The process capability indices (PCIs) are used to evaluate and monitor the process of manufacturing industry. The PCIs that used in the manufacturing industry are , , and . The machine capability is calculated by and which is in short period. The PCIs are important in manufacturing industry.
Keywords. Process capability indices; Machine capability.
A process in the manufacturing industry is very unique because the process needs the linkage of manpower, raw materials, machines, and methods. The linkage are the variation of the process that are hard to control. In order to improve the quality level of products, the capability of the process plays an important role in the manufacturing industry. Rezaie, K. 6. The process capability indices (PCIs) is also known as process capability analysis which is widely used in manufacturing industry. The PCIs is used to measure the ability of the process to meet the requirements of the customers which are also known as specification limits. The analyst used PCIs to evaluate and monitor the performance of the process in the manufacturing industry. Besides, the PCIs can use to improve the performance of the process by reducing the variation of the process. JH, S. et al. 3.
The process capability analysis can be presented graphically by using histogram and probability plot. Montgomery, D. C. 5. The graphics can determine whether the process is within specification limits (SLs) or not. Steiner, S. et al. 9. The histogram is the easiest and clear method to determine the performance of the process. If the process is in control and the data is normally distributed, the potential capability analysis can be used to improve the quality of the process. Spano, A. 8. By referring to the histogram, we can determine whether the process is off centering or not. The PCIs is used to compare the output of in control process with the SLs by 6 sigmas. PCIs are quantitative measures based on the performance and potential of the process. By doing so, the process can meet the requirements of the customers. Rezaie, K. et al. 6.
The process of the manufacturing industry is considered as capable when the process is under control. Spano, A. 6. The automotive industry was applying the PCIs in Japan and United States (US). The process capability with sampling properties and estimation procedures is measured to determine the normality of the process and the process is in statistical control or not. Kane, V.E. 4. The PCIs had been used in manufacturing industry in quantitative form to ensure the performance of the process. The numerical data will help the person in charge can modify the process by using more efficient methods. The cost spent in the process of rework and scrap will cause the loss of the industry. Hence, the high-quality production should practice in industry and try to meet the requirements. JH, S. et al. 3. The PCIs is the best method to maintain the quality of the product.
According to the requirements of the customers with the costs that needed to spend by the suppliers, the suppliers still need to set the suitable cost for their product and ensure that the products are under tolerance limits. If the process capability of the process is under control by the suppliers, we can try to improve the quality of products or the process by out of control action plan (OCAP). The process capability indices can help to analyze the capability and try to predict the machining process that can meet the expectations and tolerance limits of the customers. The process capability indices consist of , , and . Abhijit S. et al., Montgomery, D. C. 1, 5. The value will represent the performance of process. Table 1 summaries the six quality condition with its value. ?hsan K.2. The different value will represent different quality condition.
Table 1: Quality conditions and value
1.67 ? ? 2.00
1.33 ? ? 1.67
1.00 ? ? 1.33
0.67 ? ? 1.00
In manufacturing process, value is used to identify the variation of the characteristics of the product within SLs that set by the engineers or the designer. Rupesh C. et al. 7. Although many manufacturing industry had use value to determine the process capability of the process, but value cannot used to determine whether the process is off-centering and we do not know the actual performance of the process. Thus, the value is used to indicate that the process is in the SLs. The and always used in manufacturing industry in order to determine the number of the product that within the specification limits and ensure the process is well perform. ?hsan K.2. and have the same statistical properties. Since the consists of the and , most of the manufacturing industry will used instead of and .
The value widely used in manufacturing industry. The value can assume the normality and independency of the target value, T. If the sampling distribution had skewed slightly or off center slightly, the process can still considered as capable. Zhang, N. F. et al. 10. Since there are many manufacturing industry had uses the process capability, there are many study that try to use the capability indices to determine the performance of machining process. More undertakings have been given to utilizations and investigations of process capacity indices. Abhijit S. et al., JH, S. et al., Rezaie, K. et al. 1, 3, 6. In the future, the manufacturing industry might implement the capability indices to determine machining process performance.
Process Capability Indices
In the manufacturing industry, the PCIs are used to monitor the capability of the process. The , , and will relate with the process parameter that set by the industry. The PCIs always used in assessing and predicting the process performance. The PCIs provide the measurements in numerical value which can help to improve the quality of products and process easily.
1. The estimated standard deviation
The true standard deviation in a production process is always unknown. The value is always replaced by the value from the sample measurement. The value is calculated by using the equation below:
= Average of range
= Factors of center line
The function of is depend on the sample size of the process and the value of can determine by referring the Appendix VI. Montgomery, D. C. 5. The value is used when calculating the and value.
2. The value
The main reason for using value to assess the process ability to produce products with small amount of variation. The 6? is the natural tolerance of the process. The value can determine whether the manufacturing industry produce the defect items or not. The quality of the product can be maintained by industry as long as the process is statistically in control. If the process is out of control, the OCAP can be taken by manufacturing industry. The higher the value of , the higher the quality condition of the process. The estimate of the value is calculated by using the equation below:
3. The value
The main reason for using value to assess the process ability to produce products that within the SLs. The is calculated by setting the 3? between the average of the process and the closest SLs. The is determined by the minimum value of and . The value can determine the whether the industry produce the products within SLs or not. The value should closer with value because the process should not far from the target value. The value is calculated by using the equation below:
One-sided process-capability ratios for upper specification limit
One-sided process-capability ratios for lower specification limit
µ = Mean
Results and Discussion
Process not capable change tool or adjust for good accuracy.
The process is capable but average need to be adjusted.
The process capable and well adjusted.
Figure 1: The relation between and
Figure 1 is about the relation between and . JH, S. et al., Rezaie, K. et al. 3, 6. The process in manufacturing industry is considered capable if the value is equal to 1. The value should as high as possible. This is because the higher value means the variation of the process is lower. In manufacturing process, the variation of the process must be reduced in order to produce the products with constant quality level. If the value for a process is greater than 2, we can considered the process that undergo by the manufacturing industry is qualified as six sigma process. The value can only determine the variation of the process but value cannot ensure the production of the process is within the SLs. If the process is not centering, the process is considered faultily.
In order to ensure the process of the manufacturing industry is in good condition, the value is calculated. The process is consider as capable as the process is within the SLs and value must larger than 1 in manufacturing sector. If the value is equal to 1, the manufacturing industry will accept 99.73% of the product. The higher value, the process distribution become narrower. In the manufacturing industry, the quality of the products need more uniform and within the SLs. Hence, the value is considered a good measurement in manufacturing industry because it can ensure the quality of products are always within the expectation of industry. If the value is greater than 3, most of the manufacturing industry will do nothing because the process is very capable.
If the value is equal to value, the process will considered centralized. In most of the manufacturing industry, the value will not exactly equal to value. Some of the manufacturing industry will set minimum value for and as 1. Actually, and value should be more than 1.33 which means the process of the manufacturing industry is satisfied. The value will never higher than value. If the value is slightly lower than value, the process is still acceptable for manufacturing industry. The and value is important to determine the process capability in the manufacturing industry.
Figure 2: Ishikawa diagram
The environment of manufacturing sector will affect the capabilities of the process in a long period. The machine capability will not consider whether the machine is in control or not as the problems of the machine can determine by the control chart. However, the machine capability cannot use to predict the status of the process in long-term by short-term sampling plan. Thus, the capability of the machine is not suitable calculated in a long period.
Generally, the machine capability is used plus and minus three standard deviations (± 3 ). This is the baseline for the manufacturing process. By using the machine capability, the manufacturing industry can determine the condition of every single machine. The machine capability is similar with PCIs. The machine capaility incides are variation of the machine itself. The calculation for is represent while represent . Hence, the value is used to determine the capability of the process while the value is used to determine the capability of the machine.
There are some elements which will cause the variation of the process which is shown in Figure 2. All of the variation that mentioned in Figure 2 might influence the outcome. The machine capability we only determine the dependency and the centering of the machine parameters. JH, S. et al., Rezaie, K. et al. 3, 6.
The process capability indices can use in the manufacturing industry to ensure the process capability. The process capability indices can ensure the products is within the specification limits. If the products do not meet the specification limits, the corrective actions can be taken. Hence, the quality of the products can be maintained in a uniform manner. Besides, the manufacturing industry can use the process capability indices to monitor the process. The quality of the products can be improved. The machine capability needed to calculate in short term. The variation of the process should be eliminated. The overall process of the manufacturing industries can be maintained or even improved.
The author very appreciates the referees because the information and knowledge they gave are very useful in order to accomplish this paper.
1. Abhijit S., & Himadri M. (2016). Process analysis and optimization in turning of ATSM A36 through process capability index, Journal of King Saud University - Engineering Sciences.
2. ?hsan K. & Cengiz K. (2011). Process capability analyses based on fuzzy measurements and fuzzy control charts. Expert Systems with Applications, Vol. 38, Issue 4, 3172-3184.
3. JH, S., & Katikar, R. S. IMPORTANCE OF PROCESS CAPABILITY AND PROCESS PERFORMANCE INDICES IN MACHINE TOOL.
4. Kane, V. E. (1986). Process capability indices. Journal of quality technology, 18(1), 41-52.
5. Montgomery, D. C. (2007). Introduction to statistical quality control. John Wiley & Sons.
6. Rezaie, K., Ostadi, B., & Taghizadeh, M. R. (2006). Applications of process capability and process performance indices. Journal of applied sciences, 6(5), 1186-1191.
7. Rupesh C., & Jatinder K. (2014). Process Capability Analysis and Optimization in WEDM of Commercially Pure Titanium, Procedia Engineering, Vol. 97, 758-766.
8. Spano, A. (2012). Process Capability Analysis.
9. Steiner, S., Abraham, B., & MacKay, J. (1997). Understanding process capability indices. Institute for Improvement of Quality and Productivity, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1.
10. Zhang, N. F., Stenback, G. A., & Wardrop, D. M. (1990). Interval estimation of process capability index Cpk. Communications in Statistics-Theory and Methods, 19(12), 4455-4470.