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Unit 4: Quality Control

The common approach to on-line quality control is straightforward: We simply take out samples Notes
of a definite size from the ongoing production process. We afterward produce line charts of the
variability in those samples and think about their closeness to target specifications. If a trend
comes into view in those lines, or if samples fall outside pre-specified limits, we state the
process to be out of control and take action to locate the cause of the problem. These types of
charts are at times also referred to as Shewhart control charts named after W. A. Shewhart, who
is usually credited as being the first to initiate these methods.

Short Run Control Charts

The short run control chart, or else control chart for short production runs, plots interpretation
of variables or attributes for several parts on the same chart. Short run control charts were
developed to deal with the requirement that several dozen measurements of a process have to
be collected before control limits are calculated. Meeting this requirement is habitually difficult
for operations that produce a limited number of an exacting part during a production run.

Example: A paper mill may produce only three or four (huge) rolls of a particular kind
of paper (i.e., part) and then shift production to another kind of paper. But if variables, such as
paper thickness, or attributes, such as blemishes, are monitored for several dozen rolls of paper
of, say, a dozen different kinds, control limits for thickness and blemishes could be calculated
for the transformed (within the short production run) variable values of interest.

4.2.2 Control Limits

We are aware from our basic statistics course that plus and minus three standard deviations
from the mean of normal destruction will include 99.73 per cent of all data in the distribution.
When the mean absolute deviation of a data set is less than three standard deviations, it is
considered to be within acceptable limits or error. Using the same rationale, the Upper Control
Limit (UCL) is calculated as 3s and set on the chart as shown in Figure below. The Lower Control
Limit (LCL) is established in the same manner. These are the limits in which the measured
parameters are expected to fall into.

Although, industry practice is to use three standard deviations, some applications may merit the
use of wider or narrower control limits. However, the measure of limits is always based on
standard deviations.

Figure 4.1: Control Charts

Process in Statistical Control
Process Out of Statistical Control

UCL UCL
CL
CL
LCL
LCL
Time Time

We can see that the process on the left in Figure 4.1 is in apparent statistical control. All the
points lay within the Upper Control Limits (UCL) and the Lower Control Limits (LCL). The
variation seen in the points in the figure on the left is due to common cause variation, which is
considered a part of the process. Common cause variation is variation in the process that cannot
be attributed to any defect.

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