The Poisson distribution is a discrete distribution. The Poisson distribution is quite useful when you want to estimate the probabilities of events that occur randomly in some unit of measure (e.g., the number of traffic accidents at a particular intersection per month).
A way to remember when the Poisson distribution might be useful is when you hear or see the word ‘PER’. Examples of seeing or hearing the word ‘PER’:
Pp (process performance) is considered the ‘long-term’ potential capability measure. Contrast this with Cp (capability of the process) which is more of a ‘look backwards’ of where the process capability has been.
Both Cp and Pp are comparing the width of the voice of the process with the width of the voice of the customer. The voice of the customer is on top (the numerator) of the division equation. The voice of the process is on the bottom (in the denominator). What is being evaluated with the Cp/Pp index is the fatness (dispersion) of the process variation as it is compared to the specification window (i.e., the upper spec minus the lower spec). The two indices are a larger-is-better characteristic where values greater than 1.5 are generally acceptable.
Ppk (process performance index) incorporates an estimate of the ‘long-term process standard deviation’ which is standard deviation as we all know it. This includes both the within and between estimates of variation which is usually greater so it reduces the estimate of capability. Ppk is a measurement of how close the center (the mean) is to either the upper spec. or the lower spec. It is generally accepted that you want to have at least six standard deviations between the mean and the nearest specification limit. Ppk however is not measured in single standard deviation units. Instead, it is measured in three sigma sets. For example, if Ppk = 2, there would be six standard deviations between the center of the process (the mean) and the nearest specification limit. Remember the difference between population and sample. If we are measuring a population, we would be looking at sigma units. If we are using Ppk to evaluate a sample set, instead of ‘sigma’, we would be looking at ‘standard deviations.’
Pre-control is a control charting methodology that uses specification limits instead of statistically-derived control limits to determine process capability over time.
Pre-control charting is useful in initial process setup to get a rough idea of process capability, but this author doesn’t recommend its use because it is not statistical process control. Pre-control charting does not use continuous data found upstream in the process which is more in alignment with prevention thinking.
The term population refers to all of the measurements of interest. For example, if you were trying to find the average weight of United Airline passengers flying from San Francisco to Hong Kong for the month of March, the population would include all of the weights for all of the passengers who flew from San Francisco to Hong Kong for the month of March via United Airlines.
A prioritization matrix is typically an L-shaped matrix that makes pair-wise comparisons of established criteria and options. The prioritization matrix is a rigorous method and requires skill to use it effectively.
It is applicable to many situations and has several different configurations. To be used effectively, the criteria and the options must be clearly developed and a scheme for weighing them must be applied.
Probability deals with calculating the likelihood of a given event’s occurrence.
If you are using a Standard Normal Table to determine the probability of a given Z value will yield some probability from 0 to 1 of a particular data point being either above, or below a certain point. For example, if hospital stays for admitted patients at a certain hospital are measured in hours and were found to be normally distributed with some average hours and some standard deviation; maybe the team would want to find out how many stays can be expected to last over so many hours. Or, it could be expectations for being less than so many hours.
You would be using probability if you are using a Weibull analysis to determine the probability of something lasting so many years, or so many miles.
Probability theory is used with binomial data where the team might be trying to find the probability of a specific number of ‘successes’.
A Process Decision Program Chart (PDPC) is a tool for identifying and documenting the steps required to complete a process.
It is useful for anticipating any issues and problems that might surface in the implementation of the process, therefore affording the opportunity to devise countermeasures.
Quality Control is the control of the operational techniques and the activities used to fulfill requirements of quality. One way to control quality of a product or service is to provide in-process and/or final inspection. The problem with inspection is that experts maintain that even with 100% inspection, inspection is only 80% effective – at best.
A process owner is fairly self-explanatory, but many times in lean six sigma, the process owner is not identified until the ‘ideal process state’ has been put into place.
The importance of the process owner reveals itself in the last two subtasks of the control phase of DMAIC. The process which is usually somewhat of a new process needs to be managed by one person who will ensure that the improvements are sustained. Without a process owner, it is only human nature that a process will tend to go back to the old way.
