Page 170 - DMGT501_OPERATIONS_MANAGEMENT

Operations Management

Notes (e) Sampling frequency for (X, R) Charts as per Duncan’s study reveal that:
(i) If a shift in the process average causes high rate of loss as compared to cost of
inspection, it is better to take small samples quite frequently rather than large
samples less frequently e.g., it is better to take 4-5 samples every half hourly
rather than 8-10 every hour.
(ii) If it is possible to decide quickly and the cost of looking for trouble is low,
then use ‘2 r or 1.5 r’ Control limits rather than 3 r Control limits and use 3 r
Control limits if the cost of looking troubles is high.

(iii) If the unit cost of inspection is relatively high, then its better to take sample
size of 2 or 3 at relatively long intervals i.e., once or twice in a shift and use
Control limits + or 2r ( or 1.5 r).
(iv) A Control Chart schedule should take into account detection of changes in
process of required degree with desired confidence. However (X, R) charts are
not understood easily by Operators/Inspectors and these charts cannot be
used for go-on-go type of data.
2. p, np chart: This chart is applicable to Attribute Data (number of defective units of product)

(a) This chart is used to control the overall fraction defective of a process. The data
required for this chart is already available from inspection records.

(b) The chart is easily understood as compared to (X, R) chart.
(c) The chart provides overall picture of the quality. However, this charts does not
provide detailed information for Control of individual characteristic. The charts do
not recognise degree of defectiveness in units of product standard and limits vary
the sample size.
Static Standard Control Limit

np n p np 3 np(1 p) np 3 np(1 p)

Total number of defective pieces
where p =
Number of samples (k) Sample size (n)
If rejection percentage (p) is < 10 then nm chart is convenient to use with a constant sample
size and Control Limits may be read directly from the Statistical Table.
3. C chart:
(a) C chart is applicable to attribute data (number of defects per unit of product).
(b) This chart is used to control the overall number of defects per unit.
(c) This chart gives all the advantages given alone for m-charts. Additionally, it provides
the measure of degree of defectiveness in units of product.
However, it does not provide detailed information and control of individual characteristics
as in case of (X, R) charts.

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