Statistical process control charts, such as the , R, S2, S, and MR charts, have been widely used in the manufacturing industry for controlling/monitoring process performance, which are essential tools for any quality improvement activities. Those charts are easy to understand, which effectively communicate critical process information without using words and formula. In this paper, we introduce a new control chart, called the Cpp multiple process performance analysis chart (MPPAC), using the incapability index Cpp. The Cpp MPPAC displays multiple processes with the departure, and process variability relative to the specification tolerances, on one single chart. We demonstrate the use of the Cpp MPPAC by presenting a case study on some resistor component manufacturing processes, to evaluate the factory performance.
Process capability indices (PCIs) have been widely used in various manufacturing industries, to provide numerical measures on process potential and process performance. The two most commonly used process capability indices are Cp and Cpk introduced by Kane [1]. These two indices are defined in the following:
where USL and LSL are the upper and the lower specification limits, respectively, μ is the process mean, and σ is the process standard deviation. The index Cp measures the process variation relative to the production tolerance, which reflects only the process potential. The index Cpk measures process performance based on the process yield (percentage of conforming items) without considering the process loss (a new criteria for process quality championed by Hsiang and Taguchi [2]). Taking into the consideration of the process departure (which reflects the process loss), Chan et al. [3] developed the index Cpm, which measures the ability of the process to cluster around the target. The index Cpm is defined as:
where T is the target value, and d=(USL−LSL)/2 is half of the length of the specification interval (LSL, USL).
Based on the index Cpm, Greenwich and Jahr-Schaffrath [4] introduced an incapability index, called Cpp, which is a simple transformation of the Taguchi index Cpm. The index Cpp is defined as:
where D=d/3. Some commonly used values of Cpp, 9.00 (process is incapable), 4.00 (process is incapable), 1.00 (process is normally called capable), 0.57 (process is normally called satisfactory), 0.44 (process is normally called good), and 0.25 (process is normally called super), and the corresponding Cpm values are listed in Table 1.
Table 1.
Some commonly used Cpp and equivalent Cpm
Cpp Cpm
9.00 0.33
4.00 0.50
1.00 1.00
0.57 1.33
0.44 1.50
0.25 2.00
Table options
If we denote the first term (μ−T)2/D2 as Cia, and the second item σ2/D2 as Cip, then Cpp can be rewritten as Cpp=Cip+Cia. The sub-index Cip measures the relative variability, which has been referred to as the imprecision index. Some commonly used values of Cip, 1.00, 0.56, 0.44, 0.36, and 0.25, and the corresponding quality conditions are listed in Table 2. Note that those values of Cip are equivalent to Cp=1.00, 1.33, 1.50, 1.67, and 2.00 respectively, covering a wide range of the precision requirements used for most real-world applications.
Table 2.
Some commonly used precision requirements
Quality condition Precision requirement
Capable 0.56⩽Cip⩽1.00
Satisfactory 0.44⩽Cip⩽0.56
Good 0.36⩽Cip⩽0.44
Excellent 0.25⩽Cip⩽0.36
Super Cip⩽0.25
Table options
On the other hand, the sub-index Cia measures the relative departure, which has been referred to as the inaccuracy index. The advantage of using the index Cpp, is that it provides an uncontaminated separation between information concerning the process precision and process accuracy. The separation suggests a direction the practitioners may consider on the process parameters to improve the process quality.
Based on the sub-indices Cip and Cia, we introduce a control chart called the Cpp multiple process performance analysis chart (MPPAC), using the incapability index Cpp. The Cpp MPPAC displays multiple processes with the relative departure, and process variability relative to their specification tolerances on one single chart. We demonstrate the use of the Cpp MPPAC by presenting a case study taken from a resistor component manufacturing company located on an Industrial Park in Taiwan, to evaluate the factory performance.
In this paper, we introduced a new control chart, called the Cpp MPPAC, using the incapability index Cpp. The Cpp MPPAC displays multiple processes with the mean departure, and process variability relative to the specification tolerances, on one single chart. We demonstrated the use of the Cpp MPPAC by presenting a case study on some resistor manufacturing processes, to evaluate the factory performance. The Cpp MPPAC chart is an efficient tool for the shop supervisors and engineers to evaluate the overall status of shop process control activity. The Cpp MPPAC provides critical information regarding process conditions and useful to quality improvement activity
