSL finally



28


Process Capability


6.1 Relation Between Capability Index and Fraction

Nonconforming

Most of the literature on process capability shows that there is a

direct relation between a calculated Cpk value and a fractionnonconforming,

e.g.: Cpk =1.33 corresponds to 32 ppm (one-sided).

This relation is based on the normal distribution model. If the real

characteristic distribution deviates from the normal distribution,

different fractions nonconforming normally arise.



29


Process Capability


6.1 Relation Between Capability Index and Fraction

Nonconforming

Most of the literature on process capability shows that there is a

direct relation between a calculated Cpk value and a fractionnonconforming,

e.g.: Cpk =1.33 corresponds to 32 ppm (one-sided).

This relation is based on the normal distribution model. If the real

characteristic distribution deviates from the normal distribution,

different fractions nonconforming normally arise.



30


Process Capability




31


Process Capability


Effect of the Measurement System

The measuring device and measuring procedure used to measure the

parts in the random sample are very important for evaluating the

process later on.

If the measuring device is not accurate enough or if the measuring

procedure is unsuitable, the tolerance for the production process is

reduced unnecessarily.

A large %GRR value will impair the machine and process capability

indices.



32


Process Capability


Capability ratios are statistics. All statistics will vary from sample tosample, even when the underlying process doesn't change.

We will use the data in Table below to illustrate the manner in which

capability ratios vary over time.



33


Process Capability

For the data of Table 1, the grand average is 10.084, and the average

range is 4.11. Thus, the limits for an average and range chart forthese data would be:

For subgroup averages:

X = ± A2 R- = 10.084 ± (0.577)(4.11) = 7.71 to 12.46

For subgroup ranges:

D4 R- = (2.114)(4.11) = 8.69

As may be seen in graph below the data displays a reasonable degree

of statistical control. There are no indications of anything other than

routine, common-cause variation.

C



34


Process Capability

The Specifications are 3 to 17.

With these specification limits and the summary statistics from the

control chart, the capability ratio for this bead board process would

be:

Cp = (USL-LSL)/6Sigma( X ) = (17-3)/(6.0)(1.767) = 1.32

With a grand average of 10.084, the centered capability ratio is:

Cpk = (USL- X =)/3Sigma( X ) = (17-10.084)/(3.0)(1.767) = 1.30

Today, many customers ask for Cpk of 1.33 or greater. While this

process is close, it does not quite meet this magic value.

P C bilit



35


Process Capability

The calculations were are based on 500 data, and we seldom

wait until we have so much data to compute the capability

ratios. In most cases, capabilities are computed occasionally, or

periodically, using 50 or fewer values. So we shall divide our

100 subgroups into blocks of 10 subgroups each and computethe Cpk value for each block.

P C bilit



36


Process Capability

Subgroups 1 to 10: Grand average = 10.08,

average range = 4.0, and Sigma(X) = 4.0/2.326 = 1.720The centered capability ratio is:

Cpk = (17.0-10.08)/(3.0)(1.720) = 1.34

A good capability ratio -- our customer will be pleased with this.

Subgroups 11 to 20: Grand average = 9.98, average range = 3.9,

and Sigma(X) = 3.9/2.326 = 1.677

The centered capability ratio is:

Cpk = (9.98-3.0)/(3.0)(1.677) = 1.39

Congratulations, the capability ratio got better.

P C bilit



37


Process Capability



Cpk = (17.0-10.12)/(3.0)(1.935) = 1.19

What happened to cause the capability ratio to drop?


average range = 4.2, and Sigma(X) = 4.2/2.326 = 1.806


Cpk = (17.0-10.24)/(3.0)(1.806) = 1.25

This capability ratio is still not good enough -- we must do better.

P C bilit



38


Process Capability



Cpk = (17.0-10.10)/(3.0)(2.107) = 1.09

This is worse than before.




Cpk = (17.0-10.42)/(3.0)(1.677) = 1.31

Well, this is better, but our customer is asking for 1.33 or greater.

P C bilit



39


Process Capability



Cpk = (17.0-10.30)/(3.0)(2.021) = 1.11

You were supposed to be improving -- what is going on here?




Cpk = (17.0-10.06)/(3.0)(1.634) = 1.42

At last – we`ll send this data to our customer.

P C bilit



40


Process Capability



Cpk = (9.88-3.0)/(3.0)(1.505) = 1.52

Excellent capability ratio. Good work.




Cpk = (9.66-3.0)/(3.0)(1.591) = 1.40

Why is this value slipping?

P C bilit



41


Process Capability

Of course, the real answer is that we are not slipping. The process

was not getting worse, nor was it getting better. But our statisticswere changing from block to block even though the process

remained the same, and these changes were reflected in the centered

capability ratio values computed. If we placed these 10 centered

capability ratios on an XmR chart.

P C bilit



42


Process Capability

Figure 2 shows that the routine amount of variation in capability

ratios, based upon 50 values each, will allow them to go as low as0.88 or as high as 1.72, while the process is unchanging with an

average capability ratio of 1.30.

So how can you make sense of the capability ratios? Put them on a

control chart. If this chart is out of control, you can be sure that your

process is also out of control. However, the converse is not true --

your process can be out of control and still yield a control chart for

capability ratios that is in control.

Wh SPC




Data Driven Decision Making

However it is not always practical to have the

amount of data that will allow us to have this in

depth analysis of the process capability before

SOP

Therefore this analysis needs to be done after we

have enough data over a reasonable time period.The Jatco Safe Launch Plan allows us to make

this analysis.

Why SPC

Documents

13-Process Capability Training