SPC Statistics

This topic explains how key SPC statistics are calculated.

See the list of available statistics.

Means, Ranges, and Standard Deviations

Definitions

\(n\) = Number of values in a subgroup (also referred to as the subgroup size).
\(k\) = Number of subgroups with \(n \geq 1\) (a subgroup is also referred to as a data record).
\(X_{j,i}\) = \(i\)th individual value of the \(j\)th subgroup.

Subgroup Calculations

The subgroup's mean, \(\bar{X}\)

\[ \bar{X} = \frac{\sum_{i=1}^{n} X_{j,i}}{n} \]

The subgroup's range, \(R\) (only calculated when \(n \gt 1\))

\[ R = \max{X_j} - \min{X_j} \]

The subgroup's moving range, \(\text{MR}\) (only calculated for \(k \gt 1\))

\[ \text{MR} = \bar{X}_j - \bar{X}_{j-1} \]

The subgroup's sigma, \({\sigma}\), calculated as the sample standard deviation

\[ {\sigma} = \begin{cases} \sqrt{\dfrac{\sum_{i=1}^{n}(X_{j,i})^2 - \dfrac{(\sum_{i=1}^{n}X_{j,i})^2}{n}}{n - 1}} & \text{if } n \gt 1 \\\\ 0 & \text{if } n \leq 1 \end{cases} \]

Population Calculations

Population statistics are only calculated if \(k \geq 1\).

The population's mean, \(\bar{\bar{X}}\)

\[ \bar{\bar{X}} = \frac{\sum_{j=1}^{k} \bar{X}_j}{k} \]

The population's average range, \(\bar{R}\), depends on the Characteristic's Range Type and the actual subgroup size of the data records in the population.

If the Characteristic's Range Type is set to Moving Range or the population's subgroup size is determined to be 1, \(\bar{R}\) is calculated using the moving range \(\text{MR}\) of each subgroup.
Otherwise, if the Characteristic's Range Type is Sigma, \(\bar{R}\) is calculated using the sigma \(\sigma\) of each subgroup.
Otherwise, the inner-record range \(R\) is used.

\[ \bar{R} = \frac{\sum_{j=1}^{k} R_j}{k} \text{ Substituting the appropriate }R\text{ , above} \]

The population's standard deviation, \(\sigma\), depends on the Global Setting Standard Deviation Method.

When the setting is Sample, \({\sigma}\) is calculated as the sample standard deviation

\[ {\sigma} = \begin{cases} \sqrt{\dfrac{\sum_{j=1}^{k}\sum_{i=1}^{n}(X_{j,i})^2 - \dfrac{(\sum_{j=1}^{k}\sum_{i=1}^{n}X_{j,i})^2}{k}}{k - 1}} & \text{if } k \gt 1 \\\\ 0 & \text{if } k \leq 1 \end{cases} \]

When the setting is Factors, \({\sigma}\) is calculated using the factors method, which estimates the standard deviation based on \(\bar{R}\).

\[ {\sigma} = \begin{cases} \dfrac{\bar{R}}{c_4} & \text{if range type is sigma} \\\\ \dfrac{\bar{R}}{d_2} & \text{otherwise} \end{cases} \]

With the following constants

Subgroup Size	d2	c4
1	1.128	0.798
2	1.128	0.798
3	1.693	0.886
4	2.059	0.921
5	2.326	0.94
6	2.534	0.952
7	2.704	0.959
8	2.847	0.965

Control Limits

Control limits can be calculated in several different way, depending on the Characteristic, Global Settings, the population's subgroup size, whether short run analysis is being performed, and various mathematical constants.

Defintions

\(UCL_X\) = Upper control limit for subgroup averages (\(\bar{X}\)).
\(LCL_X\) = Lower control limit for subgroup averages (\(\bar{X}\)).
\(UCL_R\) = Upper control limit for ranges.
\(LCL_R\) = Lower control limit for ranges.
\(n\) = The population's subgroup size.
\(\sigma\) = The population's standard deviation based on the Global Setting Standard Deviation Method

Factors Standard Deviation Method

If \(n \gt 1\) and the Characteristic's Range Type is Range,

\[ \begin{aligned} UCL_X &= \bar{\bar{X}} + A_2\bar{R} \\ LCL_X &= \bar{\bar{X}} - A_2\bar{R} \\ UCL_R &= D_4\bar{R} \\ LCL_R &= D_3\bar{R} \\ \end{aligned} \]

If \(n \gt 1\) and the Range Type is Sigma,

\[ \begin{aligned} UCL_X &= \bar{\bar{X}} + A_3\sigma \\ LCL_X &= \bar{\bar{X}} - A_3\sigma \\ UCL_R &= B_4\sigma \\ LCL_R &= B_3\sigma \\ \end{aligned} \]

If \(n = 1\) or the Range Type is Moving Range,

\[ \begin{aligned} UCL_X &= \bar{\bar{X}} + E_2\bar{R} \\ LCL_X &= \bar{\bar{X}} - E_2\bar{R} \\ UCL_R &= D_4\bar{R} \\ LCL_R &= D_3\bar{R} \\ \end{aligned} \]

Sample Standard Deviation Method

Intermediate values are calculated: \(\sigma_{\bar{X}}\), the standard deviation of all \(\bar{X}\), and \(\sigma_R\), the standard deviation of all ranges.

\[ \begin{aligned} \sigma_{\bar{X}} &= \sqrt{\dfrac{\sum_{i=1}^{n} (\bar{X_i}-\bar{\bar{X}})^2}{n - 1}} \\ \sigma_R &= \sqrt{\dfrac{\sum_{i=1}^{n} (R_i-\bar{R})^2}{n - 1}} \\ \end{aligned} \]

Control limits can then be calculated as follows.

\[ \begin{aligned} UCL_X &= \bar{\bar{X}} + 3\sigma_{\bar{X}} \\ LCL_X &= \bar{\bar{X}} - 3\sigma_{\bar{X}} \\ UCL_R &= \bar{R} + 3\sigma_R \\ LCL_R &= \bar{R} - 3\sigma_R \\ \end{aligned} \]

Short Run

When analyzing data using short run, control limits are based on the Global Setting Short Run Method.

If the Short Run Method is Target/Nominal, control limits are calculated using the Factors or Sample standard deviation method, as described above.

If the Short Run Method is Range, control limits are set using the following table, depending on the Characteristic's Range Type.

	Range or Moving Range	Sigma
\(UCL_X\)	\(A_2\)	\(A_3\)
\(LCL_X\)	\(-A_2\)	\(-A_3\)
\(UCL_R\)	\(D_4\)	\(B_4\)
\(LCL_R\)	\(D_3\)	\(B_3\)

Mathematical Constants for Control Limit Calculations

Subgroup size	\(A_2\)	\(A_3\)	\(B_3\)	\(B_4\)	\(E_2\)	\(D_3\)	\(D_4\)
2	1.88	2.659	\(\varnothing\)	3.267	2.66	\(\varnothing\)	3.267
3	1.023	1.954	\(\varnothing\)	2.568	1.772	\(\varnothing\)	2.574
4	0.729	1.628	\(\varnothing\)	2.266	1.457	\(\varnothing\)	2.282
5	0.577	1.427	\(\varnothing\)	2.089	1.29	\(\varnothing\)	2.114
6	0.483	1.287	0.030	1.97	1.184	\(\varnothing\)	2.004
7	0.419	1.182	0.118	1.882	1.109	0.076	1.924
8	0.373	1.099	0.185	1.815	1.054	0.136	1.864

Capability

Unless otherwise specified, in this region \(\sigma\) is the population's standard deviation based on the Global Setting Standard Deviation Method.

Z Values

The Z value that is used in calculating process capability is the distance of the process average from the specification limits measured in standard deviation units.

For unilateral specifications,

\[ Z_{min} = \frac{|\text{spec}-\bar{\bar{X}}|}{\sigma} \]

For bilateral specifications,

\[ \begin{aligned} Z_{upper} &= \frac{\text{upper spec}-\bar{\bar{X}}}{\sigma} \\ Z_{lower} &= \frac{\bar{\bar{X}}-\text{lower spec}}{\sigma} \\ Z_{min} &= \min(Z_{upper},Z_{lower}) \end{aligned} \]

Cpk

The most frequently used capability index is \(C_{pk}\). \(C_{pk}\) is calculated in one of three ways, depending on how the data is distributed. There are several different types of data distributions: normal, non-normal that can be modeled by Pearson's formula, and non-normal that cannot be modeled by Pearson's formula.

Pearson's Formula

Pearson's Formula is based on the first four moments of the parent distribution. These moments are used to develop a probability density formula. This formula accurately models univariate distributions that are valid only if the distribution is in a state of statistical control. Out-of-control points are not used in the calculation of the moments and, therefore, are not explained by the probability density function. This formula must explain all the values that come from in-control data. If the predictions of this equation do not explain the data from the population that was used to generate the moments, the distribution is likely multivariate, and therefore probability cannot be assessed. These different sources of variation must be analyzed separately.

Cpk for Normal Distributions

\[ C_{pk} = \frac{Z_{min}}{3} \]

Cpk for Non-Normal, Modeled Distributions

For non-normal distributions that can be modeled by Pearson's Formula, the calculation of \(C_{pk}\) depends on the Global Setting Z-Values Method.

If the Z-Values Method is Median,

\[ \begin{aligned} d_u &= \text{point above } \text{median} \text{ where the probability of } X \gt d_u \text{ is } 0.00135 \\ d_l &= \text{point below } \text{median} \text{ where the probability of } d_l \lt X \text{ is } 0.00135 \end{aligned} \]

\[ \begin{aligned} Z_{upper} &= \frac{\text{upper spec} - \text{median}}{d_u - \text{median}} \times 3 \\ Z_{lower} &= \frac{\text{median} - \text{lower spec}}{\text{median} - d_l} \times 3 \\ C_{pk} &= \frac{\min(Z_{upper},Z_{lower})}{3} \end{aligned} \]

If the Z-Values Method is Probability, appropriate \(Z\) value is determined from Appendix C of the Ford Motor Company's manual Continuing Process Control and Process Capability Improvement, page 54, that would provide an equivalent probability of being out of specification if the distribution were normal. This \(Z\) value is divided by 3 to calculate \(C_{pk}\).

Cpk for Non-Normal, Unmodeled Distributions

For non-normal distributions that cannot be modeled by Pearson's Formula,

\[ \begin{aligned} Z_{upper} &= \frac{\text{upper spec} - \text{median}}{\max{X} - \text{median}} \times 3 \\ Z_{lower} &= \frac{\text{median} - \text{lower spec}}{\text{median} - \min{X}} \times 3 \\ C_{pk} &= \frac{\min(Z_{upper},Z_{lower})}{3} \end{aligned} \]

Other Measurements of Capability

Besides \(C_{pk}\), other measurements of capability can be calculated, which may be more useful in some situations.

Cp and Cr

\(C_p\) is the best possible \(C_{pk}\) for the population's standard deviation calculated using the Factors method; it is the \(C_{pk}\) if the process were perfectly centered. \(C_r\) is simply the inverse of \(C_p\).

\[ C_p = \begin{cases} \frac{\text{upper spec} - \text{lower spec}}{6\sigma} & \text{for bilateral specifications} \\\\ \frac{\text{upper spec} - \text{target}}{3\sigma} & \text{if only the upper spec and target are defined} \\\\ \frac{\text{target} - \text{lower spec}}{3\sigma} & \text{if only the lower spec and target are defined} \end{cases} \]

\[ C_r = \frac{1}{C_p} \]

However, if \(C_{pk} \gt C_p\), the target is probably poorly chosen and not centered. In this case, \(C_p = C_{pk}\).

Ppk

\(P_{pk}\) is a performance index that is based on the sample standard deviation.

\[ P_{pk} = \min(\frac{\text{upper spec} - \bar{\bar{X}}}{3\sigma},\frac{\bar{\bar{X}} - \text{lower spec}}{3\sigma}) \]

Pp

Similar to the relationship between \(C_p\) and \(C_{pk}\), \(P_p\) is best possible \(P_{pk}\) for the population's sample standard deviation. It is the \(P_{pk}\) if the process were perfectly centered.

\[ P_p = \begin{cases} \frac{\text{upper spec} - \text{lower spec}}{6\sigma} & \text{for bilateral specifications} \\\\ \frac{\text{upper spec} - \text{target}}{3\sigma} & \text{if only the upper spec and target are defined} \\\\ \frac{\text{target} - \text{lower spec}}{3\sigma} & \text{if only the lower spec and target are defined} \end{cases} \]

Cpm

\(C_{pm}\) considers the proximity to the Characteristic's Target in addition to the population's variation. This index may have more desirable statistical properties than \(C_{pk}\).

\[ C_{pm} = \dfrac{C_p}{\sqrt{1 + \dfrac{(\bar{\bar{X}} - \text{target})^2}{\sigma^2}}} \]

CR and PR

\(\text{CR}\) and \(\text{PR}\) can be used to measure capability (using the Factors standard deviation) and performance (using the sample standard deviation) for normal distributions. These measurements are calculated using the same formula with different standard deviations.

\[ \begin{aligned} \text{CR} &= \frac{6\sigma}{\text{upper spec} - \text{lower spec}} \\ \text{PR} &= \frac{6\sigma}{\text{upper spec} - \text{lower spec}} \\ \end{aligned} \]

Insights

Subscription Tier Required

This feature requires the Premier subscription tier or higher.

Definitions

Insights can be generated for Traceability, Users, Inspections, Locations, and Inspection Test Labels. For brevity, these fields are referred to as Traceability.
Insights are always run per standard (i.e. either a Characteristic or Short Run Standard).
Traceability with a type of Integer, Decimal, or Currency are treated as continuous. All other types are referred to as discrete.
Insights are automatically calculated for all Traceability that have not been excluded by the Retrieval or the Traceability itself.

First-Level Insights

First-Level SPC Insights are automatically calculated whenever SPC data is retrieved in a Dashboard. These Insights are calculated depending on the type of Traceability.

Discrete Traceability

Discrete Traceability Insights are based on Brown-Forsythe and ANOVA tests of the data. These statistical tests are performed against the groupings created by grouping the data by each Traceability field. For example, the tests might be run against the data grouped by Shift, then the data grouped by Machine, and then the data grouped by Location. These groups are reported individually.

The Brown-Forsythe test determines whether there is a significant difference in the variance bewteen the groups. The test results in an \(H^2\) (the magnitude of correlation) and a p-value. If the p-value is less than the Significance Level Global Setting and the \(H^2\) is greater than the Minimum Impact Global Setting, there are significant differences in the groups’ variances.

The ANOVA test determines whether there is a significant difference between the means of the groups. This test also generates an \(H^2\) and p-value. These values are compared to the same thresholds in the Global Settings to determine whether there are significant differences between the means of the groups.

Continuous Traceability

Continuous Traceability Insights are based on a linear regression. For each continuous Traceability, GS runs a linear regression on the data, with the Traceability value on the x-axis and the data record's mean as the y-axis. This results in a \(R^2\) and p-value. If the p-value is less than the Significance Level Global Setting and the \(R^2\) is greater than the Minimum Impact Global Setting, there is a significant linear relationship between the Traceability and the means.

Second-Level Insights

Second-Level Insights are generated from the overlay accessed via the Explore Effects button from the Insights overlay on SPC charts. The purpose of Level 2 Insights is to determine whether a combination of Traceability groups is introducing more variance or change in mean than either Traceability alone. Therefore, the complete combinations of pairs of Traceability are created and the data is simultaneously grouped by both Traceability to be analyzed. Continuous-Continuous pairs are skipped.

Discrete-Discrete Pairs

If both Traceability are discrete, GS uses a Two-Way Type III ANOVA to determine whether the Traceability's combined impact on the data record means is greater than expected based on their individual impacts on the data. This is referred to as the interaction term in the Two-Way ANOVA. If the interaction is significant, groups are searched for significantly different means and variances using an Analysis of Means (ANOM) and ANOMV, respectively.

See The Analysis of Means: A Graphical Method for Comparing Means, Rates, and Proportions (Nelson, Wludyka, and Copeland 2005) for a complete mathematical discussion of ANOM and ANOMV.

If the analysis determines that a group's mean or variance falls outside the ANOM or ANOMV decision limits, that group is considered significantly different.

Discrete-Continuous Pairs

If one Traceability is discrete and the other is continuous, a Two-Way ANOVA test is performed, as if both Traceability were discrete, to determine if there is a significant interaction between the Traceability. If there is a significant interaction, a linear regression is performed after filtering the data by each discrete Traceability value in the data set. For example, a regression is run against Temperature for data belonging to Machine ABC, then data for Machine JKL, and then data for Machine XYZ. All significant regressions are reported.

Notes

Perfect correlations are omitted from results.
Discrete Traceability without at least two groups with at least ten data records cannot be analyzed.

Statistical Listing

Stat	Description.
A1	Non-normal root (where the fitted curve crosses the X-axis) to the left of the mean.
A2	Non-normal root (where the fitted curve crosses the X-axis) to the right of the mean.
Chi Squared Hypothesis	Based on the _Chi Squared Value and the degrees of freedom in the dataset.
Chi Squared Value	Calculated by finding the difference between each observed and theoretical frequency for each possible outcome. Only calculated if the Distribution is Normal or Uniform .
Correlation Coefficient	A measure of the interdependence of x and y values on a trend chart. Values range from -1 to +1, indicating perfect negative correlation at -1, absence of correlation at zero, and perfect positive correlation at +1.
Count Above Control	The number of records with a mean above the UCLx value.
Count Above Fixed Control Limit	The number of records with a mean above the Upper Fixed Control Limit X value of the standard for this retrieval.
Count Above Individual Limit	Individual values above the upper individual limit. Null if no upper ind limit is set.
Count Above Range Fixed Control Limit	The number of range values that are above the Upper Fixed Control Limit R value.
Count Above Spec	Individual values above the upper spec. Null if no upper spec is set.
Count Above Spec Pred	Count of individual values predicted to fall above the upper spec based on the fitted curve.
Count Above Target	The number of records with a mean above the Target X value of the standard for this retrieval.
Count Below Control	The number of records with a mean below the LCLx value.
Count Below Fixed Control Limit	The number of records with a mean below the Lower Fixed Control Limit X value of the standard for this retrieval.
Count Below Individual Limit	Individual values below the lower individual limit. Null if no lower ind limit is set.
Count Below Spec	Individual values below the lower spec. Null is no lower spec is set.
Count Below Spec Pred	Count of individual values predicted to fall below the lower spec based on the fitted curve.
Count Below Target	The number of records with a mean below the Target X value of the standard for this retrieval.
Count Inside 1SD	The number of records with a mean within 1 standard deviation of the population mean.
Count Inside 2SD	The number of records with a mean within 2 standard deviations of the population mean.
Count Inside Control	The number of records with a mean below the UCLx value and above the LCLx value.
Count Inside Fixed Control Limit	The number of records with a mean below the Upper Fixed Control Limit X value and above the Lower Fixed Control Limit X value of the standard for this retrieval.
Count Inside Individual Limit	Individual values between the upper and lower individual limits. Null if neither limit is set.
Count Inside Spec	Individual values between the upper and lower specs. Null is neither spec is set.
Count Inside Spec Pred	Count of individual values predicted to fall inside the lower and upper specs based on the fitted curve.
Count Missing Values	Number of null values in records.
Count Non-Null Values	Number of non-null individual values in records.
Count Outside Control	The number of records with a mean above the UCLx value or below the LCLx value.
Count Outside Fixed Control Limit	The number of records with a mean above the Upper Fixed Control Limit X value or below the Lower Fixed Control Limit X value of the standard for this retrieval.
Count Outside Individual Limit	Individual values outside the upper and lower individual limits. Null if neither limit is set.
Count Outside Spec	Individual values outside the upper and lower specs. Null is neither spec is set.
Count Outside Spec Pred	Count of individual values predicted to fall outside the lower and upper specs based on the fitted curve.
Count Records	Total number of records.
Count Records With Real Time Failures	Number of records with at least one real-time failure.
Count Records With Values	Number of records that have at least one non-null value.
Count Total Real Time Failures	Total number of real-time failures in the retrieval in the retrieval. This includes all failures on each base record as well as all the individual failures.
Count Total Values	Total number of individual data values in the retrieval. Includes null values.
CP	Estimate of process capability if the process is centered between the specification limits. Process spread is based on Factors standard deviation.
CPK	Estimate of process capability if the process center moves toward one of the specification limits. Process spread is based on Factors standard deviation. A Cpk less than zero indicates that the center of the process lies outside the specification limits.
CPM	Estimate of process capability around a target.
CR	Capability ratio, the inverse of Cp.
Crosses At	Returns the x value where the current trend line is expected to cross the closest spec limit displayed on the trend chart (Crosses Limit and Crosses Limit Type).
Crosses In	Returns the number of subgroups at which the current trend line is expected to cross the closest spec limit displayed on the trend chart (Crosses Limit and Crosses Limit Type). If this number is negative, the trend line has already been crossed.
Crosses Limit	The type of the closest spec limit to the current trend line, used to calculate Crosses At and Crosses In.
Crosses Limit Type	The type (Upper or Lower) of the closest spec limit to the current trend line, used to calculate Crosses At and Crosses In.
Distribution	Distribution type of the individual values.
First Quartile	25% percentile of ordered individual values.
Inner Record R Bar	Average of all inner-record ranges.
Inner Record Range Std Dev	Standard deviation of inner-record ranges.
Insufficent Non-Normal Resolution	Set if there is not enough resolution to make valid statistical calculations on non normal data.
Is Mean Minus 3SD Within Spec	Whether the mean - 3 SD is greater than the lower spec.
Is Mean Minus 4SD Within Spec	Whether the mean - 4 SD is greater than the lower spec.
Is Mean Plus 3SD Within Spec	Whether the mean + 3 SD is less than the upper spec.
Is Mean Plus 4SD Within Spec	Whether the mean + 4 SD is less than the upper spec.
Kurtosis	The 4th standardized moment (tailedness") of the individual values. Used to determine how normal a distribution is."
Kurtosis OK	True if the kurtosis (tailedness") of the individual values follows a normal distribution."
LCL for Zones	Lower Control Limit for zone colors.
LCLr	Lower Control Limit R.
LCLx	Lower Control Limit X.
Lower Fixed Control Limit R	Lower fixed control limit R for the standard (may be standardized).
Lower Fixed Control Limit X	Lower fixed control limit for the standard (may be standardized).
Lower Individual Limit	Lower ind limit for the standard (may be standardized).
Lower Spec	Lower spec for the standard (may be standardized).
M1	Non-normal power (steepness of the fitted curve) to the left of the mean.
M2	Non-normal power (steepness of the fitted curve) to the right of the mean.
Maximum Moving Range	Max moving range between records.
Maximum Range	Maximum record range.
Maximum Record X-Bar	Maximum record \(\bar{X}\).
Maximum Value	Maximum individual value.
Mean	Average of all non-null individual values.
Mean Minus 3SD	Mean minus 3 standard deviations.
Mean Minus 4SD	Mean minus 4 standard deviations.
Mean Minus Nominal	Mean - Nominal Spec.
Mean Plus 3SD	Mean plus 3 standard deviations.
Mean Plus 4SD	Mean plus 4 standard deviations.
Median	Middle of ordered individual values. If the count of values is even, then this is the average of the two middle numbers.
Median Range	The median range value.
Median Record X-Bar	The median subgroup mean value.
Minimum Moving Range	Minimum moving range between records.
Minimum Range	Minimum record range.
Minimum Record X-Bar	Minimum record \(\bar{X}\).
Minimum Value	Minimum individual value.
Mode	Individual value that appears most frequently. If multiple numbers appear with the same frequency, this value is null.
Most Recent Date Retrieved	Created date/time of the most recent record.
Moving Average LCLr	Lower control limit of moving average ranges.
Moving Average LCLx	Lower control limit of moving averages.
Moving Average Mean	Mean of moving averages.
Moving Average R Bar	Mean of moving average ranges.
Moving Average UCLr	Upper control limit of moving average ranges.
Moving Average UCLx	Upper control limit of moving averages.
Moving Range R Bar	Average of moving ranges between records.
Moving Range Std Dev	Standard deviation of moving ranges between records.
Nominal Fixed Control Limit	If Upper Fixed Control Limit X and Lower Fixed Control Limit X are set on the standard for this retrieval, then this returns the midpoint between the two values.
Nominal Individual Limit	If UpperIndLimit and LowerIndLimit are set on the standard for this retrieval, then this returns the midpoint between the two values.
Nominal Range Fixed Control Limit	If Target R is set on the standard for this retrieval, then this stat returns the Target R value. If Target R is not set on the standard for this retrieval, but Upper Fixed Control Limit R and Lower Fixed Control Limit R are set, then this returns the midpoint between the two values.
Nominal Spec	If Target X is set on the standard for this retrieval, then this stat returns the Target X value. If Target X is not set on the standard for this retrieval, but Upper Spec and Lower Spec are set, then this returns the midpoint between the two values.
Non Normal Area	Area underneath the non-normal fitted curve.
Offset Percentage	Percentage that the mean is different from the target, based on specs.
Oldest Date Retrieved	Created date/time of the record furthest in the past.
PC	The ratio of the process spread to the specification limit spread where the process spread is determined by Factors standard deviation.
Percent Above Control	The percentage of the number of records with a mean above the UCLx value, out of the total number of records.
Percent Above Fixed Control Limit	The percentage of the number of records with a mean above the Upper Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Above Individual Limit	Precent of individual values above the upper individual limit. Null if no upper ind limit is set.
Percent Above Lower Fixed Control Limit	The percentage of the number of records with a mean above the Lower Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Above Lower Individual Limit	Percent of individual values above the lower individual limit. Null if no lower ind limit is set.
Percent Above Lower Spec	Percent of individual values above the lower spec. Null if no lower spec is set.
Percent Above Range Fixed Control Limit	The percentage of range values that are above the Upper Fixed Control Limit R value, out of the total number of records.
Percent Above Spec	Percent of individual values above the upper spec. Null if no upper spec is set.
Percent Above Spec Pred	Percent of individual values predicted to fall above the upper spec based on the fitted curve.
Percent Above Target	The percentage of the number of records with a mean above the Target X value of the standard for this retrieval, out of the total number of records.
Percent Below Control	The percentage of the number of records with a mean below the LCLx value, out of the total number of records.
Percent Below Fixed Control Limit	The percentage of the number of records with a mean below the Lower Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Below Individual Limit	Percent of individual values below the lower individual limit. Null if no lower ind limit is set.
Percent Below Spec	Percent of individual values below the lower spec. Null if no lower spec is set.
Percent Below Spec Pred	Percent of individual values predicted to fall below the lower spec based on the fitted curve.
Percent Below Target	The percentage of the number of records with a mean below the Target X value of the standard for this retrieval, out of the total number of records.
Percent Below Upper Fixed Control Limit	The percentage of the number of records with a mean below the Upper Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Below Upper Individual Limit	Percent of individual values below the upper individual limit. Null if no upper ind limit is set.
Percent Below Upper Spec	Percent of individual values below the upper spec. Null if no upper spec is set.
Percent Inside 1SD	The percentage of the number of records with a mean within 1 standard deviation of the population mean, out of the total number of records.
Percent Inside 2SD	The percentage of the number of records with a mean within 2 standard deviations of the population mean, out of the total number of records.
Percent Inside Control	The percentage of the number of records with a mean below the UCLx value and above the LCLx value, out of the total number of records.
Percent Inside Fixed Control Limit	The percentage of the number of records with a mean below the Upper Fixed Control Limit X value and above the Lower Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Inside Individual Limit	Percent of individual values between the upper and lower individual limits. Null if neither limit is set.
Percent Inside Spec	Percent of individual values within the specs. Null if neither spec is set.
Percent Inside Spec Pred	Percent of individual values predicted to fall inside the lower and upper specs based on the fitted curve.
Percent Outside Control	The percentage of the number of records with a mean above the UCLx value or below the LCLx value, out of the total number of records.
Percent Outside Fixed Control Limit	The percentage of the number of records with a mean above the Upper Fixed Control Limit X value or below the Lower Fixed Control Limit X value of the standard for this retrieval, out of the total number of records.
Percent Outside Individual Limit	Percent of individual values outside the upper and lower individual limits. Null if neither limit is set.
Percent Outside Spec	Percent of individual values outside the upper and lower specs. Null if neither spec is set.
Percent Outside Spec Pred	Percent of individual values predicted to fall outside the lower and upper specs based on the fitted curve.
Percent Records with Real Time Failures	The percentage of the number of records with at least one real-time failure, out of the total number of records.
pp	Estimate of process performance if the process is centered between the specification limits. Process spread is based on the sample standard deviation.
PP	The ratio of the process spread to the specification limit spread where the process spread is determined by the sample standard deviation.
PPK	Estimate of process performance if the process center moves toward one of the specification limits. Process spread is based on the sample standard deviation. A Ppk less than zero indicates that the center of the process lies outside the specification limits.
PPM Above Spec	PPM of individual values above the upper spec. Null if no upper spec is set.
PPM Above Spec Pred	PPM of individual values predicted to fall above the upper spec based on the fitted curve.
PPM Below Spec	PPM of individual values below the lower spec. Null if no lower spec is set.
PPM Below Spec Pred	PPM of individual values predicted to fall below the lower spec based on the fitted curve.
PPM Inside Spec	PPM of individual values within the upper and lower specs. Null if neither spec is set.
PPM Inside Spec Pred	PPM of individual values predicted to fall inside the lower and upper specs based on the fitted curve.
PPM Outside Spec	PPM of individual values outside the upper and lower specs. Null if neither spec is set.
PPM Outside Spec Pred	PPM of individual values predicted to fall outside the lower and upper specs based on the fitted curve.
PR	Performance ratio that is calculated as the inverse of Pp.
R Bar	Mean of ranges.
R Target	Target R (nominal) value for the standard (may be standardized).
Range Standard Deviation	Standard deviation of ranges. Uses the standard's setting for the range type.
Record X-Bar Standard Deviation	Sample standard deviation of the \(\bar{X}\)s of all records.
Sample Standard Deviation	Sample Standard Deviation of all individual values.
Sigma Level	Returns the smaller of the two Z values (Zl or Zu) used to calculate process capability.
Sigma R Bar	Average of all sigma ranges.
Sigma Range Std Dev	Standard deviation of sigma ranges.
Six Standard Deviations	Difference between (mean + 3 SD) and (mean - 3 SD).
Skewness	The 3rd standardized moment (asymmetry about the mean") of the individual values. Used to determine how normal a distribution is."
Skewness OK	True if the skewness of the individual values follows a normal distribution.
Slope	The slope of the line that best fits the data.
Spread Used	Spread type used to model the fitted distribution curve.
Standard Deviation	Standard deviation of all individual values. Uses the global setting for the method of calculating the standard deviation (either Factors or Sample method).
Standard Deviation Factors	Standard Deviation of all individual values using the Factors method.
Standard Deviation Forced To Sample Method	True if the standard deviation method was forced to Sample because of varying subgroup sizes.
Subgroup Size	Subgroup size of the most recent record. Used to standardize all other records.
Sum Squared Values	Sum of each value squared.
Sum Values	Sum of all non-null values.
Third Quartile	75% percentile of ordered individual values.
Tolerance Fixed Control Limit	If the Upper Fixed Control Limit X and Lower Fixed Control Limit X are set on the standard for this retrieval, returns the difference between the two values.
Tolerance Individual Lim	If the UpperIndLimit and LowerIndLimit are set on the standard for this retrieval, returns the difference between the two values.
Tolerance Range Fixed Control Limit	If the Upper Fixed Control Limit R and Lower Fixed Control Limit R are set on the standard for this retrieval, returns the difference between the two values.
Tolerance Spec	If the Upper Spec and Lower Spec are set on the standard for this retrieval, returns the difference between the two values.
UCLr	Upper Control Limit R.
UCLx	Upper Control Limit X.
Upper Fixed Control Limit R	Upper fixed control limit R for the standard (may be standardized).
Upper Fixed Control Limit X	Upper fixed control limit for the standard (may be standardized).
Upper Individual Limit	Upper ind limit for the standard (may be standardized).
Upper Spec	Upper spec for the standard (may be standardized).
Variance	Square of the sample standard deviation.
Varying Subgroup Size	True if there at least two records with different counts of non-null values.
X Target	Target X (nominal) value for the standard (may be standardized).
Y Intercept	The y value when x = 0 for the line that best fits the data.
Y Intercept LCLx	The value where the lower trend control limit intersects the Y axis.
Y Intercept UCLx	The value where the upper trend control limit intersects the Y axis.
Zl	The distance of the process average from the lower specification limits measured in standard deviation units. Set to either ZlR or ZlF based on the standard deviation method. If the data is non-normal, will be ZlNN.
Zl F	The distance of the process average from the lower specification limits measured in standard deviation units. Uses Factors standard deviation.
Zl Non-Normal	The distance of the process average from the lower specification limits measured in standard deviation units. The standard deviation is based on the non-normal curve. If set, _zlR, ZuR, ZlF, and ZuF will be null.
Zl R	The distance of the process average from the lower specification limits measured in standard deviation units. Uses the sample standard deviation.
Zu	The distance of the process average from the upper specification limits measured in standard deviation units. Set to either ZuR or ZuF based on the standard deviation method. If the data is non-normal, will be ZuNN.
Zu F	The distance of the process average from the upper specification limits measured in standard deviation units. Uses Factors standard deviation.
Zu Non-Normal	The distance of the process average from the upper specification limits measured in standard deviation units. The standard deviation is based on the non-normal curve. If set, ZlR, ZuR, ZlF, and ZuF will be null.
Zu R	The distance of the process average from the upper specification limits measured in standard deviation units. Uses the sample standard deviation.