using sample to make quality control decisions


A beverage company fills its best-selling 300ml drinks by an automatic dispensing machine. The machine is set to dispense a mean of 310ml per bottle. Uncontrollable factors in the process can shift the mean away from 310ml and cause either underfill or overfill, both of which are undesirable. In such a case the dispensing machine is stopped and recalibrated. Regardless of the mean amount dispensed, the standard deviation of the amount dispensed always has value 22ml. A quality control engineer routinely selects 30 bottles from the production line to check the amounts filled. On one occasion, the sample mean is x = 320ml the sample standard deviation is s = 25ml ounce. Determine if there is sufficient evidence in the sample to indicate, at the 1% level of significance, that the machine should be recalibrated. 

solution: 
#inputs:
sample_mean = 320
sample_std = 25
alfa = 0.01
population_mean = 310
population_std = 22
sample_size = 30 
options(digits = 3)

#calculating statistic:
z_value = (sample_mean - population_mean) / (population_std / sqrt(sample_size))


#calculating rejection region
rejection_region = data.frame("lower" =seq(-Inf,qnormGC(alfa/2,mean = 0,sd= 1 ), by = 0.01), 
                             "upper" = seq(- qnormGC(alfa/2,mean = 0, sd= 1 ), Inf, by = 0.01 ))
conclusion: 
since the value is outside of the rejection region we accept H0 and decide not to recalibrated the machines. 

Comments

Post a Comment

Popular posts from this blog

Simulation Project: Production Line Wasted Outputs

Case Study: Production Engineers of the group are planning to perform a quality improvement project aimed at controlling the output of  machine A.  I n order to run this project, the engineers designed a simulation experiment to establish a quality procedure in which the production would be ceased if Machine A started producing a sequence of flawed products. After stopping production, they could re-set up the machine and maintain it for the next round. The project is also aimed at supporting the maintenance planning department to estimate the next possible maintenance or breakdown interval.   The machine performance has been measured in a different project. The project was interested in sampling and calculating the number of "ok", "rework" and "waste"  outputs per 10000 end-products. The observation shows that  90% of the outputs are flawless, 5% need rework, and 1% are wasted.  Solutions: Based on the information, they can run a simulation project in ...
Read more

simulating production volume

Image
case study: The industrial Engineer measures the volume of production in a production company over time. Due to business transformations, the company reduces production periodically by a specific share but there are also some non-deterministic influences that relate to economics, politics etc. Using  R  we can easily simulate such a process and plot it. We start the series with a total of 5000 units of production and simulate the reduction in production with an autoregressive process that exhibits a downward movement in the long-run and has normally distributed errors  u t : production t = − 5 + 0.98 ⋅ production t − 1 + u t   solution: #simualtion of a model: set.seed(321) Date = seq(as.Date("1951/1/1"), as.Date("2000/1/1"), "year") x = c(5000, rep(NA, length(Date) - 1)) for (i in 2:length(Date)){    x[i] = -50 + .98*x[i-1] + rnorm(n = 1, sd = 200) } plot(x = Date,       y = x,       type = "l",  ...
Read more

supplier evaluation using population proportion tests hypothesis

Image
Case Study: A manufacturer of walk-behind push mowers receives refurbished small engines from two new suppliers, A and B. It is not uncommon that some of the refurbished engines need to be lightly serviced before they can be fitted into mowers. The mower manufacturer recently received 100 engines from each supplier. In the shipment from A, 13 needed further service. In the shipment from B, 10 needed further service. Test, at the 10% level of significance, whether the data provide sufficient evidence to conclude that there exists a difference in the proportions of engines from the two suppliers needing service. Solutions: #Input: sample_A_size = 100 sample_A_prop = 0.13 sample_B_size = 100 sample_B_prop = 0.10 alfa = 0.10 #STEP 1: Hypo  #H0 = Pa - Pb = D0 = 0: no difference in the test population #Ha = Pb != Pb : there is a differenc in supplier products  #STEP 2 & 3: statistic test z_statistic = (sample_A_prop - sample_B_prop - 0 )/           ...
Read more