(b) An electr product quality, components are given 100% inspection and the resu
ID: 379091 • Letter: #
Question
(b) An electr product quality, components are given 100% inspection and the results are summarized at hourly intervals. Data were recorded each hour for 15 hours, as shown in Table Q1(b) Plot a control chart of p, the fraction defective. Give comments on the pattern of data as appropriate. onics company manufactures a component called V-tube. In order to monitor the (9 marks) Number of Units outside specification Number of orUnits inspected 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 2 4 2 2 4 10 12 13 14 15 Table Q1(b) - Data Sheet of V-tube
Explanation / Answer
Total number of defectives as given in the problem ( i.e. total number of units outside specification )
= 5 + 5 + 0 + 5 + 0 + 3 + 0 + 1 + 5 + 2 + 2 + 4 + 1 + 0 + 3 = 36
Total number of units = Sample size x Number of samples = 48 x 15 = 720
Therefore , average rate of defectives =pbar = Total number of defective units/ Total number of units = 36/ 720 = 0.05
Sample size = n = 48
Thus , the control limits for p chart as follows :
Upper Control Limit = UCL = pbar + 3 x Square root ( pbar x ( 1 – pbar)/n) = 0.05 + 3 x Square root ( 0.05 x ( 1 – 0.05)/48 )
= 0.05 + 0.031 = 0.081
Lower Control Limit = LCL = pbar – 3 x Square root ( pbar x ( 1 – pbar)/n) = 0.05 - 3 x Square root ( 0.05 x ( 1 – 0.05)/48) = 0.05 – 0.031 = 0.019
Thus proportion of defectives ideally must be within control limits of 0.019 – 0.081
Basis sample size of 48, that means number of defectives ideally must be within 0.019x48 – 0.081x48 or 0.912 – 3.88.
Thus for the process to be in control, number of units outside specification should be in the range of 0.912 – 3.88
However there are 4 sets of data each with 5 number of units outside specification and 1 set of data with 4 number of units outside specification. Thus , these 5 sets of data are beyond upper control limits set by p chart. Therefore, it can be concluded that the process is not in control.
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