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 pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic? Answer letters a, b, and c. a. Find the Cp index. Comment on the ability of the process to meet specifications. b. What proportion of the specification range is used up by the process? c. If it is easier to change the process mean than to change its variability, to what value should the process mean be set to minimize the proportion of nonconforming product?arrow_forwardAssume the following: A quality manager at a popular restaurant in a New York has accurately measured the Cp & Cpk values associated with the delivery times of the food delivered by her restaurant. He has measured these values over an acceptable time period. The measured values are such that: Cp > 1, and Cpk < 1. Then: a. The process is both cappable and centered between the specification limits. b. The process is neither cappable nor centered between the specification limits. c. The process is cappable but not centered between the specification limits. d. The process is not cappable but centered between the specification limits.arrow_forwardThe 3-sigma limits for a process whose distribution conforms to the normal distribution includes _______ of the observed values, in the long run. Part 2 A. 99.74% B. 95.44% C. 68.26% D. 50%arrow_forward
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- C-Spec, Incorporated is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± 0.003 inch. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of 0.002 inch. Calculate the capability index ( Cpk��� ) for this machine. Note: Round your answer to 3 decimal places. Should C-Spec use this machine to produce this part? multiple choice Yes Noarrow_forwardA small electronic device is designed to emit a timing signal of 200.0 milliseconds (ms) duration. This device is specified as 201.0 + 10.0. In the production of this device, subgroups of six units are taken at periodic intervals and tested. Xbar and R are calculated for each subgroup and used to plot control charts. The results of inspection of 25 subgroups, ΣX = 5,000.00 and ΣR = 277.00. Determine the control limits for Xbarand R charts, and estimate the value of σ.arrow_forwardA single sampling inspection scheme for large lot of mass-produced flanges states:From each lot take and inspect a random sample of 50. If 3 or more defectives, inspect the whole lot and remove all defectives, if less than 3 are found accept the lot without further inspection.a. Obtain the equation for Pa the probability that a lot containing a fraction p of defectives will be accepted, in terms of p.b. Evaluate Pa for p=0.01, 0.02, 0.03, 0.05, 0.07, 0.10, 0.15, 0.20, 0.30. Plotthe operating characteristics and average outgoing quality curve.c. Estimate: (a) the producer’s Risk at p of 2% (b) the consumer’s Risk for pof 5%.arrow_forward
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