Info

Time

Time

Figure 6.1. Schematic representation of univariate SPC charts.

Figure 6.1. Schematic representation of univariate SPC charts.

Two kinds of errors may be committed when testing a hypothesis:

First a is selected to compute the confidence limit for testing the hypothesis then a test procedure is designed to obtain a small value for (3, if possible. (3 is a function of sample size and is reduced as sample size increases. Figure 6.1 represents this hypothesis testing graphically.

6.1.1 Shewhart Control Charts

Shewhart charts indicate that a special (assignable) cause of variation is present when the sample data point plotted is outside the control limits. A graphical test of hypothesis is performed by plotting the sample mean, and the range or standard deviation and comparing them against their control limits. A Shewhart chart is designed by specifying the centerline (C), the

Critical Value

Critical Value

Figure 6.2. Type I and type II errors.

upper control limit (UCL) and the lower control limit (LCL).

Two Shewhart charts (sample mean and standard deviation or the range) are plotted simultaneously. Sample means are inspected in order to assess between samples variation (process variability over time). Traditionally, this is done by plotting the Shewhart mean chart (x chart, x represents average (mean) x). However, one has to make sure that there is no significant change in within sample variation which may give an erroneous impression of changes in between samples variation. The mean values at times t — 2 and t — 1 in Figure 6.3 look similar but within sample variation at time t — 1 is significantly different than that of the sample at time t — 2. Hence, it is misleading to state that between sample variation is negligible and the process level is constant. Within sample variations of samples at times t — 2 and t are similar, consequently, the difference in variation between samples is meaningful. The Range chart (R chart) or

O Individual points • Mean

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