Process capability

Process capability is combined by two words. Process is "one or more actions or operations planned, executed and evaluated to achieve a stated goal" and capability is "the degree to which the process achieves the stated goal". So process capability is statistical measurable property of a process to the given specification.

Measuring Process Capability

Voice of the process (VOP) is random behavior of process. Voice of the customer (VOC) is what customers need and what they expectate for the result of the process. VOP and VOC speak in other languages. VOP knows what it produces and this is random variation. VOC consists of histograms, data and probability models which predict future behavior of process. Process capability tools interpret VOP and VOC. Process capability study estimates variation of a process and decide if it is capable of meet the targets specifed by customer. To set compartment we use LSL and USL. LSL is Lower Specification Limit. USL is Upper Specification Limit. When random variation of process is contained in this compartment we can say process is capable .

Process Capability Indices

Measures of process capability is Process Capability Indices (PCIs). Now popular is capability ratio (CR). To calculate CR we just need to calculate C_p. Estimate C_p to show where process be centered between specification. We can also calculate other indicators. For example, estimate process capability with the lower limit only or upper limit only, process capability around a target (T). C_pk is centralized indicator, but both of them shows how close you are to your average performance. Process capability is strong related with Process Performance:

• C_p : $C_{p}={\frac {USL-LSL}{6\sigma }}$

Generally accepted minimum value for C_p is 1, but expected is 1,33. Larger value is better. Then we can say process is capable. At the value 1 process yield is 99,7%, but at the value 1,33 process yield is 99,99%. For example, at the value 0,5 process yield is only 86,8%. We must remember that C_p can be not centered between users requirements.

• C_pk : $C_{pk}=min[{\frac {USL-\mu }{3\sigma }},{\frac {\mu -LSL}{3\sigma }}]$

Interpretion for C_pk is such as for C_p, but C_pk is centered indicator. When C_pk is 1,33 or more is capable and meets specification limits.

• C_pm : $C_{pm}={\frac {C_{p}}{\sqrt {1-({\frac {\mu -T}{\sigma }})^{2}}}}$

C_pm at least 1 is good and 1,33 expected. Is related to C_p. It shows potential gain to be obtained by move mean closer to target. Target can be not centered between users specifications.

• C_pmk : $C_{pmk}={\frac {C_{pk}}{\sqrt {1-({\frac {\mu -T}{\sigma }})^{2}}}}$

C_pmk at least 1 is good and 1,33 expected. Is related to C_pk. Interpretation is such as for C_pm, but with the difference C_pmk is centered between users requirements.

• C_{p lower} : $C_{pu}={\frac {\mu -LSL}{3\sigma }}$

C_{p lower} etimates capability for requirements that consist with lower limit only. With C_{p upper} is a component of C_pk.

• C_{p upper} : $C_{pl}={\frac {USL-\mu }{3\sigma }}$

C_{p upper} etimates capability for requirements that consist with upper limit only. With C_{p lower} is a component of C_pk.

Where:

• LSL - Lower Specification Limit
• USL - Upper Specification Limit
• $\sigma$ - standard deviation
• $\mu$ - mean

Assuming that the distribution is approximately normally distributed.

Examples of Process capability

• Process capability of a manufacturing system: Process capability of a manufacturing system is the ability of the system to produce a product that meets the customer's requirements. It is measured by comparing the performance of the system to the customer's desired outcome.
• Process capability of a software system: Process capability of a software system is the ability of the system to meet the customer's requirements in terms of functionality, performance, scalability and security. It is measured by comparing the performance of the system to the customer's desired outcome.
• Process capability of a customer service system: Process capability of a customer service system is the ability of the system to respond quickly and accurately to customer inquiries. It is measured by comparing the performance of the system to the customer's desired outcome.

Advantages of Process capability

Process capability has several advantages that are beneficial for the process. Some of the most important advantages include:

• Improved efficiency - Process capability helps identify areas of a process where improvements can be made, allowing for a more efficient use of resources.
• Improved quality - By understanding the capability of a process, companies can identify areas where quality can be improved, leading to a reduction in defects.
• Improved customer satisfaction - Knowing the capability of a process allows companies to better meet customer expectations, leading to improved customer satisfaction.
• Reduced costs - By better understanding the capability of a process, companies can reduce costs associated with production, resulting in cost savings.
• Increased visibility - Process capability provides companies with more visibility into their processes, allowing them to better monitor and analyze performance.

Limitations of Process capability

• Process capability does not provide any information about the stability of the process. It only measures the capability of a process to produce output within given limits.
• Process capability does not provide any insight into the causes of variation in the process. It only measures the product or process performance relative to given specification limits.
• Process capability does not guarantee that every output of the process will be within specification. It only shows how well the process is performing on average.
• Process capability does not take into account the cost of attaining the specified output and thus does not consider the economic aspect of the process performance.

Other approaches related to Process capability

• Statistical Process Control (SPC): SPC is a method used to monitor the production process, allowing for the early detection of any potential issues or defects. It uses statistical techniques to monitor the output of a process and detect any patterns of variation that may indicate a defect or issue.
• Design of Experiments (DOE): DOE is an approach used to identify the most important factors that affect a process and determine the optimal levels for these factors. It is used to improve the quality and efficiency of a process by optimizing the inputs.
• Root Cause Analysis (RCA): RCA is a method used to identify the underlying cause of a process issue. It involves gathering data, analyzing it, and determining the root cause of the issue.
• Six Sigma: Six Sigma is an approach used to achieve process excellence. It focuses on identifying and eliminating defects, improving process efficiency, and reducing variation in processes.

Summary: Other approaches related to process capability include Statistical Process Control, Design of Experiments, Root Cause Analysis, and Six Sigma. These approaches are used to identify and eliminate defects, improve process efficiency, and reduce variation in processes.

Footnotes

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Process capability — recommended articles

Process performance — Capacity analysis — Overall equipment effectiveness — Quality loss function — Statistical process control — P chart — Genichi Taguchi — Control chart — Activity measure

References

• Hawley G. O., (1962). Reliability Through Process Capability Studies, Sandia Corporation, p. 1-5
• Kortz S. and others, (1993). Process Capability Indices, CRC Press
• Pearn W. L. and others, (2006). Encyclopedia And Handbook Of Process Capability Indices: A Comprehensive Exposition Of Quality Control Measures, World Scientific
• Polhemus N. W., (2017). Process Capability Analysis: Estimating Quality, CRC Press
• Relyea D. B., (2011). The Practical Application of the Process Capability Study: Evolving From Product Control to Process Control, CRC Press
• Sleeper A., (2005). Design for Six Sigma Statistics, Chapter 6 - Measuring Process Capability, McGraw Hill Professional, p. 319-325.

Author: Adam Widła