The guidelines for preparing control charts are given as follows:
1. Homogenization for Dispersion:
If the sample size chosen is less than ten (usually the sample size is four, Five or six), then for each of the samples in the set, the range (R) should be first calculated and the average range CR) should be computed.
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Depending upon the sample size, a suitable factor D (denotes deviation) should be read from the table, and if all the ranges are found to be less than or equal to D-R, the initial data collected would be deemed to be homogeneous and acceptable for the purpose of further calculation of control limits.
In case one or more ranges are found to exceed D-R, the observations in that (those) sub-group(s) shall be discarded. For the remaining data, the above procedure shall be repeated (i.e., the calculation of the new average range R and comparison of all the remaining ranges with DR) till all the ranges are found to be within control.
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If more than 25 per cent of the samples are rejected for being out of control in this homogenization process, the entire data should be rejected and fresh data should be collected.
2. Homogenization for Central Tendency:
Calculate the average of each sample X from the homogenized data. Then calculate the average of these averages or the grand average for all the samples. If any of the averages are found to be outside the interval X ± R (where A is read from the table value for the corresponding sample size), then the observations in the corresponding sub-groups would be discarded. From the remaining data a fresh grand average should be computed and the above procedure repeated till all the average values are found to be within X ± A2R.
3. Setting Up of Control Charts:
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The processes of setting up control charts are discussed further:
X and R Charts:
Suppose standard values of the process parameters (i.e., process mean) and the process variability (o) are X and A respectively (when we do not compute the ‘o’ value conventionally, i.e., obtaining square-root of variation). Then control limits on X chart and R chart would be as follows:
4. P-Chart or Fraction Defective Chart:
P-chart or fraction defective chart is defined as the ratio of the number of defective items in a population to the total number of items in that population. The sample fraction defective (p) is defined as the ratio of the number of defective units (d) in the sample to the sample size n, i.e., p = d/n. Suppose the standard value for process fraction defective (p) is p’. Then the central line and control limits on the fraction defective chart would be:
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UCL = p’ + 3 √p’ (l-p’)/n
CL = p’
LC L =p’-3√ p’ (1-p)/n
Where ‘n’ is a sub –group size .If L.C.L is negative, it is taken as zero.
np-Chart or Chart for Number of Defectives:
The number of defective units or rip-chart is used when the sub-group size is constant. The central line and the control limits for the rip-chart will be as follows:
UCL = np + 3 √ np (1-p)
CL = np
LCL = np – 3 √np (1-p)
C-Chart or the Chart for Number of Defects per Unit:
A defective (or nonconforming) unit is a unit of product that does not satisfy one or more of the specifications. Each specific point at which a specification is not satisfied results in a defect or nonconformity. In this case, each sub-group consists of a single unit and c’ would be the number of defects observed in one unit. It should be remembered that each inspection unit must always represent an identical area of opportunity for the occurrence of defects. The control limits for the c-chart would be given by:
UCL = c’ + 3 √c’
CL = c’
LCL = c – 3 √ c’
Where ‘c’ is the standard value for the average number of defects. If L.C.L. comes out negative, it is taken as zero.