What is meant by process is capable?

PROCESS-CAPABILITY

Before determining if your company and all your processes need to be in Six Sigma Process Capability it is important to discuss what you can get for your efforts and evaluating your processes for how you get them to Six Sigma. What is a capable process? Some quality assurance experts define a capable process as one having and maintaining a CpK index of at least 1.33. This equates to a maximum defect rate of 63 ppm while others say a maximum of 3.4 ppm is the true capability process meaning of Six Sigma control.

The difference between your company’s quality processing goal of a CpK of 1.33 or a CpK of 1.5 [Six Sigma] is only an additional 60 defects. If your production run is large, more than 20,000 parts, you can anticipate random defects for a process of CpK just meeting 1.33. When your production runs are greater than 200,000 and above, even if your process is within Six Sigma or a CpK of 1.5, you will still experience random defects due to random variability of the material, equipment, and processing variables. Therefore, for small runs that many companies experience in their daily manufacturing, it is more important to know the methodology of attaining an acceptable process capability of CpK 1.33 or a CpK of 1.5 than debating over which CpK value should be selected for your companies manufacturing goal.

No matter what run size and CpK goal, the manufacturing department along with quality assurance will be working together to improving processes. These will be processes that are substantially below your selected goal or daily, ongoing processes that have had their CpK dip below your goal, due to a variable in the process going out of control.

An example of process capability can best explain this concept. A molding shop producing a product historically for years has a specified minimum CpK on the operation of 1.33 that is attainable and repeatable each time the job is run on the same machine. This is shown in Figure 3, for a process-capability study of a process running at a speed of 60 seconds overall cycle time. The process and cycle, now running at an overall mold open to mold open of 60 seconds, is set to produce the required number of parts in a specified time period. This was consistent with the machinery demands and utilization of the current customer base. The customer was very satisfied with the quality of the products shipped weekly.

Manufacturing engineering and quality assurance performed a process capability sturdy on this job and others so they would know if the process and other variables were as capable as possible after having the machine overhauled. The floor supervisor and manufacturing engineer were satisfied with the machines cycle and operation. The following data on pin length for a key customer product characteristic was evaluated on parts from a four cavity tool. A part from each cavity was initially evaluated to show the balanced runner mold was capable of producing repeatable parts cycle to cycle from each cavity. After this was confirmed, only one part from a specific cavity was measured for the process study. After 30 cycles the data points were accumulated and used for the analysis.

Data:

Specification = 1.250 in. ± 0.005 in.

Sigma = 0.0011 in.

μ = 1.2495

The sigma [process standard deviation] and μ [process mean value] were based on measurements taken from four individual cavities. Five parts were collected from each cavity for five cycles. When these were confirmed to be within specification, the single cavity was selected, cavity one, and a total of 30 parts were collected per hour and measured. These parts were considered representative of the production process.

Process-capability formulas were used to determine the process had a CpK = 1.36. As a result of the study the manufacturing process was deemed satisfactory and monitored as was typical during the manufacturing cycle. The process was considered to be capable and was in statistical control. This information was confirmed by the customer since product defects were not reported.

The customer requested additional product and a new manufacturing engineer was assigned the task of meeting this demand from sales. The initial process decision made was to reduce the cycle time by 50%, or 30 seconds, to meet the new order volume. The shop floor supervisor believed this was too great a decrease even though the material reacted, parts were ejected looking good, successfully. No visual change except part weight was lower by three tenths of a gram, which was being used as the process stability indicator.

On the first sample taken after the increased cycle time was set, the R chart indicated that the process was out of control, as confirmed by the change, lower part weight. The cycle time of 30 seconds was increased 50% more to 45 seconds and on the third sampling group the process yielded an R-chart reject. This is shown in Figure 4, on the range control chart.

With time running out and material being scrapped the engineer with help from quality assurance ran a DOE [design of experiments] to determine the critical factors in the process. Not surprisingly, cycle time was found to be the most important factor along with screw speed that affected melt temperature and setup time in the mold cavity. These were the critical variables and it was decided that mold cavity temperature would not be adjusted to assist in reducing the cycle because of the critical pin length.

Since there had not been any problem running at a 60 second cycle, the manufacturing engineer wanted to characterize the process at the 45 second cycle to see if the R-chart rejection was a random event and the cycle not yet in equilibrium. Quality assurance agreed to this request with the restriction that all product would be inspected 100% until the cycle stabilized and proved satisfactory for repeatability of product manufacture. Samples were taken as before until sufficient data points were obtained.

Analysis showed the mean had increased to 0.2497, and the standard deviation had increased to 0.0022. After calculating the process capabilities, the manufacturing engineer calculated a Cp of only 0.81 and realized that even with perfect centering, the process could not produce at a sufficient quality level to meet the company and customer requirement of CpK of 1.33. As a result the cycle was reset to 60 seconds, equilibrium again obtained, and the CpK again recalculated. The control charts again resembled those of the initial process and the manufacturing process extended into the second shift to meet the customers quantity requirements.

Process-capability is a very valuable tool and goes along with the “do it right the first time” manufacturing philosophy. When correctly used it will aid in the selection of equipment, materials, speeds, and other variables that can affect on going product quality. The process-capability formulas and language for calculating the CpK information is listed.

Cp = USL – LSL/6 sigma

Cp = Inherent process-capability index

USL = Upper specification limit

LSL = Lower specification limit

Sigma = Process standard deviation [obtained from a representative, random sample of at least 20 parts].

CpL = μ – LSL/3 sigma

CpL = Lower process-capability index

μ = Process mean [obtained from a representative, random sample of at least 20 parts].

CpU = USL – μ/3 sigma

CpU = Upper process-capability index

CpK = min {CpU, CpL}

CpK = Process-capability index

Notes:

If μ is at the nominal dimension, Cp = CpK

CpK is always equal to or less than Cp.

26.2 Process Capability

Process capability is a measure of the inherent process performance. It is defined by sigma [σ], the standard deviation. Different σ levels are used to determine process capability, depending on the customer's needs and specifications. The data included in different standard deviation ranges are as follows:

±1σ includes 68.2% of the total area under a normal distribution curve. If the process is run at ±1σ capability, 317,300 parts out of every million fall outside the specification limits.

±2σ includes 95.45% of the total area under the normal distribution curve, with 45,500 parts out of a million falling outside the control limits.

±3σ includes 99.73% of the total area under the normal distribution curve or virtually the entire area. At ±3σ, there are still 2700 defective parts out of each million produced.

±6σ includes 99.9,999,998% of the area under the normal distribution curve, and 0.002 parts per million are expected to be defective.

In a 6σ process, statisticians allow for a 1.5σ shift. This adjustment results in 3.4 defects per million parts produced [3].

As an example, assume that a sheet product is being shipped to customer RSQ, who requests the impact strength to be 13 ± 3 ft-lbs at a ±3σ level. To supply samples to RSQ, some sheet is produced and impact properties are measured. Thirty-seven data points are gathered and plotted to give a normal distribution, as shown in Figure 26.3. Based on the data, can your company supply product to RSQ that meets the customer requirements 100% of the time? The average impact value is 13 with a standard deviation of 1.25. At 3σ, the data are anticipated to range from 13 ± 3 [1.25], giving a range of 9.25–16.75. Based on the data without process improvements to lower the standard deviation, it is impossible to satisfy RSQ's impact requirements. The process is incapable of producing product with 13 ± 3 ft-lbs at 3° that meets the customer's requirements 100% of the time. If the order is accepted based on the current operation, the product will be produced and sent to the customer that is outside the specification limit.

Process capability measures the process repeatability relative to the customer specifications. Figure 26.4 shows two normal distribution curves defining product property profiles with specification limits. Process A is capable of producing a product that meets the customer's specifications 100% of the time, whereas process B is an incapable process.

Process capability is measured through a capability index, Cpk, defined by Eqns [26.4] and [26.5], where USL is the upper specification limit and LSL is the lower specification limit. A Cpk value