Q 527. Sigma Shift of 1.5 is used while calculating the short term capability of discrete data. Why is this approximation usually unsuitable for continuous data?

 

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Background 

 

Mean is the arithmetic average of a data set.
Central tendency is the tendency of data to be centred on this mean.
Standard Deviation (also known as Sigma or σ) determines the spread (deviation) from this mean/central tendency.

The more the number of standard deviations that fits between process average and acceptable process limits, the less likely it is that the process performs beyond the acceptable process limits, and it causes a defect. It is for this very reason that a 6σ (Six Sigma) process performs better than 1σ, 2σ, 3σ, 4σ, 5σ processes.

Specification Limits &Control Limits

LSL and USL refer to “Lower Specification Limit” and “Upper Specification Limit”. Specification Limits are obtained from the customer requirements, and they specify the minimum and maximum acceptable limits of processes. Control limits indicate variation in the process performance. It is the actual values that the process is operating on or a real time value.

Sigma Shift

 

At Motorola Six Sigma practitioners analysed samples of their processes and deduced that process capability tends to drift over time. In order to ensure the long-term process achieved a target defect rate, and realising that they could only measure their processes in the short term, they concluded that the short-term process tended to ‘accommodate’ more standard deviations between the mean and the specification limits, and concluded that an additional 1.5 standard deviations from the short-term process was about right. The ‘additional’ 1.5 standard deviations is known as the Sigma Shift. The difference over the short and long term between the Sigma Levels of a process is called Sigma Shift. Allowing 1.5 sigma shift results in the generally accepted six sigma value of 3.4 defects per million opportunities (DPMO).

Processes tend to behave in a different manner over the short and long terms:

• A greater Sigma Shift suggests that process could be improved to a great degree.
• A low Sigma Shift suggests that process is well controlled already and no further control methods are necessitated.

Process Capability & Stability

 

A capable process is one that gives an output that meets customer specifications. A stable process has controlled variations and operates within the control limits.

There are several methods to measure process capability index and ratio including an estimation of the PPM (defective parts per million) .Capability indices such as Cp, Cpk, Pp, Ppk are the most prime ones. The Cp and Cpk indices denote capability indices. Cp{Capability Index} shows whether the distribution can potentially fit inside the specification, while Cpk{Capability Ratio} shows whether the overall average is centrally located. If the overall average of the process is in the center of the specification, the Cp and Cpk values will be the same. Higher value of Cpk, is advantageous. Cpk values less than 1.0 is considered pretty poor and the process is considered not capable. Values between 1.0 and 1.33 of Cpk is considered barely capable, and values greater than 1.33 is considered capable. Process Capability measures, what the requirements are versus the distribution of the process outcome. The difference between the USL & LSL is the specification spread; also sometimes referred to as the Voice of the Customer. The process spread is the distance between the highest value and the lowest value generated, also sometimes referred to as the Voice of the Process. Ppk is a performance index that measures how close the real time value or the current process is to the specification limits.

Think of the Specification Spread as the sides of the garage – those are static, they are not moving, and it is important that the process puts values inside those bounds. The Process Spread is the size of the car we are trying to fit in.

 

Process Stability refers to the consistency of the process with respect to critical process parameters. If the process is consistent over a period of time, we  say the process is stable or in control. A process is said to be stable when all of the response parameters that we use to measure the process show both constant means and constant variances over time, and also have a constant distribution. Statistical Process Control Charts are used to ascertain Process Stability. Some charts are used to assess the stability of the process location .Example, Xbar charts that monitor the process average etc, other charts are used to assess the stability of the process variation. Example- range or standard deviation charts. 

Process stability and process capability are different concepts altogether and there is no inherent relationship between them.

Although, there exists no direct relationship between process stability and process capability, there is an important connection: Process capability assessment should only be performed after process stability has been ascertained.

 

For Continuous Data Zoverall (Overall Performance) and Zwithin (Within Performance) can be calculated independently because of which Sigma Shift approximation of 1.5 usually unsuitable for continuous data. However, for Discrete Data we cannot calculate the Zoverall (Overall Performance) and Within (Within Performance) independently and we have to take Sigma Shift approximation of 1.5.

There are no correct answers. Below is the answer which I was looking for - 

 

1.5 Sigma shift is used for Discrete data and not for Continuous data. For Continuous data, we need the mean and standard deviation to calculate Sigma Level. For Discrete data, we first calculate the DPMO or DPU or Yield and then we convert them to Sigma Level.

Short term capability is typically for a rational sub-group and for continuous data we can independently determine the mean and standard deviation for sub-groups. Hence we don't need the approximation.

For Discrete data, the # of defects or defectives could be zero for a rational sub-group and in such cases Sigma Level cannot be determined. Hence, we have to use the 1.5 Sigma shift approx.