Production Management

# The Procedure for the Construction of Control Charts (X-R Charts)

The procedure for construction of a control chart for mean and range (or for any other variable) consists of the following steps:

(1) Choice of the variable. The variables chosen for control charts of mean-range and mean-standard deviation should be measurable in quantitative terms. A number of features of the product may be measurable and, therefore, one specific feature must be chosen. Normally, that variable should be chosen which allows maximum scope for possible cost reduction.

(2) Selection of rational sub-groups. Rational grow means sub-divisions of observations into smaller sub-groups. The success of control charts depends largely on the discrimination used in the selection of these sub-groups. The sub-groups (samples) should be chosen in such a way that make each sub-group as homogeneous as possible and provides maximum scope for variations from one sub- group to another. All items in one sub-group should be those produced at one time while the next sub-group should consist of items produced at a single later time (at same future date) with sufficient interval between the two.

Size of the sub-group is another important consideration. Need to minimize scope for variation within a sub-group requires that sub-group should be as small as possible. But the distribution of average (X) cannot be normal unless the sub-group consists of four or more terms. Four may be the ideal size but in practice five is better due to case of computation. If the cost of testing is very high, sub-groups of two or three may be used.

Large sub- groups of 10 or 20 may be used where it is desirable to make the control chart very sensitive to small variations from the process average. As the sub-group increases in size, the control limits become very narrow which are helpful in detecting any small variations more easily. When the number of units exceeds 15 mean and standard deviation (X, a) chart rather than mean and range (X, R) chart should be used.

(3) Choice of frequency. The choice of the frequency of sub- group depends upon the problem concerned. However, the samples should be taken at successive intervals and measurements should be recorded sample-wise. The frequency may be expressed as a percentage of products manufactured.

4. Computation of average and range for each subgroup or sample.

5. Compute grand average and average if range of all the samples.

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