# All statistics and graphs for Variables Acceptance Sampling (Accept/Reject Lot)

Find definitions and interpretation guidance for every statistic and graph that is provided with the analysis of your variables sample data.

## Mean

Minitab determines the mean from your data. The mean is the average of the data, which is the sum of all the observations divided by the number of observations.

## Historical standard deviation

The historical standard deviation is the known standard deviation of your process. Use a historical standard deviation when you have collected enough data over time to state with confidence what the process standard deviation is. If the process is stable and in control, then you can use a historical standard deviation instead of a calculated standard deviation.

## Lower specification limit (LSL) and upper specification limit (USL)

The lower specification limit (LSL) is the minimum allowed value for the product or service. This limit does not indicate how the process is performing but how you want it to perform.

The upper specification limit (USL) is the maximum allowed value for the product or service. This limit does not indicate how the process is performing but how you want it to perform.

You must specify at least one specification limit for a variables acceptance sampling plan.

### Interpretation

Use the LSL and USL to define customer requirements and to evaluate whether your process produces items that meet the requirements.

Minitab compares your process data to the specification limits to determine whether to accept or reject an entire lot of product.

## Z.LSL and Z.USL

Minitab determines the mean and standard deviation from your data and calculates the Z-values. If you specify a historical standard deviation, Minitab uses that value for the calculations.
• Z.LSL = (mean – lower specification) / standard deviation
• Z.USL = (upper specification – mean) / standard deviation

### Interpretation

If the Z-values are greater than the critical distance, and if the standard deviation is less than the maximum standard deviation, then accept the entire lot. Otherwise, reject it.

## Critical distance (k value)

The critical distance is the value that Minitab uses to compare with the sample mean and specification limits to determine whether to accept or reject a lot.

### Interpretation

For example, suppose you sample lots of plastic pipes. Your sample plan calls for randomly sampling 104 of the 2500 pipes in a shipment. The lower specification for wall thickness is 0.09 inches. Minitab determines the critical distance to be 3.55750.

If the Z-values are greater than the critical distance, and if the standard deviation is less than the maximum standard deviation, then accept the entire lot. Otherwise, reject it.
Generated Plan(s) Sample Size 104 Critical Distance (k Value) 3.55750 Z.LSL = (mean - lower spec)/historical standard deviation Accept lot if Z.LSL ≥ k; otherwise reject.

## Maximum standard deviation (MSD)

Minitab calculates the maximum standard deviation (MSD) when you provide both LSL and USL and do not provide a historical standard deviation.

### Interpretation

If the Z-values are greater than the critical distance, and if the standard deviation is less than the maximum standard deviation, then accept the entire lot. Otherwise, reject it.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy