Machine Capability Studies: How many parts needed?

[Dawn]

I'm looking but not finding a general statement anywhere here stating exactly how many parts should be checked as a general guideline for a machine capability study. Any body?

[AJLenarz]

Hello Dawn,

The rule of thumb as stated in both the SPC manual is “25 or more subgroups containing about 100 or more individual readings give a good test for stability and, if stable, good estimates of the process location and spread”.

This can be found in SPC manual pg 31.

The PPAP manual states: “… at least 100 individual samples…”

This can be found in PPAP manual pg 6.

Dawn,

I'm not sure if you will find a definitive standard. The guidelines in the AIAG manual are at the best "adequate"

What I like to consider is the product being produced, the tools used, and cycle time. At a minimum I would consistantly graph 5 samples per subgroup during and 8 hour continuous production cycle.

This is not to mean inspect every part, just measure and plot one group and when that is done get the next 5 pieces, production continues while you are doing the study.

This is probably labor intensive but by doing it through 1 or 2 production shifts you will be able to get a handle on both random and assignable causes of variation.

ASD...

I agree that the SPC Reference Manual and the PPAP Manual quantities are pretty standard.

Here is a method based on an article called "Recent Developments in Process Capability Analysis" by Robert N. Rodriguez (JQT, October, 1992)

I'll show it in Excel format:

XX=DELTA-NORMSINV(A/100)*SQRT((1/(9*N))+(CPK^2/(2*(N-1))))

where
A is the Type I confidence level expressed as a percentage, typically 90 or 95, {0<B<A<100}. n increases as A increases.

CPK is the upper bound estimate of the Cpk, n increases as the CPK estimate increases.

DELTA is the desired resolution. Half-width of the desired one-sided lower confidence interval. n increases as DELTA decreases toward zero.

In all the above inputs, if unsure, use the more conservative value - the one that would provide the larger sample size n.

N is a proposed sample size that will be evaluated using the XX value.

Start with N = N' shown below:

N'=CEILING(NORMSINV(A/100)^2*(1/9+CPK^2/2)/DELTA^2,1)

Increase the value of N by integers until the smallest positive value for XX is obtained. The resulting N is the recommended sample size, n. Of course this assumed normality.

Typically the final number n is simply N'+1.

We typically use a minimum of 25 subgroups. Most of the customers for special machines we build ask for 25 subgroups of 5.

[Dawn]

Thanks!
If you are running a study for 8 hours, 20 hours, 24 hours, etc., is this without ANY adjustments?

Dawn,

That is with adjustments and are noted on the control chart as a reference.

ASD...

[AJLenarz]

Capability indices can be divided into two categories: short-term and long term. Short-term capability studies are based on measurements taken from one operating run (the time frame could vary depending your particular production process). The data are analyzed with a control chart for evidence that the process is operating in a state of statistical control. If no special causes are found (a machine adjustment could be considered as a special cause), a short-term capability index can be calculated. This type of study is often used to validate the initial parts produced from a process for customer submission. Another use is for machine capability studies.

Long-term capability studies consist of measurement consist of measurements that are collected over a longer period of time. The data should be collected for long enough, and in such a way, as to include all expected sources of variation.