Concept explainers
a
Interpretation:
The control limits for the p chart
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample
b
Interpretation:
The probability (P) of detecting the shift when the percentage of defective increased to 20 percent
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample
c
Interpretation:
The number of days required to detect the shift
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample
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Production and Operations Analysis, Seventh Edition
- A machine is used to fill cans of motor oil additive. A single sample can is selected every hour and the net weight of the can is obtained. Since the filling process is automated, it has very stable variability, and long experience indicates that s = 0.02 oz. The process target (process mean when in control) is 8.02 oz. A tabular cusum is being used for this process with standardized values h=4.5 and k=0.5. If the values of Cumulative sums at the end of measurement 7 were C," + = 0.030 and C,¯ = 0.0 , and measurement 8 is equal to Xg = 8.071, what will be the Cumulative sum at the end of measurement 8, that is C3 + = ? 0.041 0.071 0.051 0.046 0.061arrow_forwardLinda Boardman, Inc., an equipment manufacturer in Boston, has submitted a sample cutoff valve to improve your manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean (u) of 12.00 and a standard deviation (o) of 0.06. Your desired performance is u = 12.00 ±3 standard deviations, where o = 0.070. For the given information, the process capability index (Cpk) = (round your response to three decimal places)arrow_forward57. A manufacturer of large appliances maintains a p chart for the production of washing machines. The machines may be rejected because of cosmetic or functional defectives. Based on sampling 30 machines each day for 50 consecutive days, the current estimate of p is .0855. a. What are the control limits for a p chart? (Assume 3ơ limits.) b. Suppose that the percentage of defective washing machines increases to 20 per- cent. What is the probability that this shift is detected on the first day after it occurs? c. On average, how many days would be required to detect the shift?arrow_forward
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- Linda Boardman, Inc., an equipment manufacturer in Boston, has submitted a sample cutoff valve to improve your manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean of 8.00 and a standard deviation of .04. Your desired performance is = 8.0 ± 30, where o = 0.047. Is the following statement true or false? Can Boardman produce the valve within the specified tolerance? (TRUE=yes, it can; FALSE=no, it cannot) O True O Falsearrow_forwardAt Isogen Pharmaceuticals, the filling process for its asthma inhaler is set to dispense 170 milliliters (ml) of steroid solution per container. The average range for a sample of 4 containers is 5 ml. Use the accompanying table to establish control limits for sample means and ranges for the filling process. Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. The UCLR equalsz____________ml and the LCLR equals _________________ml. (Enter your responses rounded to two decimal places.)arrow_forwardThe specifications for a gasket that installs between two engine parts calls for a thickness of 6.0 mm ± .2 mm. The standard deviation of the process is estimated to be 0.05 mm. The process is known to operate at a mean thickness of 6.1 mm What are the upper and lower specification limits for the gasket? What are the Cp and Cpk values for this process? Is this process capable of producing the desired part?arrow_forward
- A metal fabricator produces connecting rods with an outer diameter that has a 1± 0.02 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.005 inches with a standard deviation of 0.003 inch. Calculate the process capability index for this example. Note: Round your answer to 3 decimal places. Process capability indexarrow_forwardNauticaB is a company that makes little boats. This company controls its production process by periodically taking a sample of 100 units from the production line. Each product is inspected for defective features. Control limits are developed using three standard deviations from the mean as the limit. During the last 16 samples taken, the proportion of defective items per sample was recorded as follows: .01 .02 .01 .03 .02 .01 .00 .02 .00 .01 .03 .02 .03 02 .01 .00 The supply chain of Nautica has the following information: Supplier Factory Wholesale Retailer Inventory in days* Accounts 30 90 40 20 receivable in days 20 45 30 40 Accounts payable in days Purchasing unit cost Added unit cost Sales unit price On-time 30 45 60 37 $ 5 $10 $20 $20 $25 $55 $55 $10 $70 $ 70 $ 30 $110 delivery (%) 85 95 75 95 * This is also the throughput time in days. Compute the cash-to-cash cycle time for each of the four entities separately. Based on this calculation, who is benefiting the most?arrow_forwardHow many ppm defective parts would be expected in a +/- 4 sigma normally distributed unstable process? Assume the mean shifted by +/- 1.5σ from the target.arrow_forward
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