# PROCESS CAPABILITY

20/08/2021

**Overview**

This blog is to provide basic concepts and points to consider for evaluating process capability to prove that a manufacturing process has the ability to consistently achieve intended quality levels, and for taking actions to the outcome of such evaluation.**Purpose**

Based on the results of the process capacity calculation, the manager can know whether the production stages are stable, an d the current quality is good or not good.**Terms and definitions**

No. |
Term |
Definitions |

1 | Process capability | The ability to achieve quality requirements of a process in a controlled state. |

2 | Process capability index | A quantified measure of process capability, and “a value calculated by dividing the specification range by 6σ for a certain characteristic” ”Process in a controlled state” in the definition above for process capability means that the characteristic value is normally distributed, and this forms the basis of the process capability index. |

3 | Standard deiviation | One of the numeric values which correspond to the distribution of statistical values and random variables, and expressed by σ. 6 σ represents the value of σ (standard deviation) multiplied by six times. |

**Requirements**

*1. Concept of Process Capability*Process capability is the ability of a stable process to achieve the required quality, and which is expressed by X±3σ representing the distribution range of dispersion of product quality produced by a standardized process.

σ：Standard deviation

n：Number of data

：Individual data

: Mean value of individual data

*2. Process Capability Index.*Process capability index is expresses as Cp (an index used when the center (= average) of the distribution of data plotted at the median between the upper and lower limits) or Cpk (used when the mean is displaced from the center between the upper and lower limits).

*(The “k” in Cpk stands for “Katarori” in Japanese language for shift or offset.)*

- Process Capability Index (Cp)

· If Cp ≧ 1.67, the process capability is perfect, almost no nonconforming products will be produced. (99.999945% or more products are within the specification range), (~0.6 PPM defective products).

· If 1.67> Cp ≧ 1.33, the process capability is almost perfect, almost no nonconforming products will be produced. (99.9937% or more products are within the specification range), (0.6~63 PPM defective products).

· If 1.33 > Cp ≧ 1.00, the process capability is not considered adequate, however almost no nonconforming products will be produced. (99.732 % or more products are within the specification range), (~63~268 PPM defective products) .

· If 1.00 > Cp ≧ 0.67, the process capability is not good, (99.597% or more products are within the specification range, (~268~443 PPM defective products).

- Process Capability Index (Cpk)

which takes deviation into consideration.

Take appropriate action for the mean value to be the center of the specification limits if the mean is shifted from the center.

*3. Calculation of Process Capability Index*· When the measurement parameter has upper limit and lower limit

When K ＞1, is outside the upper or lower limit.

When the median value equals to , K = 0.

· When the measurement parameter has only the upper limit.

· When the measurement parameter has only the lower limit.

*4.*

*Process Capability Judgment and Measures*Following examples demonstrate the determination process capabilities by the process capability based on the process capability index and subsequent responses.

Relationship between distribution & specifications |
Cpk | Judgment | Estimated percent defective |
Measures | ||

Cpk ≥1.67 | Perfect | 0.6 PPM | Inspection method: 100% inspection or sampling inspection. Slight increase in product dispersion is of no concern Consider simplification of control, reduction of costs, etc. |
|||

1.67 > Cpk ≥ 1.33 | Good | 0.60~63 PPM | Inspection method: 100% inspection or sampling inspection. This is the ideal state, so it is maintained. |
|||

1.33 > Cpk ≥ 1.00 | Process capability is not sufficient. |
63~268 PPM | Inspection method: Sampling tests are completed and no nonconformity is found, or a procedure is employed to take retroactive action for the possible nonconforming product lot before dispatching from the supplier. Process improvement is required until a Cpk of 1.33 is achieved. Maintain the process in a controlled state. |
|||

1.00 > Cpk ≥ 0.67 | Process capability is insufficient. |
268~443 PPM | Inspection method: determine whether or not the lack of process capability is due to a displacement of the median or dispersion. Investigate and take measures. |

*5. Key Points for process capability*a) Correct sampling: points to estimate the characteristics of the general population are as follows.

- Random sampling = do not use data collected only under the same conditions.
- Measurement accuracy= calculate to one more decimal place than the specification value.
- Avoidance of factors causing problems = obtain data from the condition in which problem factors do not exist.
- Clarify the definition of the lot and comprehend lot-to-lot dispersion. Check at least 3 lots and determine the acceptance by increasing n.

- Confirm data distribution and its shape (on a normal distribution)

- Check dispersion from the median with Cpk.
- Use sufficient quantity of n. If n is small, it is important to take into account that the reliability of data may be reduced when making the judgment (increase

or adjust the number of n, if it is very close to 1.33).

- When determining process capability based on data analysis, judgment shall be made taking into consideration the preceding sections a) and b) Where

conditions affecting results are under control, it can be said that a process has an acceptable process capability if manufacturing output is confirmed to be within the specification range even if conditions are slightly deviate from the upper and lower limits. - Condition setting with appropriate allowance backed by data is important.

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