# Study On The Process Capability Mechanics Essay

Process capability compares the requirement limits by usingcapability indices to the output of anin-controlprocess . The comparison is done by forming the ratio of the spread inbetween the process qualification to the stretch of the process values, as calculated by six process standard deviation units.

Process capability analysis entails comparing its specifications to the performance of a process . It is said that a process is proficient if virtually all of the achievable variable values fall inside the specification limits.

### Definitions

Cp is the process Capability is a simple and direct indicator of process capability.

Cpk is the one which denotes process Capability Index is nothing but the adjustment of Cp for the effect of noncentralized distribution.

Process performance index is the one which denotes the process Performance is nothing but a simple and direct indicator of process performance.

Ppk is the one which denotes the process performance index and is the adjustment of Process perfomance for the effect of non-centralized distribution.

### Interpreting Cp , Cpk

Cpk is nothing but the index that measures how closely the process is running to its requirement limits, relative to the usual inconsistency of the process. The bigger the index, the probablility that any item will be outside the requirements is less.

Cpk is the one which measures how close we are to your destination and how regular we are around our average performance. A person might be performing with lowest difference but he could be far away from his goal towards one of the requirement limit, which shows lower Cpk, while Cp will be high. Alternatively, a person might be on average just at the target, but the difference in performance is high but then it is still lower than the acceptance band i.e. requirement interval. In that case aswell Cpk will be lower only, but Cp would be high. Cpk would be higher only when you are attaining the target every time with a minimum variation.

The value of Cpk must be 1.33 [4 sigma] or more to satisfy most customers.

The value of Cpk =1 means we are just touching the nearest edge

The value of Cpk=2 means width can grow 2 times before touchingThe value of Cpk=3 means our width might grow by 3 times before touching.

To get a brief idea of the value of the Cpstatistic for process with varying widths, consider the following plot:

This can also be expressed numerically bythe following table:

 USL - LSL 6sigma 8sigma 10sigma 12sigma Cp 1.00 1.33 1.66 2.00 Rejects .27% 64ppm .6 ppm 2 ppb % of spec used 100 75 60 50

### Interpreting Pp, Ppk.

Process Performance Index chiefly tries to check if the sample that you have produced from the process is able to satisfy Customer CTQs (needs). Samples from the lot may be needed to be little large to represent the variation in the lot. We use Process Performance only when process control cannot be evaluated.Example of this is a short pre-production run. sample sigma is commonly used by Process Performance in its calculation. Process capability uses the process sigma value unwavering from either the Moving Range, Range, or Sigma control charts.

### Differences Between Cpk and Ppk

Cpk

1. Cpk is for a short term where as Ppk is for a long term.
2. Cpk refers to the variation to your specification limits.
3. Cpk tells you what the process can do in future, assuming it stays in a state of statistical control.
4. Cp and Cpk are used for computing the index relating to the sub grouping of your data.
5. Cp and cpk should be greater than 2.0 and 1.5 respectively for a good process which is under statistical control.

Ppk

1. Ppk lets us know in what way the procedure had performed earlier. We cannot use it to find out the future, as done with Cpk, as the process is not under the state of control.
2. Pp and Ppk are for the entire process (no subgrouping)

### Formulae for calculating Cpk

1. Cp = (USL - LSL) / 6*(standard deviation)
2. Cpl = (Mean - LSL) / 3*(standard deviation)
3. Cpu = (USL-Mean) / 3*(standarddeviation)
4. Cpk = Min (Cpl,Cpu)

Cpk is calculated by use of an estimation of the standard deviation calculated using R-bar / d2. Ppk uses the common form of the standard deviation i.e, the square root of the sum of squares divided by n-1or the root of the variance . The R-bar/D2 assumption of the standard deviation has a soothing effect.

Cpk is generally calculated by using (RB ar / d2 ) or (SB ar/ c4 for Sigma in the denominator of your equation. This calculation of Sigma needs the process within the state of statistical control. If the process is not in control, the calculation of Sigma and Cpk is completely useless which means it is valid only wen it is in-control.