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Since a process capability is null and void unless the process is stable and in control, always look at the  control charts, (X Bar and R Bar), first. Once statistical control is established, then the histogram and process capability may be analyzed properly. What is considered ‘stable and in control’ becomes another issue.

Interpreting the Histogram

If your data is from an even and symmetrical distribution, such as the proverbial ‘Normal Distribution’, the data will be evenly distributed around the center of the mean. If the data is not roughly evenly distributed around the center or mean of the Histogram, it is called ‘skewed’. If it appears skewed, you should understand the cause of the ‘skewness’.

If several peaks occur in the distribution, look for the possibility that the data is coming from two different sources, such as two separate production lines, or two different people.

How Assembly Yields Are Affected by Process Shifts

By looking at the yield tables below, you can see how just shifting the distribution one sigma can impact the yield. Also see RTY – Rolled throughput yield.

Overall Yield per Specification

Distribution Centered

# of parts +/- 3 Sigma +/- 4 Sigma +/- 5 Sigma +/- 6 Sigma
10 97.33% 99.94% 99.9994% 99.999998%
20 92.74 99.87 99.9989 99.999996
30 92.21 99.81 99.9983 99.999994
40 89.75 99.75 99.9977 99.999992
50 87.36 99.68 99.9971 99.999990
60 85.03 99.62 99.9966 99.999988
70 82.76 99.56 99.9960 99.999986
80 80.55 99.49 99.9954 99.999984
90 78.40 99.94 99.9948 99.999982

Distribution Shifted One Sigma

# of parts +/- 3 Sigma +/- 4 Sigma +/- 5 Sigma +/- 6 Sigma
10 79.42% 98.66% 99.968% 99.9997%
20 63.07 97.33 99.937 99.9994
30 50.09 96.03 99.905 99.9991
40 39.78 94.74 99.873 99.9989
50 31.59 93.47 99.842 99.9986
60 25.09 92.21 99.810 99.9983
70 19.93 90.98 99.779 99.9980
80 15.82 89.75 99.747 99.9977
90 12.57 88.55 99.715 99.9974

Interpreting the Capability Indices

Compare the abnormal and normal indices. Capability indices are quite sensitive to assumptions of the distribution.

A Capability index is a statistic, subject to statistical error.

Most Engineers or Black Belts consider a capable process to be one that has a Cpk of 1.33 or better, and a process operating between 1.0 and 1.33 is "marginal." Many companies now suggest that their suppliers maintain even higher levels of Cpk.

A Cpk exactly equal to 1.0 would imply that the process variation exactly meets 3 Sigma. A Cpk exactly equal to 1.33 would imply that the process variation exactly meets 4 Sigma. If the process shifted slightly, and the out of control condition was not immediately, if not sooner, detected, then the process would produce scrap. This is the reason for the extra .33. It allows for some small process shifts to occur that could go undetected. The Table located here, provides an indication of the level of improvement effort required in a process to meet these escalating demands, where "PPM Out of Specification" refers to the average defect level measured in parts per million, (PPM).


Using Defects Per Unit To
Benchmark Different Products

  • Given equivalent design margins and levels of process control, DPU is proportional to parts count.

  • Therefore, we can benchmark different products if we know (or can estimate), DPU and parts count.

  • We normalize products with different parts count by calculating PPM/part

PPM/part = DPU
————————
Parts Count

To achieve this in six sigma, you can use our free software.

Also see DPO, (defects per opportunity), and DPMO, (defects per million opportunities).

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Last Updated: Saturday, 10-Jun-06 15:50:57 PDT

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