About

Quality Control is a subsection of the collection of statistical tools introduced by Sir Ronald A. Fisher, Joseph M. Juran, Philip B. Crosby, Walter Shewhart, W. Edwards Deming, and Genichi Taguchi. In general, the tools most often associated with quality control can refer to either:

1. Statistical Quality Control
2. Process Capability

Statistical Quality Control is usually monitored via Statistical Process Control (SPC) methods such as Shewhart Charts or Control Charts. Control charts are modified time series plots, usually with some average value and control limits plotted three standard deviations above and below the center line. They do not include the tolerance band of the process. Such charts include, but are not limited to:

• $\overline{X}-R$: (Average and range)
• $\overline{X}-s$: (Average and standard deviation)
• $IX-MR$: (Individual and Moving Range, sometimes $X-MR$)
• $c$: (counts)
• $u$: (counts with varying subgroup size)
• $p$: (proportion with varying subgroup size)
• $np$: (proportion)
• EWMA: (exponentially weighted moving average)

Process Capability is often measured as some relationship between the process distribution and the engineering specification for the process. Charts for such analysis are usually based upon histograms with the target value, upper specification level, and lower specification level (T, USL, and LSL) superimposed. These indexes include, but are not limited to:

• $C_p$: It represents the best case ratio of the spec. and the process.
• $C_r$: It is simply the inverse of $C_p$.
• $C_{a}$: A representation of the accuracy of the process.
• $C_{pa}$: A variation of $C_{pk}$ for asymmetrical processes.
• $C_{pk}$: $C_{p}$ modified by the factor $k$.
• $C_{p-}$: The difference between $C_p$ and $C_{pk}$.
• $C_M$: "Capability of the Machine;" it uses a wider range of possible process outcomes than $C_p$
• $C_{pm}$: Similar to $C_{pk}$, it relates the process in comparison to the spec. limits and a target value. It is most useful with asymmetrical tolerances.
• $C_{pp}$: "Incapability Index" based upon $C_{pm}$ and similar to $C_r$.
• $C_{pmk}$: $C_{pm}$ modified by the factor $k$.
• $C_pT$: replaces $\hat{\mu}$ in $C_{pk}$ with target value $T$.
• $Z_{bench}$: Represents capability as a $Z_{score}$ and works with continuous or discrete data.
• $Q_k$: When no tolerance range exists, the Mean Standard Error of the process can be used to evaluate this index.
• $C_{p\omega}$: A weighted index which can be used to calculate approximations for $C_p$, $C_{pm}$, and $C_{pk}$.
• $C_p\left ( u,v \right )$: An index which can calculate $C_p$, $C_{pm}$, $C_{pk}$, and $C_{pmk}$.
• $C_{p\log}$: Similar in use to $C_p$, it can be used for lognormal distributions.
• $C_{p(\ln)}$: An alternate to $C_{p\log}$; used for lognormal distributions.
• $C_{pk(\ln)}$: A version of $C_{pk}$ used for lognormal distributions.
• $C_s$: Useful for any skewed distribution.
• $C_{npk}$: Useful for any distribution, as long as the parameters can be determined.
• $C_f$: Used for proportions of non-conforming units.
• $C\%$: Used with FTY/RTY data; capability of percent non-conforming.
• $P_p$: A long-term version of $C_p$.
• $P_{pk}$: A long-term version of $C_{pk}$.