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Management must know how to distinguish between systematic and special variation and decide on the type and time of an action to be taken on the system. Management must focus attention; first, on those functions, which are not stable, not those functions whose performance is merely low. Statistical Process Control (SPC) is the mathematical tool aiming at classifying variation as systematic or special. The field of statistics is split into four schools:
Descriptive Statistics that is concerned with the following problem: "Given a data set, summarise, in a few numbers or graphs, the information contained in it".
Probability Theory that is concerned with the following problem: "Given a random phenomenon, find the mathematical model best describing it".
Statistical Inference that is concerned with the opposite problem of the Probability Theory: "Given a sample, find the probability model -which best describes the population it was drawn from."
Statistical Process Control (SPC) that is concerned with the validity of the Statistical Inference question. "Given several samples, were they drawn from one population?"
Dr. Doming has convincingly shown that for the purposes of improvement, distribution and calculation of means, modes, standard deviations, chi charts, t-tests, etc. can only be used if the data was produced in a state of stability. Tools from the Statistical Inference school have the following assumptions built into them: a conceptual population exists, the conceptual population is unique and that the samples were objectively drawn from a population that closely corresponded to this conceptual population.
As the mathematical model describing distribution of samples that were drawn from several conceptual distributions is of no use, SPC questions the validity of these three assumptions. The first step in examining response time is, accordingly, to question the state of stability that produced the sample. The way to do so is to plot the points in the order of production, using a control chart. A control chart has a base line, often in time order, on which measurements or points represent counts. The points are the statistical signals by which the system 'talks' to us.
A control chart has a centre line placed between the upper and the lower control limits. The centre line is an estimate of the process's average. The control limits reflect variation of the system performance, as is, not what we wish it to be. Control limits must be calculated rather than placed by judgement or specifications. Placement of control limits based on specification, as a substitute to calculation, leads to over or under adjustments and perpetuates existing problems.
The calculation of the control limits is a job for a competent statistician and is beyond the scope of this paper. To calculate control, limits in our case, one should take into consideration that the opportunity for defects is large, that the probability of defects is less then 10% of the opportunity, that the defects (locking) may occur more then once per transaction and that the sample size varies from one day to the other. If a sample falls outside of the control limit, and a trend is absent, the variant is probably special.
However, if several values fall out of the range, or a trend is present, the variation is probably systematic. A simple, but not simplistic way of analysing control charts is to count continuous points on one side of the average. To see how this method (named 'Run about the central line") provides evidence of a process change, consider chances at tossing a coin. Tossing two heads in succession is not remarkable. Even three heads in a row will happen fairly often. Four in a row is more interesting, as would be five, six, or seven. In the same way, when (say) eight or more successive points fall on the same side of the central line of an average chart, they may be considered to be evidence of a sustained shift of the response time average, even when no point falls outside the control limit.
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